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Restorative Councils Help Pakistani Police
August 4th, 20112 comments
Ali Gohar in a meeting on jirga matters. (Photo courtesy of Ali Gohar.)
Ali Gohar updates jirga
As the founding director of JustPeace International, Ali Gohar (MA '02) has worked at updating the practice of jirga, an ancient tradition in Pakistan whereby respected and wise elders deliberate in an open community forum to resolve conflicts. In 2003, he and fellow CJP graduate Hassan Yousufzai (MA '03) co-authored Pukhtoon Jirga, a book available for downloading at www.justpeaceint.org.
In a 2010 interview with Insight on Conflict, Gohar explained that he was raised in a traditional Pashtun culture: "My family was involved in enmities, which affected my childhood so much that I promised to do something against the traditions of revenge, honour killing, shame factors, and cruelties by the name of honour." As an adult, he worked as a social welfare commissioner for Afghan refugees, where he saw "more violence, destruction, kidnapping, murder, and displacement of refugees."
In April 2011, Gohar told journalist Lis Horta Moriconi of Comunidad Segura (www.comunidadesegura.org) that EMU professor Howard Zehr and his teachings on restorative justice inspired Gohar to tap his own jirga system as a "means to mitigate conflict and contribute towards peacebuilding."
Gohar studied with Zehr as a Fulbright scholar in 2001. Upon returning to Pakistan in 2003, Gohar encountered Malik Naveed, then inspector general of police for the district of Khyber Pakhtunkhwa (he retired in 2010). This very high-ranking police official had become familiar with restorative justice as an official visitor to Japan.
With Naveed's support, Gohar opened dispute-resolution offices, staffed by respected and trained community elders, in 73 village-level police stations (now 93 stations). Gohar told Comunidad Segura that restoring the principles of traditional elder councils has meant "promoting consensus" in areas where, according to him "peace is a touchy subject and men wear guns like women wear ornaments."
An abridged and slightly revised version of the Comunidad Segura interview follows. It is printed with Gohar's, Moriconi's, and the Brazilian publisher's permission.
What is innovative about the dispute resolution project?
The dispute resolution project in Khyber Pukhtoon Khwa Province involved training elders and police in alternative dispute resolution, our traditional jirga system and in restorative justice. Our other project, "diversion," diverts youths from police stations and from entering the court system. The same elders of the dispute resolution program also take part in this diversion program, especially in cases that would involve offending by youths from the community, with the goal of rehabilitating them.
When did the project with the police start?
The police project started in 2008 with financial assistance of the Asia Foundation and the Australian embassy. This funding ended in 2010. Today we still work with the police on a volunteer basis.
What inspired you to involve elders?
I am from the Pukhtoon tribe, in Afghanistan and Pakistan, and we consider ourselves the world's largest and oldest tribe. Our 5,000-year history is well known. One traditional system has remained with us, called jirga: the elder council. It not only resolves conflict, but when there was no state, it ruled the Pukhtoon area through consensus.
We organized the first international seminar on restorative justice in Pakistan in 2003 led by Malik Naveed, then Director FIA KPK, and supported by Senator Asfundyar khattak, the late Dr. Kabir and myself. In 2008 we introduced [restorative-justice trained] elders into police stations in two trial districts. The result was very successful, from minor issues to murder. The elders resolved family conflicts and many other disputes.
In the work with police stations, which elements of conflict transformation and restorative justice are present, and how?
We teach all methods of peace building. The common practice is arbitration, but we try to change it to mediation and restorative justice. Jirga traditionally dispenses punishment for offenders, but we try to update it by including restorative elements of community work, to bring it closer to the modern human rights values.
Ali Gohar (center) with a police official. (Photo courtesy of Ali Gohar.)
How would you describe the elders' contribution towards conflict resolution and peacebuilding?
Due to the prolonged, expensive, corrupt and win/lose character and situation of the criminal justice system, decisions taken in the court system result in hostility and enmity for years after, since in the official system there is no reconciliation. One of the best aspects of the "Muslahathi" (reconciliation) committees is that they can resolve, reconcile, rehabilitate and follow up the parties until full-fledged friendly, brotherly relationships are established, and enmities are finished once and for all.
Why "Muslahathi committees"?
Muslahathi in our language means to make wrongs right, while adal, means justice done. So Muslahathi committees are concerned with making wrong right, preferably with reconciliation, while adal (justice) is done by the court.
Is it correct to say that these committees are a new "modernized version" of the jirga system of elder councils?
Yes, the Muslahathi committee is a new version of the jirga. The jirga worked according to the traditional practices, but their decisions were verbal, and women were not allowed to participate. In contrast, the Muslahathi committee decisions are taken according to modern scientific principles of conflict transformation, peace building, and restorative justice. Every decision is written down and registered. Women are also trained (forming their own committees) and a connection is made to the male committees. However the women's decisions mostly take effect at the community level because of the strict rules of cultural and religious traditional practices.
How do you choose the elders?
We choose people with good reputations. Since the police know the communities well, this is verified by the police intelligence agencies, and their track records are selected by the high police officials.
More: Disaster and Peace
[To view a video on the modern practice of jirga in Pakistan or for more information, visit JustPeace International.]
Issue: Spring-Summer 2011
Topics: Ali Gohar, jirga, JustPeace International, Pakistan, police, restorative justice
2 Responses to "Restorative Councils Help Pakistani Police"
Rukhshanda says:
It is surprising to see EMU publishing an article which contains many factual errors and protrays a win-win situation. Unfortunately facts are reverse. These Musalihat Committees do not have any legal status/cover, nor any rules of business, nor any selection criteria for it members(mostly persons on these committee are gender-blind and close confidente's of the local police officers (in other words the front men) who use extortion, coersion and police pressure to get issues settled. So one must explore, this is so-called justice at who's cost? Certainly at the cost of the vulnerable, the weak, the one who has already been wronged & his/her Human rights violated. This process has unleashed a vicious cycle of corruption with police, revenue staff collusion and infringed upon the rights and entitlemens of the vulnerable. There is no gender balance in these commitees…. its the strong & powerful men who decide matters as part of the police musalihati committee….. Musalihat means reconcialtion, not co-ersion as is practiced by these commitees….. resultantly, the weak are being pushed to the wall. These committees do not follow the basic human rights, have any respect for the local laws or international conventions. Instead they use their person judgement, little tribal know how and personal biases to make and enforce their decisions. These decisions 'being most illegal' are not recorded anywhere.
In most of the districts where this project was launched, the communities demanded of their administrations to wind up these corruption houses (so-called musalihat committees) immediately. therefore the donors have also with-drawn their support. The police, particularly the corrupt officials likes of Malik Naveed (who is currently facing multiple charges of corruption in various departments he has served in National Accountability Courts and was under arrest on court orders) wish this malicious corruption cycle to continue as these committees (also called thana or police committees) provide the 'daily bread & butter' for the corrupt police officials at local level…..
Please verify these facts from the local communities in districts where these committees were established…..
Appreciate your understanding. thanks
Ali Gohar says:
Thanks for the valuable comments of Rukhshanda. Her feedback will give us further guidance to go in the right direction, as the issue is complex and needs many inputs from different stakeholders.
Before I address her criticisms in detail, I just want to stress that all of us recognize that the situation in Pakistan is bad. There are allegations of corruption and political malfeasance against a thousand people in the Pakistani courts. There are many things not functioning in a healthy, just manner—there is political pressure, nepotism, different mafia-type groups, warlords, militants and so forth. But we cannot just stand and accuse people of being bad and doing bad things. We must offer and work toward alternatives. And we must try to work with anyone who seems willing to do the same. What choice do we have? For that reason, I am happy to work with Rukhshanda, and I invite her to contact me personally through my website, http://www.justpeaceint.org. I answer all sincere e-mails myself.
Concerning Rukhshanda's specific concerns, firstly, it is possible for people to assume that jirga is the one function throughout Pakistan, while in fact there are different systems–Punchayth, Fasilo and Kacher–doing many wrong things with women. The inhuman acts committed by these various systems are credited to jirga by many civil society organizations. Secondly, many of our colleagues–especially those with less knowledge of jirga and restorative justice systems–still consider jirga as composed of illiterate, traditional, narrow-minded people, while in reality most people involved are more educated even than modern westernized English medium-educated people. In Muslahathi committees there are lawyers, social workers, civil society members, religious leaders, even minorities' representatives–they decide the case on its merit and according to the human rights rules. The cases are registered in the police station, along with the procedures followed and with the signatures of the committee's members and parties. The outcome of the case can be seen and challenged, if necessary, by anyone in the courts. I know of cases that were brought to the courts and Muslahathi committees members were asked to defend their decisions, and the courts the rendered the same verdicts (as in case of Abbottabad). I also know of cases that were referred by courts to the committees for resolution.
In the Peacebuilder magazine article it is mentioned that the reconciliation committee is known as Muslahathi. "Muslahath" in local language means "making wrongs right" as it is also in restorative justice system. While "adal" refers to justice that is done by the courts. In the present scenario, true justice may not be gotten in the courts in Pakistan. Similarly, truly "making wrongs right" may not be achieved through the Muslahathi committees. It is not realistic under present circumstances to expect ideal functioning from either system. I agree that jirga is without women–that's why we started Muslahathi committees to include women's human rights violations, along with improving the treatment of young people and children. Reviving jirga was intentional on our part; first we did research on it, and then we traced the joint linkages with the restorative justice system and we arranged an international seminar in 2003. In 2008, we started implementing it in a new shape and spirit, in the form of Muslahathi committees at each police station. In the international seminar in 2003 and in the 2008 implementation phase, Malik Naveed khan took the lead, initially as Director FIA, and then as Inspector General of Police. Senator Afrasyab Khattak, Dr. Kabir (late) and I assisted him to introduce the restorative justice system in Pakistan. It was important to link it to the system of jirga, because jirga has been in the Pukhtoon culture since long ago and it is still in practice, as there is an official figure that 90% cases in rural areas and 70% in urban areas are still resolved through jirga. Everywhere in the world, it is important for restorative justice practices to be embedded in the local culture and context, or local people will not feel that they "own" them.
This is not the time or place for me to address the corruption case you mentioned involving Malik Naveed khan, since it is in court and I do not know all the particulars (though I must add that in Pakistan in our current mistrustful and dysfunctional situation, there are numerous charges and counter-charges of corruption of officials, and it is not always clear whether the charges are politically or honestly motivated). Personally, though, I found him to be one of the best police officers in terms of working closely with me to revive the system of jirga and introducing the restorative justice system in the police department. The main reason for the introduction of Muslahathi committees was to cleanse the THANA culture and to make an effort to correct corruption in the police department—this is what Malik Naveed put on the table to us before implementation of the project in 2008. I agree that corruption is in the police department. For that reason, we established these committees in the police station to record each case, and to develop checks and balances for that. A mechanism was developed so that elders could report police officers to higher ups if they were believed to be involved in corruption. Similarly, if the elders were involved in human rights violations, they too should be checked by police and courts together. If the checks and balances are not working as well as we would hope, they are still better than nothing!
Malik Naveed took another bold step, by opening offices for the Muslahathi committees at each police station. This means, for the first time in the history of Pakistan, elders of the community now sit at police stations, without the permission or involvement of the police. Any member of the community–male, female, children–can approach straight to them for any complaint to be launched and for it to be settled. Before that THANA (police station) culture was a symbol of terror for vulnerable groups like women, children, who could not easily access the police. Now they can approach very easily since their own community people are sitting there.
Regarding female committees, we have made progress but of course there is still room for improvement. Women have been trained separately and linked to the committee in police stations in the following locations: Nowshera police station (Malik Juma Khan Convener); Havealian Muslahathi committees; Abbottabad Muslahathi committees; and Harpur Cant Muslahathi committees. In some place like Nowshera Kalan, women sit in police stations along with male committee members on a regular basis. In some cases minority women (Hindu, Sikh, and Christian) have representation, as in case of Mardan and Nowshera, as well as in Haripur, Abbottabad, and Manshera. In some places–like Mardan, Swabi, even in Peshawar—the traditional culture and ways of thinking have blocked the representation of women. In these cases, the best we can do is to continue to work at showing traditional men how it is a benefit to all to include women.
The legal status of these committees? Malik Naveed khan–then Inspector general of police–issued a standing order that is law and valid for five years for the establishment of Muslahathi committees. He further inducted Muslahathi committee's rule of business into the police rule, which is a legal document for police personnel to follow. He also issued a special order for establishment of Muslahathi committees offices in each new police station construction from then onward. For the legal back- up we consulted different people, especially the provincial assembly secretariat. The speaker Karamatullah Khan Chgarmattai stated that the Muslahathi committees were well backed up by custom as we have had an indigenous jirga system for conflict resolution in our system since long ago. He told the evaluation team that he himself practiced as a "jirga mar" (jirga member); being a lawyer of the high court, he often referred cases to jirga. He gave an example of a famous Dabangai enmities case that was resolved by him through jirga after long bloodshed. Other lawyers we consulted also viewed jirga as a simple, cheap, easy justice system that often reconciles the parties in conflict. By contrast, the criminal court system might render a decision, but it does not reconcile the parties in conflict–even after years of litigation, an acquitted person is often killed on the same day, even going home from the court.
Another form of legal backing was under the district government ordinance implemented by General Musharaf that worked under Nazim of union council. This backing was given to Muslahathi Jirga, Ansaf Committees, justice committees, and Muslahathi Anjuman. These were not as successful as the Muslahathi committees established under Malik Naveed khan's orders, because the police forces were not involved and it is hard to have any success without the two main actors in Pakistani culture: Thana Moharar (mirza) and Revenue department Patware, as Thana Mirza is sitting at the police station while Patware is asked to attend any conflict if needed. (For further detail, there will soon be published and posted online some new research done for Just Peace International, "Access to Informal Justice System," conducted for UNICEF Pakistan). Since UNDP started Muslahathi Jirga again in the Province of KPK, I am also planning now to link it to Muslahathi committees to address the conflict from one platform. I need support/help from friends like Rukhshanda to join hands with us for the unification of Muslahathi jirga UNDP project (having legal back-up under district government ordinance 2002 and Muslahathi committees, IGP standing order 2008).
The system of Muslahathi committees is not perfect in any sense, but I believe the committees are almost always an improvement over what communities previously used to seek justice. (Restorative justice professor Howard Zehr explains that restorative justice is not a final solution; it is a compass that gives us direction.) Civil society is still struggling in Pakistan, but I believe the revival of jirga in the form of Muslahathi committees is a step in the right direction. It is certainly better than giving up and doing nothing! At Just Peace International, we are not seeking perfection, just step by step improvements toward a better society.
Regarding stoppages of funding, seed funds were given to the Asia Foundation by the Australian embassy to start an initiative for resolving small issues on the grassroots level. The Asia Foundation, in turn, provided funding to Just Peace International. The funder gave no further commitment, as the situation of the province was very violent in 2007-8 and funders were hesitant to commit to a full-fledged program without the guarantee of tangible results. The flood of 2010 also diverted attention of the donors to immediate rehabilitation. We are still working hard on a volunteer basis to offer training and assistance for the Muslahathi committees to work effectively. Recently in 2011 we started Muslahathi Committees in the violent areas of SWAT administrative district, upper and lower DIR Districts, with another very active police officer Qazai Jamil, who was Deputy Inspector General of the Police in Malkand, now DIG Elite Force Peshawar.
For the achievements and progress of the Muslahathi committees, anyone is welcome to approach Just Peace International, The Asia foundation, Muslahathi Committee offices at Abbottabad, Manshera, Harpur, Nowshera, and the Sociology Department of Peshawar University, where students recently did research on Muslahathi committees. The students not only studied our project area in seven Districts (now eleven), but also went to the South Zone of KPK province, where concerned district police officers started Muslahathi committees on their own. For information on the students' extensive report to the department of sociology, please contact Professor Rashid Khan, who is the head of the research project. Along with the reports, I also invite anyone interested to see my Facebook page where I daily post information on resolved cases of feuds, land, violence, and issues involving women and children. Some of these have been published in Urdu newspapers, which are also accessible via the Internet.


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CapeNature and the award-winning South African musician Jimmy Nevis have collaborated to bring conservation tourism to the masses through music. A first of its kind two-night outdoor sleepover with one of the Cape's coolest pop hit-makers will be held in the Cederberg Wilderness Area in 2019.
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Much of these efforts are in remote areas out of the public eye, but have a direct bearing on the quality of life of millions of people in the province.

redpajama_set_name: RedPajamaCommonCrawl


How do you encrypt a file such that it can be decrypted after a date, but not before? Use serial computations for proof-of-work using successive squaring, chained hashes, or witness encryption on blockchains.
In cryptography, it is easy to adjust encryption of data so that one, some, or all people can decrypt it, or some combination thereof. It is not so easy to achieve adjustable decryptability over time, a "time-lock crypto": for some uses (data escrow, leaking, insurance, last-resort Bitcoin backups etc), one wants data which is distributed only after a certain point in time.
I survey techniques for time-lock crypto. Proposals often resort to trusted-third-parties, which are vulnerabilities. A better time-lock crypto proposal replaces trusted-third-parties with forcibly serial proof-of-work using number squaring and guaranteeing unlocking not after a certain point in time but after sufficient computation-time has been spent; it's unclear how well number-squaring resists optimization or shortcuts. I suggest a new time-lock crypto based on chained hashes; hashes have been heavily attacked for other purposes, and may be safer than number-squaring. Finally, I cover obfuscation & witness-encryption which, combined with proof-of-work, can be said to solve time-lock crypto but currently remain infeasible.
Julian Assange/Wikileaks made some headlines in 2010 when they released an "insurance file", an 1.4GB AES-256-encrypted file available through BitTorrent. It's generally assumed that copies of the encryption key have been left with Wikileaks supporters who will, in the appropriate contingency like Assange being assassinated, leak the key online to the thousands of downloaders of the insurance file, who will then read and publicize whatever contents as in it (speculated to be additional US documents Manning gave Wikileaks); this way, if the worst happens and Wikileaks cannot afford to keep digesting the files to eventually release them at its leisure in the way it calculates will have the most impact, the files will still be released and someone will be very unhappy.
Of course, this is an all-or-nothing strategy. Wikileaks has no guarantees that the file will not be released prematurely, nor guarantees that it will eventually be released. Any one of those Wikileaks supporters could become disaffected and leak the key at any time - or if there's only 1 supporter, they might lose the key to a glitch or become disaffected in the opposite direction and refuse to transmit the key to anyone. (Hope Wikileaks kept backups of the key!) If one trusts the person with the key absolutely, that's fine. But wouldn't it be nice if one didn't have to trust another person like that? Cryptography does really well at eliminating the need to trust others, so maybe there're better schemes.
Now, it's hard to imagine how some abstract math could observe an assassination and decrypt embarrassing files. Perhaps a different question could be answered - can you design an encryption scheme which requires no trusted parties but can only be broken after a certain date?
In addition to the basic use of 'sending messages to the future', there are many other potential uses of timed-release crypto. Rivest, Shamir and Wagner 1996 suggest, among other uses, delayed digital cash payments, sealed-bid auctions and key escrow. Boneh & Naor 2000 define timed commitments and timed signatures and show that they can be used for fair contract signing, honesty-preserving auctions and more.
Our main contribution is an offline submission protocol which enables an author being currently offline to commit to his document before the deadline by continuously solving an RSA puzzle based on that document. When regaining Internet connectivity, he submits his document along with the puzzle solution which is a proof for the timely completion of the document.
Here is one possible use case: imagine an offline digital cash system, so i.e. the bank will not accept the same token twice. To protect against an unscrupulous seller, the buyer pays by giving the seller a time-lock puzzle with the tokens; if the goods are not delivered by some deadline, the buyer will deposit the tokens at the bank, thus preventing the seller from doing so. Otherwise the seller solves the puzzle and makes the deposit. This is basically an anonymity-preserving escrow service, though in practice there are probably simpler approaches.
This use generalizes beyond darknet markets to all services or entities holding Bitcoins: the service can provide users with a time-locked version of the private keys, and regularly move its funds - if the service ever goes down, the users can retrieve their funds. One not-so-cute use is in defeating antivirus software. "Anti-Emulation Through Time-Lock Puzzles", Ebringer 2008 outlines it: one starts a program with a small time-lock puzzle which must be solved before the program does anything evil, in the hopes that the antivirus scanner will give up or stop watching before the puzzle has been solved and the program decrypts the evil payload; the puzzle's math backing means no antivirus software can analyze or solve the puzzle first. The basic functionality cannot be blacklisted as it is used by legitimate cryptography software such as OpenSSL which would be expensive collateral damage.
One could encrypt the file against information that will be known in the future, like stock prices - except wait, how can you find out what stock prices will be a year from now? You can't use anything that is public knowledge now because that'd let the file be decrypted immediately, and by definition you don't have access to information currently unknown but which will be known in the future, and if you generate the information yourself planning to release it, now you have problems - you can't even trust yourself (what if you are abruptly assassinated like Gerald Bull?) much less your confederates.
At this point, let's see what the crypto experts have to say. Googling to see what the existing literature was (after I'd thought of the above schemes), I found that the relevant term is "time-lock puzzles" (from analogy with the bank vault time lock). In particular, Rivest/Shamir/Wagner have published a 1996 paper on the topic, "Time-lock puzzles and timed-release crypto". Apparently the question was first raised by Timothy C. May on the Cypherpunks mailing list in an email from 10 February 1993. May also discusses the topic briefly in his Cyphernomicon, ch14.5; unfortunately, May's solution (14.5.1) is essentially to punt to the legal system and rely on legal privilege and economic incentives to keep keys private.
Use 'time-lock puzzles' - computational problems that can not be solved without running a computer continuously for at least a certain amount of time.
Use trusted agents who promise not to reveal certain information until a specified date.
Rivest et al then points out that the most obvious approach - encrypt the file to a random short key, short enough that brute-forcing takes only a few months/years as opposed to eons - is flawed because brute-forcing a key is very parallelizable and amenable to special hardware3. (And as well, the randomness of searching a key space means that the key might be found very early or very late; any estimate of how long it will take to brute force is just a guess.) One cute application of the same brute-forcing idea is Merkle's Puzzles where the time-lock puzzle is used to hide a key for a second-party to communicate with the first-party creator, but it has the same drawback: it has the creator make many time-lock puzzles (any of which could be used by the second-party) and raises the cost to the attacker (who might have to crack each puzzle), but can be defeated by a feasibly wealthy attacker, and offers only probabilistic guarantees (what if the attacker cracks the same puzzle the second-party happens to choose?).
An interesting question is how to protect such a computation from errors. If you have an error in year 3 that goes undetected, you may waste the next 32 years of computing. Adi Shamir has proposed a slick means of checking your computation as you go, as follows. Pick a small (50-bit) prime c, and perform the computation modulo c⋅n rather than just modulo n. You can check the result modulo c whenever you like; this should be a extremely effective check on the computation modulo n as well.
Further refinements to the modular exponentiation proposal have been made, such as Kuppusamy & Rangasamy 2015.
We know of no obvious way to parallelize it to any large degree. (A small amount of parallelization may be possible within each squaring.) The degree of variation in how long it might take to solve the puzzle depends on the variation in the speed of single computers and not on one's total budget. Since the speed of hardware available to individual consumers is within a small constant factor of what is available to large intelligence organizations, the difference in time to solution is reasonably controllable.
But I wonder how true this is. Successive squaring does not seem to be a very complex algorithm to implement in hardware. There are more exotic technologies than GPUs we might worry about, like field-programmable gate arrays which may be specialized for successive squaring; if problems like the n-body problem can be handled with custom chips, why not multiplication? Or, since squaring seems simple, is it relevant to forecasts of serial speed that there are graphene transistor prototypes going as high as 100GHz? Offhand, I don't know of any compelling argument to the effect that there are no large constant-factor speedups possible for multiplication/successive-squaring. Indeed, the general approach of exponentiation and factoring has to worry about the fact that the complexity of factoring has never been proven (and could still be very fast) and that there are speedups with quantum techniques like Shor's algorithm.
Let's think about alternatives to successive squaring.
The first approach that jumps to mind and seems to be crypto folklore is to encrypt the file, but with a relatively short or weak key, one which will take years to bruteforce. Instead of a symmetrical key at 256 bits, perhaps one of 50 bits or 70 bits?
we realize that we can guarantee on average how much work it will take to bruteforce the key, but we cannot guarantee how much time it will take. A weak key could be cracked at any time given good luck, and across many uses of time-lock crypto, there will be instances where a weak key would be cracked almost immediately, to the potentially extreme harm of the encrypter.
differing amounts of computing resources, particularly parallel computing: It may take a CPU years to bruteforce a chosen key-length, but take a cluster of CPUs just months.
Or worse than that, without invoking clusters or supercomputers - devices can differ dramatically now even in the same computers; to take the example of Bitcoin mining, my laptop's 2GHz CPU can search for hashes at 4k/sec, or its single outdated GPU can search at 54M/second5. This 1200x speedup is not because the GPU's clockspeed is 2400GHz or anything like that, it is because the GPU has hundreds of small specialized processors which are able to compute hashes, and the particular application does not require the processors to coordinate or anything like that which might slow them down. Incidentally, this imbalance between CPUs and highly-parallel specialized chips has had the negative effect of centralizing Bitcoin mining power, reducing the security of the network.6 Many scientific applications have moved to clusters of GPUs because they offer such great speedups; as have a number of cryptographic applications such as generating7 rainbow tables.
Someone who tries to time-lock a file using a parallelizable form of work renders themselves vulnerable to any attackers like the NSA or botnets with large numbers of computers, but may also render themselves vulnerable to an ordinary computer-gamer with 2 new GPUs: it would not be very useful to have a time-lock which guarantees the file will be locked between a year and a millennium, depending on how many & what kind of people bother to attack it and whether Moore's law continues to increase the parallel-processing power available.
There doesn't seem to be any obvious way to solve this with a key mechanism. Even if one is using 100 layers of encryption, each short key can be brute-forced almost arbitrarily fast by a well-resourced or even state-level actor.
This doesn't solve the serial/computing-power objection: some actors will be able to crack each short key much faster by using highly parallel resources, and it makes little difference whether it's one weak key or many - they will still open it earlier than other actors.
So public or symmetrical encryption may not be directly usable as the time-lock primitive. We want an approach which is inherently serial and unparallelizable.
For example, one could take a hash like bcrypt, give it a random input, and hash it for a month. Each hash depends on the previous hash, and there's no way to skip from the first hash to the trillionth hash. After a month, you use the final hash as the encryption key, and then release the encrypted file and the random input to all the world. The first person who wants to decrypt the file has no choice but to redo the trillion hashes in serial order to reach the same encryption key you used.
Nor can the general public (or the NSA) exploit any parallelism they have available, because each hash depends sensitively on the hash before it - the avalanche effect is a key property to cryptographic hashes.
Another simple implementation of serial hashing (SHA-256) for time-locking has been written in Python.
Specifically, you could use a hash for which highly optimized implementations have already been created and put into mass production as ASICs, which have been hand-optimized down to the minimal number of gates possible (probably a few thousand). Because of Bitcoin mining, SHA-256 is a plausible candidate here. (There is one proposal for slightly faster circuits, but it would be unusable for time-locks on its own because it would deterministically fail on some hashes, which would likely be encountered while following a hash-chain.) Serial speedups would lead to proportional reductions in time to unlock.
It is not impossible to combine the decrypter programs with a specified time-locked file, creating a self-extracting archive - which stores data safely encrypted; cannot be decrypted before a certain time period; and requires no third-parties whatsoever. In other words, chained-hashes satisfy our original desire for a self-decrypting file.
We want to force the public to expend more computation - potentially much more - than we put in. How can we do this?
I don't know how one would let the public decrypt the result of the homomorphic encryption without also letting them tamper with the loop.
Suppose one specifies that the final output is encrypted to a weak key, so one simply has to run the homomorphic system to completion and then put in a little effort to break the homomorphic encryption to get the key which unlocks a file; what stops someone from breaking the homomorphic encryption at the very start, manually examining the running program, and shortcutting to the end result? Of course, one could postulate that what was under the homomorphic encryption was something like a hash-chain where predicting the result is impossible - but then why bother with the homomorphic encryption? Just use that instead!
and in any case, homomorphic encryption as of 2013 is a net computational loss: it takes as much or more time to create such a program as it would take to run the program, and is no good.
An infinite sequence of nothing-up-my-sleeve numbers are taken as an infinte sequence of ECC public keys. Searching the pow involves finding distinguished points along a Pollard's rho DLP solution trying to crack the key. When the key is cracked the problem is advanced to the next key.
People can then encrypt messages with all of the keys between now and sometime in the future and network will crack them, achieving a timelock.
Probably incompatible with merged mining and other POW schemes.
Making the difficulty adaptive either makes far in the future messages impossible (because the problem size wouldn't be known long in advance), or requires increasingly big headers as the difficulty would require working on multiple problems concurrently.
The obvious constructions using ECDLP as the asymmetric problem are not progress free.
To explain this idea in a little less jargony form, as best as I understand it: take some standard PRNG; come up with a seed in some publicly acceptable way, such as using the binary expansion of the constant π; define every, say, 100 bits of the output as a public key (with an as-yet-unknown corresponding private key); anyone who wants to timelock a file can encrypt the file using one of these "public keys" and releases the encrypted file to the public as normal; now, people interested in unlocking them ("miners") work on brute-forcing each chunk of 100 bits one by one, and then the messages for that key can be read by anyone; depending on how much computing power is collectively being spent by the miners, you specify intervals by picking a public key X keys in the future (eg if each 100 bit key takes 1 month to crack and you want to delay opening by a year/12 months, then you encrypt your file to the 12th uncracked key). Or if you are worried about people 'skipping ahead' and targeting a future key specifically, the protocol could be that each file is encrypted to all successive keys (so it would be an onion of encryption layers: #1(#2(#3(…(#12(plaintext file))))), so it can only be directly attacked by a loner when the first 11 keys have been cracked).
A timelock altcoin could incentivize participation in unlocking files and be more predictable than solo hash-chain files.
If one could create a program which is a blackbox such that running the program reveals nothing about its contents besides its output, then one has the start of a time-lock: create a normal encrypted archive, create a blackbox which only emits its content after certain conditions are met, stick the key inside the blackbox, and distribute both the blackbox and the archive. The encrypted archive is uncrackable on its own, and if the blackbox really does obfuscate its contents beyond recognition, the key is safe too. But once the proper conditions are met, anyone with a copy of both can reveal the data.
What are proper conditions and how does a program tell the true time? The local computer's clock is a lie, and trusting any timestamp servers reintroduces trusted third-parties. But this is the same problem as digital currency faces, and the solution can be the same: rely on proof-of-work as embodied in the Bitcoin blockchain! The blackbox can ask a copy of the blockchain and check that n blocks have passed and thus a ungodly number of hashes have been spent to create this blockchain; to the extent that no entity has as much hashpower as the Bitcoin blockchain's miners collectively do, this is a reliable and trustworthy 'clock'. (Amusingly, anyone who wanted to spend hashpower to try to open the blackbox early, would be best off becoming a Bitcoin miner, to both defray their expenses and to cause a short speedup of blocks until the mining difficulty ratchets up to compensate.) With time is redefined as blocks which happen every ~10 minutes, someone who wants to release data in a year could include the current block's hash and specify that the blackbox wants at least 52596 more valid blocks before it will unlock & print the decryption key9.
This scheme gains several benefits over chained-hashes/multiple-weak-keys/successive-squaring/Maxwell's-distributed-key-cracking: no one needs to invest computations to create the time-lock (aside from creating the blackbox), no one (much less redundant decrypters) needs to invest computations to unlock it on schedule (as long as the Bitcoin blockchain keeps ticking, it will unlock 'on its own'), and the timing can be made much more precise (likely down to the day given the stochastic nature of finding blocks which uncertainty is much less than that in how much computing powers decrypters would invest or how optimized their implementations of squaring etc would be). The user wouldn't even need to install crypto software or download the full Bitcoin blockchain since the blackbox could be combined with the encrypted archive and a Internet API to the blockchain to create a secure, one-click convenient, self-decrypting self-extracting file. The blackbox approach is the best of all worlds and could be said to entirely solve time-lock crypto.
So it works in principle but not in practice.
Bitansky et al 2015 show that given obfuscation, one can construct a normal proof-of-work time-lock without using an external clock, where the blackbox stalls for many time-steps before spitting out the key, but without the potentially-expensive setup of chained-hashes.
Fortunately, indistinguishability obfuscation may be overkill. A weaker but more computable crypto, witness encryption, has also recently popped up: where an obfuscated blackbox can make its computation/requirement arbitrarily complicated and is Turing-complete, witness encryption instead lets one encrypt a file such that the decryption key is the solution to a (possibly unsolved) NP-complete problem like 3SAT.
This raises the question: is it possible to encode a check of future Bitcoin blockchain length as a NP problem and thus create an encrypted file which can only be decrypted after enough ticks of the Bitcoin clock?
Jager in his 2015 paper "How to Build Time-Lock Encryption" and Liu et al 2015 answer: yes! Jager shows that a check of the blockchain (specifically, that the SHA-256 hash included in each block represents adequate proof-of-work) can be encoded, and so the construction is at least possible (although feasibility remains unclear), and Liu et al 2015 provide a C program to check proof-of-work which can be compiled into a conjunctive normal form formula whose solution is NP-complete and hence is usable as a witness encryption.
Thus, Jager/Liu indicate that witness encryption could help provide the best of both worlds: the ticking clock is still done by proof-of-work as in successive squaring, but the PoW is a now-hyper-optimized hash so there is little risk of future optimization opening the time-lock early like in chained hashes, and since the Bitcoin blockchain will continue to be built regardless of any interest in time-locks, the clock keeps ticking without the risk of no-one caring enough to try to open the time-lock as the time-lock is piggybacking on the bruteforcing already being done.
The two main downsides are that the hashes are not necessarily inherently serialized or unique, and the need for exotic witness encryption.
The first means that the security offered by a Bitcoin blockchain time-lock is going to be, like PoW on transactions, an economic kind of security: hypothetically, a powerful actor could if it really wanted to, construct an entire fake 'chain' (ie a set of hashes with sufficient leading zeroes); if the time-lock encodes the consensus rules, they can exploit the difficulty adjustment to ratchet difficulty down as fast as possible to eventually generate hashes for free. As of 2018, to create valid Bitcoin PoW hashes at all requires vast mining farms and for almost all intents & purposes, this is adequate security, much as it is for the financial transactions on the Bitcoin blockchain. One could probably include additional conditions like "difficulty cannot decrease more than 50% total for the blocks" (equivalent to specifying a minimum number of leading zeroes for all hashes involved), although this then risks opening too late (what if Bitcoin difficulty crashes for years to come because of a bubble?), and the time-locker is forced to make a tradeoff. Depending on the exact encoding, there may be still other ways to cheat - could one use hashes from other blockchains or past hashes? So there are details which need to be worked out.
Secondly, unfortunately, as is common with new & exotic cryptography, the current implementations of witness encryption seem to be slow enough that like obfuscation, witnesses are not yet a viable solution. However, witness encryption seems likely to be optimized much further and it is possible that there are more specialized solutions for blockchains, so it is an approach well worth watching.
One could also try to make a time-lock token on top of Ethereum under the logic that an exchange rate serves as an additional way to penalize attackers, but of course this adds complexity and potentially additional vulnerability - an attacker could buy in, run attacks while collecting fees, exploit decrypted data for profit, sell their stake, set up shorts, and then deliberately reveal successful attacks to crash the token exchange rates and profit 3 different ways from the attack.
if anyone obtains a secret key from a secret-sharer (eg by hacking them or buying it from them), they have an incentive to betray them by revealing the secret key early and claiming the fraction of their deposit. This provides crypto-economic security against early revelation of secret keys by avoiding "nothing at stake".
This contract seems like it would indeed ensure that keys are released after time t, which is one half of a working time-lock (reliable global decrypting after a certain point without further participation by the original locker). But the other half, reliable non-decryption before time t, appears to be flawed: unfortunately, this doesn't seem like it would work because despite the deposit-precommitment+defection-incentive, there is still "nothing at stake" for a participant because there's no way to prove on-blockchain that the file hasn't been decrypted before time t. On-blockchain visibility is adequate for Proof-of-Work and Proof-of-Stake because participants in PoW can observe any double-spending and punish the PoW owners (who own ASICs and large capital investments) via social mechanisms like forks, and for Casper-style slashing PoS because double-validating can be proven on-chain and their stakes slashed, but the invisibility of decryption means that a defrauded locker can never prove that any or all of the secret-sharers have defrauded them by colluding & decrypting early.
Because of this, the contract is vulnerable to Sybil attacks: if the contract is profitable and the ETH fees cover the cost to participants of making deposits/key storage/uptime, then a large entity can by definition profitably participate while pretending to be most/all participants, and easily decrypt many files even if lockers require a large k to decrypt. (The require capital might be quite small; JoinMarket only required $32k Bitcoin capital to de-anonymize transactions, well within the capability of many individuals, never mind attackers like blockchain analysis companies.) A large entity also benefits from some degree of economies of scale compared to a truly distributed quorum, as it only needs 1 blockchain copy, and can more easily invest in 100% uptime to avoid accidentally losing deposits to downtime, allowing it to outcompete; it can further increase profits potentially enormously by systematically decrypting & exploiting anything locked (as it is likely that any file anyone is going to the trouble of time-locking is a valuable file to someone, otherwise why bother?). So such a contract is vulnerable to a self-funding, undetectable, unpreventable, permanent Sybil attack.
The vulnerability may extend to actual distributed quorums as well: individual shares can be bribed and attacked, and it's not clear that the deposit mechanism can prevent all counter-measures or computations. (They probably aren't as efficient as the main Sybil attack, but would allow attacking prior time-locks or for attacking just a few time-locks.) For example, an attacker can try to defuse the slashing condition and buy shares from k secret-sharers simply by publishing Ethereum contracts with exactly the same mechanism but providing an additional deposit+fee-share from the attacker; this insures the secret-sharers from defection - they can sell their share to the attacker and if the attacker 'defects', they merely claim the second deposit and are made whole; thus, either way they get back their deposit and their share of the fee, and since the attacker no longer benefits on net, the attacker won't defect. Counter-contracts may not be stable (the sharer could defect in turn), but an attacker has additional options: like secret-sharing itself, an attacker could take advantage of multi-party computation to enable bribed sharers to reconstruct the full key in secret without risking revealing their individual shares & thus their deposits. More attacks may be possible, and the smart contract must be robust to all possible attacks and counter-contracts bribing the secret-sharers.
A time-lock puzzle with a linear gap in parallel time. Although our negative results rule out 'strong' time-lock puzzles, they still leave open the possibility for a weaker version: one that can be generated with n parallel queries to the oracle but requires n rounds of adaptive queries to solve. In a positive result, we show that such a puzzle can indeed be constructed…Although this work rules out black-box constructions (with a super-constant gap) from one-way permutations and collision-resistant hash functions, we have no reason to believe that time-lock puzzles based on other concrete problems (e.g., lattice-based problems) do not exist. Extending our approach to other general assumptions (e.g., trapdoor permutations) is also an interesting open problem.
That is, the puzzle constructor can construct the puzzle in parallel, and the solver has to solve it serially.
Of course, one could ask the same question of my original proposal - what makes you think that hashing can't be sped up? You already supplied an example where cryptographic hashes were sped up astonishingly by a GPU, Bitcoin mining.
2. Provide an abstract function and prove an asymptotically tight amortized lower bound on the number of memory accesses required to compute an acceptable proof of effort; specifically, we prove that, on average, the sender of a message must perform many unrelated accesses to memory, while the receiver, in order to verify the work, has to perform significantly fewer accesses; 3. Propose a concrete instantiation of our abstract function, inspired by the RC4 stream cipher; 4. Describe techniques to permit the receiver to verify the computation with no memory accesses; 5. Give experimental results showing that our concrete memory-bound function is only about four times slower on a 233 MHz settop box than on a 3.06 GHz workstation, and that speedup of the function is limited even if an adversary knows the access sequence and uses optimal off-line cache replacement.
…we give experimental results for five modern machines that were bought within a two-year period in 2000-2002, and which cover a range of performance characteristics. All of these machines are sometimes used to send e-mail-even the settop box,which is employed as a quiet machine in a home…None of the machines have huge caches-the largest was on the server machine, which has a 512KB cache. Although the clock speeds of the machines vary by a factor of 12, the memory read times vary by a factor of only 4.2. This measurement confirms our premise that memory read latencies vary much less than CPU speeds.
…At the high end, the server has lower performance than one might expect, because of a complex pipeline that penalizes branching code. In general, higher clock speeds correlate with higher performance, but the correlation is far from perfect…Second, the desktop machine is the most cost-effective one for both CPU-bound and memory-bound computations; in both cases, attackers are best served by buying the same type of machines as ordinary users. Finally, the memory-bound functions succeed in maintaining a performance ratio between the slowest and fastest machines that is not much greater than the ratio of memory read times.
Existing widely used hash functions produce outputs of up to 512 bits (64 bytes), closely matching the cache line sizes of modern CPUs (typically 32-128 bytes), and the computing time required to hash even a very small amount of data (typically 200-2000 clock cycles on modern CPUs, depending on the hash used) is sufficient that the memory latency cost (typically 100-500 clock cycles) does not dominate the running time of ROMix.
However, as semiconductor technology advances, it is likely that neither of these facts will remain true. Memory latencies, measured in comparison to CPU performance or memory bandwidth, have been steadily increasing for decades, and there is no reason to expect that this will cease — to the contrary, switching delays impose a lower bound of Ω(log N ) on the latency of accessing a word in an N-byte RAM, while the speed of light imposes a lower bound of Ω( √N ) for 2-dimensional circuits. Furthermore, since most applications exhibit significant locality of reference, it is reasonable to expect cache designers to continue to increase cache line sizes in an attempt to trade memory bandwidth for (avoided) memory latency.
In order to avoid having ROMix become latency-limited in the future, it is necessary to apply it to larger hash functions. While we have only proved that ROMix is sequential memory-hard under the Random Oracle model, by considering the structure of the proof we note that the full strength of this model does not appear to be necessary.
When used for interactive logins, it is 35 times more expensive than bcrypt and 260 times more expensive than PBKDF2; and when used for file encryption — where, unlike bcrypt and PBKDF2, scrypt uses not only more CPU time but also increases the die area required — scrypt increases its lead to a factor of 4000 over bcrypt and 20000 over PBKDF2.
That is quite a difference between the hashes, especially considered that bcrypt and PBKDF2 were already engineered to have adjustable difficulty for similar reasons to our time-lock crypto puzzles.
Even in the original paper, the authors struggled to find a plausible use for it. To actually use the construction as a "time-lock" requires predicting the speed of CPUs in the future, resulting, at best, in a fuzzy release-date. This assumes that someone cares enough to want what is allegedly wrapped up in the puzzle to bother to compute the puzzle in the first place. It is not obvious that in the majority of situations, this would have a clear advantage over, say, leaving the information with a legal firm with instructions to release it on a particular date. Although this paper proposes a practical use for time-lock puzzles, the original authors would probably be dismayed that there is still not a widespread usage that appears to be of net benefit to humanity.
An important consideration to be made is that CPU-bound hash functions are still vulnerable to hardware implementations. For example, the literature provides efficient hardware implementations of SHA-1 in as low as 5000 gates, and able to produce a result in less than 400 clock cycles2. Since multi-million gate FPGAs can be purchased at less than $100 price points3, it follows that an attacker can build a fully unrolled hardware cracker for about $5000. Such a design, if clocked at 100MHz can try about 300,000 keys/second for the algorithm proposed above.
Based on the SEMATECH National Technology Roadmap for Semiconductors (1997 edition), we can expect internal chip speeds to increase by a factor of approximately 13 overall up to 2012, when the clock rates reach about 10GHz. After that improvements seem more difficult, but we estimate that another factor of five might be achievable by 2034. Thus, the overall rate of computation should go through approximately six doublings by 2034.
To add checkpoints, one could release both the original seed of the chain A, and a number of pairs of hashes (x0,y0)(x1,y1) … Let's say you wanted to do 1-month chains. Hash the seed A for a week, then take the current value x0 such that H(B)=x0. You know the value of B, since you've been computing the chain. Pick another random value y0, and continue the chain with H(By0). Write (x0,y0) in the output, and hash for another week. Do the same for (x1,y1) (x2,y2) and (x3,y3). Each chain then has a seed value and 4 pairs of 'checkpoints'. When unlocking the crypto puzzle, these checkpoints can't be used to jump ahead in the computation, but they can tell you that you're on the right track. I think that you could even use a secondary hash chain for the yn values, so yn+1=H(yn). If you also derived y0 from A (e.g. y0=H(Aconst)), you would just need to publish the seed value A and each checkpoint hash xn in order to have a fully checkpointed crypto puzzle.
Fast CPUs run much faster than slow CPUs - consider a 2.5GHz PC versus a 33MHz Palm PDA. Moreover, in addition to high clock rates, higher-end computer systems also have sophisticated pipelines and other advantageous features. If a computation takes a few seconds on a new PC, it may take a minute on an old PC, and several minutes on a PDA. That seems unfortunate for users of old PCs, and probably unacceptable for users of PDAs…we are concerned with finding moderately hard functions that most computer systems will evaluate at about the same speed. We envision that high-end systems might evaluate these functions somewhat faster than low-end systems, perhaps even 2-10 times faster (but not 10-100 faster, as CPU disparities might imply). Moreover, the best achievable price-performance should not be significantly better than that of a typical legitimate client…A memory-bound function is one whose computation time is dominated by the time spent accessing memory. The ratios of memory latencies of machines built in the last five years is typically no greater than two, and almost always less than four. (Memory throughput tends to be less uniform, so we focus on latency.) A memory-bound function should access locations in a large region of memory in an unpredictable way, in such a way that caches are ineffectual…Other possible applications include establishing shared secrets over insecure channels and the timed release of information, using memory-bound variants of Merkle puzzles [Merkle 1978] and of time-lock puzzles [May 1993; Rivest et al. 1996], respectively. We discuss these also in section 4.


Mirjana Stojic joined Wescorp in January, 2001 and from this time has considerably developed her role of Sales Support and Financial Administration. She began at WS with the sole responsibility of coordination of export shipments, including the completion of documentation and some customer liaison. Today Mirjana has established solid relationships with overseas customers, liaising with them on export issues. She has established procedures that are relevant to the documentation process such as the letter of credit process, the terms of the money transfer options and administration procedures. She liaises and educates the customers to ensure that both shipping and payment terms are compliant with the relevant shipments. This ensures that there are no delays to the shipments and payments are received promptly.
Mirjana is also responsible for completing shipping documents and ensuring quarantine checks are completed within the correct timeframe.
Mirjana also attends to the bookkeeping and payroll for various companies within the Group.
Two years working in a trading bank and three years in the finance industry also helped her to understand letters of credit and the security this process offers to clients and to Wescorp. Regular contact with overseas bankers has also enabled her to learn the protocols involved in overseas banking procedures.


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Just after the Master of the Ocean competition, Cabaret hosts the International Sand castle Competition during the first week of March.
This weeklong music festival, held each June in Puerto Plata, features blues, jazz, merengue and folk concerts held at the San Felipe Fort. Santo Domingo-based groups perform traditional music and dance, including salsa and African spirituals.
Merengue is essentially the Dominican Republic's national music style and a festival celebrating it is held each October - the first week, generally - in Puerto Plata. The entire Malecón, a seaside promenade, is cordoned off to traffic for the festival, in which famous Merengue singers perform on stage, food stalls are set up along the streets and a great crafts fair makes for interesting finds.
With its tropical climate, when you learn Spanish in the Dominican Republic you are subject to an "eternal summer", meaning there's really no bad time to visit. While the North Coast's rainfall picks up a bit from October to March, precipitation generally comes in the form of heavy rainstorms that clear up after an hour.


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Serge TREFEU: Hello Karuhat, and thank you for grant me this interview, how are you?
KARUHAT SOR SUPAWAN: Hello, very well!
We were five children in the family!
You had brothers who fought?
VERY YOUNG, KARUHAT ALREADY HAD THE "FIGHTING SPIRIT"!
My father was a big enthusiast of boxing, it's him who made us like sport to me and my brother!
You always stayed in camp or you were in another camp?
I gained the belt of Lumpinee in 112 lbs against Pairojnoi Sor Sayamchai and twice the belt of Lumpinee in 122 lbs against Chatchai Paiseethong and Meechok Sor Ploenchit, I fought for the belt of Lumpinee 115 lbs against Langsuan but I lost in points, I also fought against Wangchannoi for the belt of Lumpinee in 122 lbs, and Oley Kiatoneway, I lost in points!
I have make 190 fights for 165 victories, 23 defeats and 2 draws!
I gained approximately 20 fights by KO!
I was " Fimeuu " (technician)!
I liked to counter attacks in legs of my opponents with a poke!
There was several but my hardest fight was against Boonlai Sor Thanikul because it was big and very technical, against Wangchannoi also was hard one we met three times and he beat me three times, also against Hippy I faced him four times, I once beat him, we made a draw and he beat me twice!
When I gained my first belt of Lumpinee against Pairojnoi Sor Sayamchai!
Yes in Japan, in New Zealand, in Russia and in France!
You fought in France, it was in which year?
For me the best foreign fighters in Thailand are Ramon Dekkers (RIP) and Chong Skarbowsky!
Yes I very well made my living thanks to the boxing, I have to earn a lot of money!
Yes of very good purse, I gained purse between 180 000 bahts and 240 000 bahts!
KHRU KARUHAT IN THE SITKARUHAT GYM WITH BOTH CHAMPIONS CHAYLEK ET CHAYAY!
KARUHAT WITH BOTH BROTHERS CHAYLEK ET CHAYAY!
KARUHAT SOR SUPAWAN, CHAYAY SITKARUHAT, CHAYLEK SITKARUHAT!
Karuhat " The castle " made left from the champions of " the age of gold " of Muay Thai in Thailand, in the 90s exceptional champion was dreaded, being small for his category Karuhat had to display a very skillful boxing to beat his opponents often bigger than him. Magnificent technician mastered in the perfection the techniques of counter and of poke, during a match with Karuhat his opponents were almost to make certain to finish the fight with a cut at the face!
Karuhat had several fighters' nicknames because the fans of Muay Thai in Thailand adored his style of very clean boxing, for his renamed was called "YodSiyan" (The Superstar), for his intelligent boxing was nicknamed "Yodmuayèchriya" (The Genius of the boxing) and "Aysiyan" (The gifted)!
Karuhat often fought with important dumpan, as his fight against the star Nungubon where the dumpan in game was 700 000 bahts, dumpan gained by the Team of Karuhat!
Karuhat also gained big purses when he was at the top of his career, one of his biggest purses which he has to gain was 300 000 bahts for his fight against Kaensak Sor Ploenchit (Best boxer of the year in 1989 and 1990) on May 21st, 1993 in Lumpinee, fight to gain by Karuhat!
KARUHAT SOR SUPAWAN AGAINST KAENSAK PLOENCHIT, CLASSIC, THE TWO CHAMPIONS MET FOUR TIMES WITH A WIN FOR KAENSAK AND THREE WINS FOR KARUHAT!
Karuhat dominated the category 122 lbs in the 90s, the beginning of 2000, Karuhat fought abroad with more or less of success but was not any more the same than in his peak. Karuhat did not train seriously, he lost fights hard as in 2000, in 32 years, when he met young Russian, not to train, " The Gifted " had been put KO by a young champion named Alexei Pekarchik who was later all the same three times a world champion of Muay Thai!
This great champion was considered by numerous specialists as the best fighter of the category of 122 pounds of the 90s!
Karuhat beat great champions such as Chainoi Muangsurin, Lamnamoon Sor Sumalee, Chatchai Paiseethong, Pairojnoi Sor Sayamchai, Nungubon Sitlergchai, Kaensak Sor Ploenchit, Kruekchai Kaewsamrit (TKO), Matee Jedipitak, Weerapon Sahaprom, Meechok Sor Ploenchit, Hippy Singmanee, Pongsiri Rambo Por Rumrudee!
KARUHAT SOR SUPAWAN MADE MANY COVER OF MAGAZINES SPECIALIZED!
KARUHAT SOR SUPAWAN « AYSIYAN » !


text:
Q: Fill out a group table with 6 elements Let $G=\{0,1,2,3,4,5\}$ be a group whose table is partially shown below:
\begin{array}{ c| c | c | c | c |c|c|}
            * & 0& 1 & 2 & 3& 4 & 5\\
            \hline
            0 & 0 & 1  & 2 & 3 & 4 & 5 \\
            \hline
            1 & 1 & 2 & 0 & 4 &    &  \\
            \hline
            2 &  2 &    &    &   &     & \\
            \hline
            3 & 3  & 5  &  &   &  & 1\\
            \hline
            4 & 4  &    &  &   &  &  \\
            \hline
            5 &  5 &   &  &   & & \\
            \hline
        \end{array}

Complete the table.

Needed to use Inverses, cancellation and No 1 element can repeat per row/col, but got the wrong table.
\begin{array}{ c| c | c | c | c |c|c|}
            * & 0& 1 & 2 & 3& 4 & 5\\
            \hline
            0 & 0 & 1  & 2 & 3 & 4 & 5 \\
            \hline
            1 & 1 & 2 & 0 & 4 &  5   & 3 \\
            \hline
            2 &  2 &  0  & 1   & 5  &  3   & 4 \\
            \hline
            3 & 3  & 5  & 4  & 2  & 0 & 1\\
            \hline
            4 & 4  &  3  & 5 & 0  & 1 & 2 \\
            \hline
            5 &  5 & 4  & 3 & 1  & 2& 0\\
            \hline
        \end{array}
What is the correct table?

A: I am guessing it is isomorphic to the dihedral group on $6 $ elements. You have gone wrong in the last "quater" of the grid.
\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & 2 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & 2 & 3 & 4 & 5 \\
   \hline
   1 & 1 & 2 & 0 & 4 &  5   & 3 \\
   \hline
   2 &  2 &  0  & 1   & 5  &  3   & 4 \\
   \hline
   3 & 3  & 5  & 4  & \color{red}{0}  & \color{blue}{2} & \color{blue}{1}\\
   \hline
   4 & 4  &  3  & 5 & \color{blue}{1}  & \color{red}{0} & \color{blue}{2} \\
   \hline
   5 &  5 & 4  & 3 & \color{blue}{2}  & \color{blue}{1}& \color{red}{0}\\
   \hline
  \end{array}
$D_6 = \{ e,a,a^2,b,ab,a^2b \mid a^3=b^2=e \, \, \,  ab=ba^2 \}$ The elements $\color{red}{b,ab \text{ and } a^2 b}$ are of order $\color{red}{2}$.

A: Let's take it slow
$\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & 2 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & 2 & 3 & 4 & 5 \\
   \hline
   1 & 1 & 2 & 0 & 4 &    &  \\
   \hline
   2 &  2 &    &    &   &     & \\
   \hline
   3 & 3  & 5  &  &   &  & 1\\
   \hline
   4 & 4  &    &  &   &  &  \\
   \hline
   5 &  5 &   &  &   & & \\
   \hline
  \end{array}$
As each row and column must be distinct we can start by "soduku"ing the $1*a$ row.
$\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & 2 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & 2 & 3 & 4 & 5 \\
   \hline
   1 & 1 & 2 & 0 & 4 &  \color{blue}5  & \color{blue}3 \\
   \hline
   2 &  2 &    &    &   &     & \\
   \hline
   3 & 3  & 5  &  &   &  & 1\\
   \hline
   4 & 4  &    &  &   &  &  \\
   \hline
   5 &  5 &   &  &   & & \\
   \hline
  \end{array}$
Now $1*2=0$ so $2=-1$ So if we replace $2$ with $-1$ and use $\pm 1*m=k\iff m=\pm 1* k$ and $k*\pm 1=m \iff k=m*\mp 1$ we can get the following ($\color{green}{green}$ for $1/-1$ and $\color{blue}{blue}$ for "sudoku"ing):
$\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & -1 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & -1 & 3 & 4 & 5 \\
   \hline
   1 & 1 & -1 & 0 & 4 &  \color{blue}5  & \color{blue}3 \\
   \hline
   -1 &  -1 &  \color{green}0  &  \color{green} 1  &  \color{green}5 & \color{green}3    & \color{green}4\\
   \hline
   3 & 3  & 5  & \color{green}4 &   &  & 1\\
   \hline
   4 & 4  &  \color{blue}3  & \color{green}5 &   &  &  \\
   \hline
   5 &  5 & \color{blue}4  & \color{green}3 &   & & \\
   \hline
  \end{array}$
Now $3*5 = 1$ so $3*5*-1 = 0$ and $3*3=0$
And knowing $a*b = a*0*b = (a*1)(-1*b)=(a*-1)(1*b)$ we see:  $3*3= 4*1*-1*4=4*4;3*3=5*-1*1*5=5*5=0$.
$\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & -1 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & -1 & 3 & 4 & 5 \\
   \hline
   1 & 1 & -1 & 0 & 4 &  \color{blue}5  & \color{blue}3 \\
   \hline
   -1 &  -1 &  \color{green}0  &  \color{green} 1  &  \color{green}5 & \color{green}3    & \color{green}4\\
   \hline
   3 & 3  & 5  & \color{green}4 & \color{red}0  &  & 1\\
   \hline
   4 & 4  &  \color{blue}3  & \color{green}5 &   & \color{red}0 &  \\
   \hline
   5 &  5 & \color{blue}4  & \color{green}3 &   & & \color{red}0\\
   \hline
  \end{array}$
We can "sudoku" the rest (and replace $-1$ with $2$)
$\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & 2 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & 2 & 3 & 4 & 5 \\
   \hline
   1 & 1 & 2 & 0 & 4 &  \color{blue}5  & \color{blue}3 \\
   \hline
   2 &  2 &  \color{green}0  &  \color{green} 1  &  \color{green}5 & \color{green}3    & \color{green}4\\
   \hline
   3 & 3  & 5  & \color{green}4 & \color{red}0  & \color{blue}2 & 1\\
   \hline
   4 & 4  &  \color{blue}3  & \color{green}5 & \color{blue}1  & \color{red}0 & \color{blue}2 \\
   \hline
   5 &  5 & \color{blue}4  & \color{green}3 & \color{blue}2  & \color{blue}1& \color{red}0\\
   \hline
  \end{array}$
Hmm, though actually we haven't verified that what we were given would be a group.  We just took it on faith.  But we can verify by associativity it holds.
====
Here's an expansion and David Splutterwit's answer.  This is hopefully not such a haphazard guessing game and hopefully will unquestionably be a group.
First, let's not use numbers, that confusing.
Let's use $e=0,a=1,b=2,c=3,d=4,g=5$.($e$ is the identity.)
We know $a^2 = b$ $(1*1=2)$ and $a*b = a*a^2 = a^3=0$ $(1*2 = 0)$
So we have $\{e,a, a^2, c,d,g\}$
We have the three following relations: $a*c=d$, $c*a=g$, and $c*g=c^2a=a$.  Which would therefore mean $c^2 = e$
So we have $\{e,a,a^2,c,ac,ca|a^3 = c^2= e\}$. $ac\ne ca$.
Now $a*e = a, a*a= a^2, a*a^2 = e, a*c = ac$ and $a*ac\ne ac$.  So $a*ac = ca$
So we have $\{e, a, a^2, c,ac,a^2c|a^3=c^2=e, a^2c = ca\}$.
And that's enough to describe a group.
Or $\{0, 1, 1^2=2, 3, 1*3=4, 1^23=5|1^3=3^2=0, 1^23=3*1\}$.
You can fill in the table from there.
Wish I had thought of that first.  It's much more "grown-up" than filling in a table.

A: Suppose you had got this far and needed to fill out the rest:
\begin{array}{ c| c | c | c | c |c|c|}
   * & 0& 1 & 2 & 3& 4 & 5\\
   \hline
   0 & 0 & 1  & 2 & 3 & 4 & 5 \\
   \hline
   1 & 1 & 2 & 0 & 4 &  5   & 3 \\
   \hline
   2 &  2 &  0  & 1   & 5  &  3   & 4 \\
   \hline
   3 & 3  & 5  & 4 & ? \\
   \hline
   4 & 4  &  3  & 5  \\
   \hline
   5 &  5 & 4  & 3 \\
   \hline
  \end{array}
One way to proceed would be to use the property of associativity, which says that $(ab)c = a(bc)$. Let $a = 3^2$, and consider $3^3$: since $(3^2)3 = 3(3^2)$, we have $a\cdot3=3\cdot a$. In other words, $3$ and $a$ commute, and since $a \in \{0,1,2\}$, we see that $a=0$.
It's important to understand that the group multiplication table has more properties than just containing a permutation of the elements in each row and column; otherwise you merely have a Latin square.

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