one of the most widely used public key algorithm used to create digital signatures is known as rsa. its security is based on the classical difficulty of factoring the product of two large and unknown primes into the constituent primes. the integer factorization problem is believed to be intractable on any conventional computer if the primes are chosen at random and are sufficiently large. however, to factor the product of two n-bit primes, a quantum computer with roughly 6n bits of logical qubit memory and capable of executing a program known as shor’s algorithm will easily accomplish the task. shor's algorithm can also quickly break digital signatures based on what is known as the discrete logarithm problem and the more esoteric elliptic curve discrete logarithm problem. in effect, a relatively small quantum computer running shor's algorithm could quickly break all of the digital signatures used to ensure the privacy and integrity of information on the internet today.