  A problem of developing the consensus protocols in public blockchain systems
which spend a combination of energy and space resources is addressed. A
technique is proposed that provides a flexibility for selection of the energy
and space resources which should be spent by a player participating in the
consensus procedure. The technique originates from the cryptographic
time-memory-data trade-off approaches for cryptanalysis. The proposed technique
avoids the limitations of Proof-of-Work (PoW) and Proof-of Space (PoS) which
require spending of only energy and space, respectively. Also, it provides a
flexibility for adjusting the resources spending to the system budget. The
proposed consensus technique is based on a puzzle where the problem of
inverting one-way function is solved employing a dedicated Time-Memory-Data
Trade-Off (TMD-TO) paradigm. The algorithms of the consensus protocol are
proposed which employ certain unconstrained and constrained TMD-TO based
inversions. Security of the proposed technique is considered based on the
probability that the honest pool of nodes generate a longer extension of the
blockchain before its update, and a condition on the employed parameters in
order to achieve desired security have been derived. Implementation complexity
of the proposed consensus protocol is discussed and compared with the
complexities when PoW and PoS are employed.

Cryptography and Security