Computational records with aging hardware: Controlling half the output of SHA-256

Abstract

SHA-256 is a secure cryptographic hash function. As such, its output should not have any detectable property. This paper describes three bit strings whose hashes by SHA-256 are nevertheless correlated in a non-trivial way: the first half of their hashes XORs to zero. They were found by "brute-force", without exploiting any cryptographic weakness in the hash function itself. This does not threaten the security of the hash function and does not have any cryptographic implication.This is an example of a large "combinatorial" computation in which at least 8.7 × 10 22 integer operations have been performed. This was made possible by the combination of: 1) recent progress on algorithms for the underlying problem, 2) creative use of "dedicated" hardware accelerators, 3) adapted implementations of the relevant algorithms that could run on massively parallel machines.The actual computation was done on aging hardware. It required seven calendar months using two obsolete second-hand bitcoin mining devices converted into "useful" computational devices. A second step required 570 CPU-years on an 8-year old IBM BlueGene/Q computer, a few weeks before it was scrapped.To the best of our knowledge, this is the first practical 128-bit collision-like result obtained by brute-force, and it is the first bitcoin miner-accelerated computation.

Development of a secure multi-factor authentication algorithm for mobile money applications

“…The security technologies and compresses them to produce a 256-bit fixed-length hash value which is in a 64-digit hexadecimal number Bensalem et al, 2021;Bouam et al, 2021;Nakamura et al, 2021;Phan et al, 2021;Patra & Patra, 2021).…”

“…Here, the 256-bit hash value is calculated from the 512 bits input message by dividing it into several 512bit data blocks and processing using the compression function one at a time. When the last block is less than 512 bits, padding is added by appending bits until it is 512-bit (Wu et al, 2020;Bouam et al, 2021). In hash computation, a hash value is obtained by repetitive generation of the message schedule, functions, constants, and word operations.…”