Solving Degree Bounds For Iterated Polynomial Systems

arXiv:2310.03637v2 Announce Type: replace
Abstract: For Arithmetization-Oriented ciphers and hash functions Gr\"obner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gr\"obner basis algorithms is only understood for special cases, and it is needless to say that these cases do not apply to most cryptographic polynomial systems. Therefore, cryptographers have to resort to experiments, extrapolations and hypotheses to assess the security of their designs. One established measure to quantify the complexity of linear algebra-based …

algorithms arxiv attack attacks attack vector cases ciphers competitive complexity cryptographic cs.cr functions hash hash functions special systems