Impossibility of Construction of OWHF and UOWHF from PGV Model Based on Block Cipher Secure Against ACPCA

Abstract

In 1993, Preneel, Govaerts and Vandewalle [11] considered 64 block cipher based hash functions (64 PGV-hash functions). In 2002, Black, Rogaway and Shrimpton [3] proved that 20 of 64 PGV-hash functions are collision resistant, assumed that a block cipher is a random block cipher. In 2002, Hirose [4] defined ACPA(Adaptive Chosen Plaintext Attack) model and ACPCA(Adaptive Chosen Plaintext/Ciphertext Attack) model and he showed that, for every PGV-hash function, there exist block ciphers secure against ACPA such that the PGV-hash function based on them is not a OWHF which has the properties of preimage resistance and second-preimage resistance. Recently, Lee et al. [6] generalized the definition of PGV-hash function into a hash family and showed that 42 of 64 PGV-hash families are collision resistant. In this paper, we show that, for every PGV-hash function, there exist block ciphers secure against ACPCA such that the PGV-hash family based on them is not a OWHF. We also show that, for every PGV-hash family, there exist block ciphers secure against ACPCA such that the PGV-hash family based on them is not a UOWHF.KeywordsHash FunctionBlock CipherCompression FunctionHash FamilySecurity NotionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.