Two-permutation-based hashing with binary mixing

Journal of mathematical cryptology

article

Atul Luykx¹  Bart Mennink¹  Bart Preneel¹  Laura Winnen¹ 

[1] Department of Electrical Engineering;iMinds

关键词: Hash function;    permutation-based;    wide-pipe;    collision resistance;    preimage resistance;   

DOI  :  10.1515/jmc-2015-0015

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider the generic design of compression functions based on two n -bit permutations and XOR-based mixing functions. It is known that any such function mapping n+α${n+\alpha }$ to α bits, with 1≤α≤n${1\le \alpha \le n}$, can achieve at most min{2α/2,2n/2-α/4}${\min \lbrace 2^{\alpha /2},2^{n/2-\alpha /4}\rbrace }$ collision security. Using techniques similar to Mennink and Preneel [CRYPTO 2012, Lecture Notes in Comput. Sci. 7417, Springer, Heidelberg (2012), 330–347], we show that there is only one equivalence class of these functions achieving optimal collision security, and additionally min{2α,2n/2}${\min \lbrace 2^{\alpha },2^{n/2}\rbrace }$ preimage security. The equivalence class compares well with existing functions based on two or three permutations, and is well-suited for wide-pipe hashing.

【 授权许可】

CC BY|CC BY-NC-ND