Evaluate the security margins of SHA-512, SHA-256 and DHA-256 against the boomerang attack

Abstract

For an n-bit random permutation, there are three types of boomerang distinguishers, denoted as Type I, II and III, with generic complexities 2ⁿ, 2^n/3 and 2^n/2 respectively. In this paper, we try to evaluate the security margins of three hash functions namely SHA-512, SHA-256 and DHA-256 against the boomerang attack. Firstly, we give a boomerang attack on 48-step SHA-512 with a practical complexity of 2⁵¹. The correctness of this attack is verified by providing a Type III boomerang quartet. Then, we extend the existing differential characteristics of the three hash functions to more rounds. We deduce the sufficient conditions and give thorough evaluations to the security margins as follows: Type I boomerang method can attack 54-step SHA-512, 51-step SHA-256 and 46-step DHA-256 with complexities 2⁴⁸⁰, 2²¹⁸ and 2²³⁶ respectively. Type II boomerang method can attack 51-step SHA-512, 49-step SHA-256 and 43-step DHA-256 with complexities 2^158.50, 2^72.91 and 2^74.50 respectively. Type III boomerang method can attack 52-step SHA-512, 50-step SHA-256 and 44-step DHA-256 with complexities 2^223.80, 2^123.63 and 2^99.85 respectively.

摘要

创新点

本文研究了飞去来器方法对 SHA-512, SHA-256 和 DHA-256 三种哈希函数的攻击效率。 首次给出了对 48 轮 SHA-512 的实际飞去来器攻击结果, 攻击复杂度为$2^{51}$。 通过扩展现有的查分路径, 证明:

• I 型飞去来器方法可以攻击 54 轮 SHA-512, 51 轮 SHA-256 和 46 轮 DHA-256。 攻击复杂度分别为$2^{480}$, $2^{218}$和$2^{236}$。

• II 型飞去来器方法可以攻击 51 轮 SHA-512, 49 轮 SHA-256 和 43 轮 DHA-256。 攻击复杂度分别为$2^{158.50}$, $2^{72.91}$和$2^{74.50}$。

• III 型飞去来器方法可以攻击 52 轮 SHA-512, 50 轮 SHA-256 和 44 轮 DHA-256。 攻击复杂度分别为$2^{223.80}$, $2^{123.63}$和$2^{99.85}$。