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Title:
A Uniform Class of Weak Keys for Universal Hash Functions
Authors: Kaiyan Zheng, Peng Wang
Abstract:In this paper we investigate weak keys of universal hash functions (UHFs) from their combinatorial properties. We find that any UHF has a general class of keys, which makes the combinatorial properties totally disappear, and even compromises the security of the UHF-based schemes, such as the Wegman-Carter scheme, the UHF-then-PRF scheme, etc. By this class of keys, we actually get a general method to search weak-key classes of UHFs, which is able to derive all previous weak-key classes of UHFs found by intuition or experience. Moreover we give a weak-key class of the BRW polynomial function which was once believed to have no weak-key issue, and exploit such weak keys to implement a distinguish attack and a forgery attack against DTC - a BRW-based authentication encryption scheme. Furthermore in Grain-128a, with the linear structure revealed by weak-key classes of its UHF, we can recover any first (32+b) bits of the UHF key, spending no more than 1 encryption and (2^{32} + b) decryption queries.
ePrint: https://eprint.iacr.org/2017/436
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