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Title:
Ubiquitous Weak-key Classes of BRW-polynomial Function
Authors: Kaiyan Zheng, Peng Wang, Dingfeng Ye
Abstract:BRW-polynomial function is suggested as a preferred alternative of polynomial function, owing to its high efficiency and seemingly non-existent weak keys. In this paper we investigate the weak-key issue of BRW-polynomial function as well as BRW-instantiated cryptographic schemes. Though, in BRW-polynomial evaluation, the relationship between coefficients and input blocks is indistinct, we give out a recursive algorithm to compute another (2^{v+1}-1)-block message, for any given (2^{v+1}-1)-block message, such that their output-differential through BRW-polynomial evaluation, equals any given s-degree polynomial, where v\ge\lfloor\log_2(s+1)\rfloor. With such algorithm, we illustrate that any non-empty key subset is a weak-key class in BRW-polynomial function. Moreover any key subset of BRW-polynomial function, consisting of at least 2 keys, is a weak-key class in BRW-instantiated cryptographic schemes like the Wegman-Carter scheme, the UHF-then-PRF scheme, DCT, etc. Especially in the AE scheme DCT, its confidentiality, as well as its integrity, collapses totally, when using weak keys of BRW-polynomial function, which are ubiquitous.
ePrint: https://eprint.iacr.org/2018/014
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