International Association for Cryptologic Research (IACR)
Doi
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 (2v+1−1)-block message, for any given (2v+1−1)-block message, such that their output-differential through BRW-polynomial evaluation, equals any given s-degree polynomial, where v≥⌊log2(s+1)⌋.
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