New Constructions of Public-Key Encryption Schemes from Conjugacy Search Problems

Cryptanalysis of matrix conjugation schemes

“…We also discuss a related work by L. Wang et al (see [22]) which proposes a non-commutative version of Diffie-Hellman type encryption protocol which uses conjugation in noncommutative monoids and demonstrate their inadequacy.…”

“…Both papers, [5] and [22], use almost the same set of parameters. They use the semigroup G of 3×3 matrices of 1000-truncated polynomials in 10 variables over Z 11 (in [5]) and over Z 12 (in [22]). To be consistent with the notation above, we have n = 3, N = 1000, k = 10 and m = 11 or m = 12.…”

“…The main contribution of this paper is a heuristic algorithm for solving the conjugacy search problem in matrices over a semigroup of N -truncated polynomials. The heuristics used in the algorithm allow us to solve the conjugacy search problem on a majority of inputs generated using the parameters proposed in [5,22] which invalidates the security claims. We also argue that the proposed sampling procedure with high probability generates trivial instances of the conjugacy problem.…”

“…The choice of Z 11 or Z 12 gives different algebraic structures with, perhaps, very different algorithmic properties. To have a more complete picture, we analyze the protocol from [22] for both cases: Z 11 and Z 12 in Section 3.…”

“…Wang-Wang-Cao-Okamoto-Shao cryptosystem. Wang et al in [22] propose several public key encryption schemes based on the CSP over a noncommutative monoid G. The most basic of the protocols works as follows. Fix A, X ∈ G, with X being invertible, and a number K ∈ N. Public/private keys in Wang et al protocol are:…”