Volume 3, Issue 4

We give some results towards the conjecture that are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and are any positive integers and X ( d, n ) = Σ 1≤ i 1 < i 2 <⋯< i d ≤ n x i 1 x i 2 ⋯ x i d .

A known recursive construction for perfect hash families multiplies the number of factors by q , where q is the largest prime power not exceeding the number of symbols. This is generalized to permit multiplication of the number of factors by powers of q ; it is also improved upon by restricting the structure of the ingredient designs. For a perfect hash family of strength t , it may be possible to order its rows so that, for each , the first N i rows form a perfect hash family of strength . This ‘matroshka’ ordering underlies a sometimes substantial reduction in the number of rows generated by the recursive construction. Perfect hash families with useful matroshka orderings are generated using linear orthogonal arrays, and with an effective one-row-at-a-time greedy algorithm.

We analyze a variant of the well-known Miller–Rabin test, that may be useful in preventing side-channel attacks to the random prime generation on smart cards: In the Miller–Rabin primality test for a positive integer n , one computes repeatedly the expression a ω (mod n ) for random bases a ∈ ℕ and exponents ω such that ω divides n – 1 and ( n – 1)/ ω is a power of 2. In each round one chooses, at random, a different base a, and uses binary exponentiation to compute a ω (mod n ). ‘Listening’ to many rounds, it seems at least plausible that an outside spy could retrieve the integer n – 1. In the variant we consider, one chooses in each round two positive random integers a and ρ and applies the test with base a and exponents ωρ , ω as above. This increases the safety against side-channel attacks. However at the same time, it decreases the performance of the Miller–Rabin test. In this article we use elementary means to analyze this variant. We will not be able to obtain results as strong as those by Damgård, Landrock and Pomerance on prime generation using the original Miller–Rabin test. However by imposing restrictions on the random parameter ρ , we obtain satisfactory estimates on the variant described here which justify practical implementation.

This paper describes a cryptanalysis of MST 3 , a public key cryptosystem based on nonabelian groups recently proposed by Lempken, Magliveras, van Trung and Wei.

In this paper, first we discuss the security model for deterministic challenge-response identification protocols. For such protocols, we are able to simplify the CR2 security model in [Bellare, Fischlin, Goldwasser, and Micali, Identification protocols secure against reset attacks: 495–511, Springer, 2001] which captures concurrent attacks and reset attacks. Then we propose an extremely simple identification protocol and prove that its CR2 security is equivalent to the hardness of the Strong Diffie–Hellman problem.

We study the hash function from a finite field 𝔽 q into an elliptic curve over 𝔽 q which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conjectured by T. Icart for the image size of this function.