Band 6, Heft 2

Abstract. We present a heuristic asymptotic formula as for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree , with fixed discriminant, with rho-value bounded by a fixed such that , and with prime subgroup order at most x .

Abstract. This paper studies degree 3 Boolean functions in n variables which are rotation symmetric, that is, invariant under any cyclic shift of the indices of the variables. These rotation symmetric functions have been extensively studied in the last dozen years or so because of their importance in cryptography. Let denote the (Hamming) weight of the Boolean function f . We extend and simplify results of Bileschi, Cusick and Padgett, who gave an algorithm for finding a recursion for the sequence , where is the cubic rotation symmetric function generated by the monomial We show that the weights for the function (note this is just the sum of the first terms in the definition of ) satisfy the same recursion as the weights for . We prove the recursion for the weights of by a method based on the work by Bileschi–Cusick–Padgett, but we are able to avoid a lot of the complications in their proofs. In particular, we do not need the technical notion of “ g terms” or the elaborate proof of similarity of certain matrices.

Abstract. There is no linear hull effect in linear cryptanalysis.

Abstract. The McEliece cryptosystem is one of the few systems to be considered secure against attacks by Quantum computers. The original scheme is built upon Goppa codes and produces very large keys, hence recent research has focused mainly on trying to reduce the public key size. Previous proposals tried to replace the class of Goppa codes with other families of codes, but this was revealed to be an insecure choice. In this paper we introduce a construction based on Generalized Srivastava codes, a large class which includes Goppa codes as a special case, that allows relatively short public keys without being vulnerable to known structural attacks.

Abstract. Bergman's ring , parameterized by a prime number p , is a ring with p 5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974. In 2011, Climent, Navarro and Tortosa described an efficient implementation of using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. We present a deterministic polynomial time reduction of the discrete logarithm problem in to the classical discrete logarithm problem in , the p -element field. In particular, the discrete logarithm problem in can be solved, by conventional computers, in sub-exponential time.