Volume 7, Issue 2

Abstract. We introduce a truncated addition operation on pairs of N -bit binary numbers that interpolates between ordinary addition mod and bitwise addition in . We use truncated addition to analyze hash functions that are built from the bit operations add, rotate, and xor, such as Blake , Skein , and Cubehash . Any ARX algorithm can be approximated by replacing ordinary addition with truncated addition, and we define a metric on such algorithms which we call the sensitivity . This metric measures the smallest approximation agreeing with the full algorithm a statistically useful portion of the time (we use ). Because truncated addition greatly reduces the complexity of the non-linear operation in ARX algorithms, the approximated algorithms are more susceptible to both collision and pre-image attacks, and we outline a potential collision attack explicitly. We particularize some of these observations to the Skein hash function.

Abstract. In this paper, we study a special class of recently introduced quasigroups called multivariate quadratic quasigroups (MQQs) and solve several open research problems about them. Our main contributions are threefold. The first is to provide a standard form of the MQQ generating function. Secondly, we show how to explicitly construct MQQs of higher orders and give lower bounds on the number of MQQs, which so far were open problems. Last, but not least, we refine the definition of MQQs of different types by introducing the notion of “MQQs of strict type”. The new concept has the advantage of being invariant under invertible affine transformations over the set of the rows, columns and symbols of the multiplication table of an MQQ. It is therefore better suited to characterize the complexity of the underneath multivariate quadratic system.

Abstract. The purpose of this paper is to consider the problem of determining the exact values of the complexities of the three graph access structures on six participants, which are unsolved in van Dijk's paper [Des Codes Cryptogr 6 (1995), 143–169]. For each of these access structures, we obtain the upper bound 3/2 on the complexity, establishing the exact value of the complexity.

Abstract. Logarithmic signatures for finite groups are the essential constituent of public key cryptosystems and . Especially they form the main component of the private key of . Regarding the use of , it has become a vital issue to construct new classes of logarithmic signatures having features that do not share with the well-known class of transversal or fused transversal logarithmic signatures. For this purpose Baumeister and de Wiljes recently presented an interesting method of constructing aperiodic logarithmic signatures for abelian groups. In this paper we introduce the concept of strongly aperiodic logarithmic signatures and show their constructions for abelian p -groups on the basis of the Baumeister–de Wiljes method.