Band 7, Heft 4

Abstract. An n -player -secure robust secret sharing scheme is a ( t , n )-threshold secret sharing scheme with the additional property that the secret can be recovered, with probability at least , from the set of all shares even if up to t players provide incorrect shares. The existing constructions of robust secret sharing schemes for the range have the share size larger than the secret size. An important goal in this area is to minimize the share size. In the paper, we propose a new unconditionally-secure robust secret sharing scheme for the case with share size equal to the secret size. This is the minimum possible size as dictated by the perfect secrecy of the scheme. We further extend our scheme to realize a class of multilevel access structures that satisfy a special condition. The property that the share size is equal to secret size is preserved in the extended scheme. The proposed scheme is the first known robust secret sharing scheme realizing multilevel access structure.

Abstract. This paper shows a generic method of constructing CCA-secure public key encryption schemes with leakage-resilience on the secret key. It is based on a new kind of universal 2 hash proof system which accepts an auxiliary parameter. Specifically, two schemes are presented, basing on the DCR assumption and DLIN assumption respectively.

Abstract. Non-linear feedback shift register (NLFSR) ciphers are cryptographic tools of choice of the industry especially for mobile communication. Their attractive feature is a high efficiency when implemented in hardware or software. However, the main problem of NLFSR ciphers is that their security is still not well investigated. The paper makes a progress in the study of the security of NLFSR ciphers. In particular, we show a distinguishing attack on linearly filtered NLFSR (or LF-NLFSR) ciphers. We extend the attack to a linear combination of LF-NLFSRs. We investigate the security of a modified version of the Grain stream cipher and show its vulnerability to both key recovery and distinguishing attacks.

Abstract. Safe primes and safe RSA moduli are used in several cryptographic schemes. The most common notion is that of a prime p , where is also prime. The latter is then a Sophie Germain prime. Under appropriate heuristics, they exist in abundance and can be generated efficiently. But the modern methods of analytic number theory have – so far – not even allowed to prove that there are infinitely many of them. Thus for this notion of safe primes, there is no algorithm in the literature that is unconditionally proven to terminate, let alone to be efficient. This paper considers a different notion of safe primes and moduli. They can be generated in polynomial time, without any unproven assumptions, and are good enough for the cryptographic applications that we are aware of.

Abstract. Multiple right-hand side (MRHS) equations over finite fields are a relatively new tool useful for algebraic cryptanalysis. The main advantage is in an efficient representation of the cryptographic primitives. The main methods to solve systems of MRHS equations are gluing, that relies on merging equations, and various versions of local reduction, that relies on removing partial solutions. In this paper we present a new algorithm to solve MRHS systems. The core of the algorithm is a transformation of the problem of solving an MRHS equation system into a problem of group factorization. We then provide two alternative algorithms to solve the transformed problem. One of these algorithms provides a further transformation to the well-studied closest vector problem. A corollary of our research is that the solution of the group factorization problem arising during the process of solving an MRHS equation system must be as difficult as the cryptanalysis of a corresponding block cipher described by this MRHS system.