We examine the popular proof models for group key establishment of Bresson et al. (LNCS 2248: point out missing security properties addressing malicious protocol participants. We show that established group key establishment schemes from CRYPTO 2003 and ASIACRYPT 2004 do not fully meet these new requirements. Next to giving a formal definition of these extended security properties, we prove a variant of the explored proposal from ASIACRYPT 2004 secure in this stricter sense. Our proof builds on the Computational Diffie Hellman (CDH) assumption and the random oracle model.

Abstract. A protocol compiler is described, that transforms any provably secure authenticated 2-party key establishment into a provably secure authenticated group key establishment with 2 more rounds of communication. The compiler introduces neither idealizing assumptions nor high-entropy secrets, e. g., for signing. In particular, applying the compiler to a password-authenticated 2-party key establishment without random oracle assumption, yields a password-authenticated group key establishment without random oracle assumption. Our main technical tools are non-interactive and non-malleable commitment schemes that can be implemented in the common reference string (CRS) model.

Abstract. Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a "hidden" element α of a finite field IFp of p elements from rather short strings of the most significant bits of the remainder modulo p of αt for several values of t selected uniformly at random from IF * p . We use some recent bounds of exponential sums to generalize this algorithm to the case when t is selected from a quite small subgroup of IF * p . Namely, our results apply to subgroups of size at least p 1/3+ε for all primes p and to subgroups of size at least p ε for almost all primes p, for any fixed ε > 0. We also use this generalization to improve (and correct) one of the statements of the aforementioned work about the computational security of the most significant bits of the Diffie-Hellman key.

A group authenticated key exchange (GAKE) protocol allows a set of parties belonging to a certain designated group to agree upon a common secret key through an insecure communication network. In the last few years, many new cryptographic tools have been specifically designed to thwart attacks from adversaries which may have access to (different kinds of) quantum computation resources. However, few constructions for group key exchange have been put forward. Here, we propose a four-round GAKE which can be proven secure under widely accepted assumptions in the Quantum Random Oracle Model. Specifically, we integrate several primitives from the so-called Kyber suite of post-quantum tools in a (slightly modified) compiler from Abdalla et al. (TCC 2007). More precisely, taking as a starting point an IND-CPA encryption scheme from the Kyber portfolio, we derive, using results from Hövelmanns et al. (PKC 2020), a two-party key exchange protocol and an IND-CCA encryption scheme and prove them fit as building blocks for our compiled construction. The resulting GAKE protocol is secure under the Module-LWE assumption, and furthermore achieves authentication without the use of (expensive) post-quantum signatures.

Logarithmic signatures are a special type of group factorizations, introduced as basic components of certain cryptographic keys.Thus, short logarithmic signatures are of special interest. We deal with the question of finding logarithmic signatures of minimal length in finite groups. In particular, such factorizations exist for solvable, symmetric, and alternating groups.We show how to use the known examples to derive minimal length logarithmic signatures for other groups. Namely, we prove the existence of such factorizations for several classical groups and-in parts by direct computation-for all groups of order <175 560 (= ord(J1), where J1 is Janko's first sporadic simple group). Whether there exists a minimal length logarithmic signature for each finite group still remains an open question.