Volume 11, Issue 4

Breaking RSA is one of the fundamental problems in cryptography. Due to its reliance on the difficulty of the integer factorization problem, no efficient solution has been found despite decades of extensive research. One of the possible ways to break RSA is by finding the value p+q{p+q}, which requires searching the set of all even integers. In this paper, we present a number of formulas for p+q{p+q} that depend on the form of n=p⁢q{n=pq}. These formulas make the set to be searched much smaller than the set of all even integers.

The security of the asymmetric cryptosystem MST1{{}_{1}} relies on the hardness of factoring group elements with respect to a logarithmic signature. In this paper we investigate the factorization problem with respect to logarithmic signatures of abelian groups represented in primary decomposition. We present an efficient factorization algorithm for logarithmic signatures, where descending into factor groups induced by period subgroups is possible. Especially, we show that a logarithmic signature is tame when all its blocks are of prime size.

Typically, secure channels are constructed from an authenticated key exchange (AKE) protocol, which authenticates the communicating parties based on long-term public keys and establishes secret session keys. In this paper we address the partial leakage of long-term secret keys of key exchange protocol participants due to various side-channel attacks. Security models for two-party authenticated key exchange protocols have been developed over time to provide security even when the adversary learns certain secret values. This paper combines and extends the advances of security modelling for AKE protocols addressing more granular partial leakage of long-term secrets of protocol participants. Further, we fix some flaws in security proofs of previous leakage-resilient key exchange protocols.