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We investigate the security of the family of MQQ public key cryptosystems using multivariate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular, the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature scheme MQQ-SIG and the encryption scheme MQQ-ENC, although using different types of MQQs, share a common algebraic structure that introduces a...
We propose a new multivariate probabilistic encryption scheme with decryption errors MQQ-ENC that belongs to the family of MQQ-based public key schemes. Similarly to MQQ-SIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasigroups, and a minus modifier with relatively small and fixed number of removed equations. To make the decryption possible and also efficient, we use a universal hash function to eliminate possibly wrong plaintext...
The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar (UOV) signature scheme (Eurocrypt '99) minimizing the length of the signatures. By now the Rainbow Band Separation attack is the best key recovery attack known. For some sets of parameters it is even faster than a direct attack on the public key. Unfortunately the available description of the attack is very ad hoc and does not provide deep insights. In this article we provide another...
This document contains the Intellectual Property Statement and the technical description of the MQQ-SIG - a new public key digital signature scheme. The complete scientific publication covering the design rationale and the security analysis will be given in a separate publication. MQQ-SIG consists of $n - \frac{n}{4}$ quadratic polynomials with $n$ Boolean variables where $n=160$, $192$, $224$ or $256$.