Cryptanalysis of the birational permutation signature scheme over a non-commutative ring

Cryptanalysis of the Birational Permutation Signature Scheme over a Non-commutative Ring

In 2008, Hashimoto and Sakurai proposed a new efficient signature scheme, which is a non-commutative ring version of Shamir’s birational permutation signature scheme. Shamir’s scheme is a generalization of the OSS (Ong-Schnorr-Shamir) signature scheme and was broken by Coppersmith et al. using its linearity and commutativity. The HS (Hashimoto-Sakurai) scheme is expected to be secure against th...

New Digital Signature Scheme Using Polynomials Over Non- Commutative Groups

Digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications, like, electronic contract signing, certified email, and secure web browsing etc. However, many existing signatures schemes lie in the intractability of problems closure to the number theory tha...

Attacks on the Birational Permutation Signature Schemes

Directed prime graph of non-commutative ring

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$.  Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...

Quo Vadis Quaternion? Cryptanalysis of Rainbow over Non-commutative Rings

The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar Signature Scheme (Eurocrypt '99) minimizing the length of the signatures. Recently a new variant based on non-commutative rings, called NC-Rainbow, was introduced at CT-RSA 2012 to further minimize the secret key size. We disprove the claim that NC-Rainbow is as secure as Rainbow in general...