Aperiodic logarithmic signatures

Strongly aperiodic logarithmic signatures

Logarithmic signatures for finite groups are the essential constituent of public key cryptosystems MST1 and MST3. Especially they form the main component of the private key of MST3. Constructing new classes of logarithmic signatures having features that do not share with the well-known class of transversal or fused transversal logarithmic signatures, has become a vital issue regarding the use o...

Aperiodic logarithmic signatures

In this paper we propose a method to construct logarithmic signatures which are not amalgamated transversal and further do not even have a periodic block. The latter property was crucial for the successful attack on the system MST 3 by Blackburn et al. [1]. The idea for our construction is based on the theory in Szabó’s book about group factorizations [12].

Logarithmic size ring signatures without random oracles

Ring signatures enable a user to anonymously sign a message on behalf of group of users. In this paper, we propose the first ring signature scheme whose size is O(log2N), where N is the number of users in the ring. We achieve this result by improving Chandran et al.’s ring signature scheme presented at ICALP 2007. Our scheme uses a common reference string and non-interactive zero-knowledge proo...

Minimal Logarithmic Signatures for Sporadic Groups

As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2 and MST3. An LS with the shortest length is called a minimal logarithmic signature (MLS) and is even desirable for cryptographic constructions. The MLS conjecture states that ever...

On Minimal Logarithmic Signatures of Finite Groups