Minimal Logarithmic Signatures for Sporadic Groups

Minimal logarithmic signatures for finite groups of Lie type

New methods are developed to construct algorithmically good logarithmic signatures for affine algebraic groups, using Singer subgroups. The well known conjecture about the existence of minimal logarithmic signature (MLS) for simple groups is shown to be true for some finite simple groups of Lie type.

On Minimal Logarithmic Signatures of Finite Groups

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...

Weak Keys in MST1

The public key cryptosystem MST1 has been introduced in [9]. Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify ‘wild-like’ logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We give tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree ≥ 5. Hence, basin...

Some Remarks on the Logarithmic Signatures of Finite Abelian Groups

In the paper about the cryptosystem MST3, Svaba and Trung proposed a way to build a cryptosystem based on the concept of logarithmic signatures, and they choose Suzuki’s group, which is not abelian for implementing. Recently, to reason why these methods cannot be applied to abelian groups; Svaba, Trung and Wolf developed some algorithms to factorize the fused transversal logarithmic signatures ...