International Association
for Cryptologic Research

In the paper about the cryptosystem MST3, Svaba and Trung pro-

posed a way to build a cryptosystem based on the concept of logarithmic signa-

tures, and they choose Suzuki\'s group, which is not abelian for implementing.

Recently, to reason why these methods cannot be applied to abelian groups; Sv-

aba, Trung and Wolf developed some algorithms to factorize the fused transver-

sal logarithmic signatures (FTLS). Their attacks can be avoided by some mod-

ications, which is the aim of this paper, where we will use the weakness of the

discrete logarithm problem (DLP) to propose two cryptosystems. The rst one

is based on the new concept about quasi-logarithmic signature of nite solvable

groups, which is the generalization of logarithmic signatures. The second is

built on the logarithmic signatures of nite cyclic 2-groups, which include two

interesting examples on Pell\'s curves and elliptic curves over nite elds.