Cryptology ePrint Archive: Report 2015/962

SOME REMARKS ON THE LOGARITHMIC SIGNATURES OF FINITE ABELIAN GROUPS

Thuong T. Dang, Tri T. Ton, Van H. Dang, Thuc D. Nguyen

Abstract: 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- i cations, 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.

Category / Keywords: public-key cryptography /

Date: received 4 Oct 2015

Contact author: dangtuanthuong at yahoo com vn

Available format(s): PDF | BibTeX Citation

Version: 20151006:143417 (All versions of this report)

Short URL: ia.cr/2015/962

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