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Logarithmic signatures for finite groups are the essential constituent of public key cryptosystems and . Especially they form the main component of the private key of . Regarding the use of , it has become a vital issue to construct new classes of logarithmic signatures having features that do not share with the well-known class of transversal or fused transversal logarithmic signatures. For this purpose Baumeister and de Wiljes recently presented an interesting method of constructing aperiodic logarithmic signatures for abelian groups. In this paper we introduce the concept of strongly aperiodic logarithmic signatures and show their constructions for abelian p-groups on the basis of the Baumeister-de Wiljes method. [ABSTRACT FROM AUTHOR]

A new type of public key cryptosystem, called MST3, has been recently introduced on the basis of covers and logarithmic signatures for non-abelian finite groups. The class of Suzuki 2-groups has been proposed for a possible realization of the generic scheme. Due to their simple structure, the groups enable us to study the security of the system and also provide an efficient implementation. An earlier relevant result of the cryptanalysis has shown that the transversal logarithmic signatures are unfit for use in this realization. In this paper we present a revised version of MST3 for the Suzuki 2-groups and show a thorough study of its security. Using heuristic and algebraic methods we establish strong lower bounds for the workload of conceivable direct attacks on the private key of the scheme. We then develop a powerful chosen plaintext attack which allows us to rule out the usage of a certain class of logarithmic signatures. In addition, we show a class of logarithmic signatures withstanding this attack and thus to our knowledge they could be used in the realization of the scheme. Finally, we describe and discuss the implementation issues of the scheme in detail and include data of its performance obtained from an experimental result. [ABSTRACT FROM AUTHOR]

A symmetric key cryptosystem based on logarithmic signatures for finite permutation groups was described by the first author in [6], and its algebraic properties were studied in [7]. In this paper we describe two possible approaches to the construction of new public key cryptosystems with message space a large finite group G, using logarithmic signatures and their generalizations. The first approach relies on the fact that permutations of the message space G induced by transversal logarithmic signatures almost always generate the full symmetric group S[subG] on the message space. The second approach could potentially lead to new E1Gamal-like systems based on trapdoor, one-way functions induced by logarithmic signature-like objects we call meshes, which are uniform covers for G. [ABSTRACT FROM AUTHOR]