Based on ElGamal system, a group-oriented threshold signature and authenticated encryption scheme was put forward. After being signed by a signer group employing ) , ( n t threshold signature scheme, the message m was transmitted to a particular verifier group, and then the signature was verified through the cooperation of k ones from the verifier group with l members. Similarly, a general auth...

Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the D...

Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the D...

In the original ElGamal signature scheme and it’s variants, two secret integers-private key and one-time secret key are required to produce a signature on a message, m. The private key of a system will be used throughout the life of the system whereas the one-time secret key only be used once and must be regenerated (different one-time secret key) when signing different message. This paper intr...

We provide a new security proof for a variant of ElGamal proposed by Damg̊ard, showing that it is secure against non-adaptive chosen ciphertext. Unlike previous security proofs for this cryptosystem, which rely on somewhat problematic assumptions, our computational problem is similar to accepted problems such the Gap and Decision Diffie-Hellman problems.

We give an improved presentation of the protocol first published in [23]. That paper contained some minor misprints, and was thin on formal proofs of correctness; both shortcomings are addressed in the current version. We also make some brief comparisons with, and criticisms of some more recent publications which build on the results presented in [23]. In particular, we point out that, in contr...

In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation. We tabulate these parameters. We also compare the discrete logarithm problem in the group of circulant matrices with the discrete logarithm problem in finite...