Related papers: Insecure primitive elements in an ElGamal signatur…
This study is mainly about the discrete logarithm problem in the ElGamal cryptosystem over the abelian group U(n) where n is one of the following forms p^m, or 2p^m where p is an odd large prime and m is a positive integer. It is another…
The goal of this paper is to analyze the discrete Lambert map x to xg^x modulo a power of a prime p which is important for security and verification of the ElGamal digital signature scheme. We use p-adic methods (p-adic interpolation and…
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…
In this work, a new digital signature based on elliptic curves is presented. We established its efficiency and security. The method, derived from a variant of ElGamal signature scheme, can be seen as a secure alternative protocol if known…
In the ElGamal signature and encryption schemes, an element $x$ of the underlying group $G = \mathbb{Z}_p^\times = \{1, \ldots, p-1 \}$ for a prime $p$ is also considered as an exponent, for example in $g^x$, where $g$ is a generator of G.…
The need of exchanging messages and images secretly over unsecure networks promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this paper, a particular public key cryptosystem called the…
In this paper, a new variant of ElGamal signature scheme is presented and its security analyzed. We also give, for its theoretical interest, a general form of the signature equation.
The ElGamal cryptosystem is the most widely used public key cryptosystem. It uses the discrete logarithm problem as the cryptographic primitive. The MOR cryptosystem is a similar cryptosystem. It uses the discrete logarithm problem in the…
The MOR cryptosystem is a natural generalization of the El-Gamal cryptosystem to non-abelian groups. Using a $p$-group, a cryptosystem was built by this author in 'A simple generalization of El-Gamal cryptosystem to non-abelian groups'. It…
In this thesis, we propose some directed signature schemes. In addition, we have discussed their applications in different situations. In this thesis, we would like to discuss the security aspects during the design process of the proposed…
This article presents a new signcryption scheme which is based on the Schnorr digital signature algorithm. The new scheme represents my personal contribution to signcryption area. I have been implemented the algorithm in a program and here…
As applications of biometric verification proliferate, users become more vulnerable to privacy infringement. Biometric data is very privacy sensitive as it may contain information as gender, ethnicity and health conditions which should not…
A new scheme of probabilistic subgroup-related encryption is introduced. Some applications of this scheme based on the RSA, Diffie-Hellman and ElGamal encryption algorithms are described. Security assumptions and main advantages of this…
Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to…
Aiming for strong security assurance, recently there has been an increasing interest in formal verification of cryptographic constructions. This paper presents a mechanised formal verification of the popular Pedersen commitment protocol,…
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the…
In this work, we extend modular techniques for computing Gr\"obner bases involving rational coefficients to (two-sided) ideals in free algebras. We show that the infinite nature of Gr\"obner bases in this setting renders the classical…
A quantum tamper-evident encryption scheme is a non-interactive symmetric-key encryption scheme mapping classical messages to quantum ciphertexts such that an honest recipient of a ciphertext can detect with high probability any meaningful…
The Welch map $x \rightarrow g^{x-1+c}$ is similar to the discrete exponential map $x \rightarrow g^x$, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to…
This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining…