McEliece cryptosystem is a public-key cryptosystem based on error-correcting codes. It constitutes one of the few alternatives to cryptosystems relying on number theory. We present a modification of the McEliece cryptosystem which strengthens its security without increasing the size of the public key. We show that it is possible to use some properties of the automorphism groups of the codes to ...

In 1984, Shamir [1] introduced the concept of an identity-based cryptosystem. In this system, each user needs to visit a key authentication center (KAC) and identify him self before joining a communication network. Once a user is accepted, the KAC will provide him with a secret key. In this way, if a user wants to communicate with others, he only needs to know the “identity” of his communicatio...

Based on an idea by Hin, the method of obtaining the original message after selecting k of n coordinates at random in the McEliece public-key cryptosystem is improved. The attack, which is more efficient than the attacks previously proposed, is characterized by a systematic method of checking and by a random bit swapping procedure. An optimization procedure similar to the one proposed by Lee an...

Medium Field Equation (MFE) multivariate public key cryptosystems were broken by High Order Linearization Equation (HOLE) attack. In order to avoid HOLE attack, we proposed an improvement of MFE, Cubic MFE public key encryption scheme. In our construction, multiplications of three second order matrices were used to get a set of cubic polynomials in the central map. Through theoretical analysis ...

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 e...

Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based cryptosystem, proposed by McEliece. However, it has a number of drawbacks such as; large public key length and low security level. On the other hand, Low Densi...

Ajtai recently found a random class of lattices of integer points for which he could prove the following worst-case/average-case equivalence result: If there is a probabilistic polynomial time algorithm which nds a short vector in a random lattice from the class, then there is also a probabilistic polynomial time algorithm which solves several problems related to the shortest lattice vector pro...

A new general mathematical problem, suitable for publickey cryptosystems, is proposed: morphism computation in a category of Abelian groups. In connection with elliptic curves over finite fields, the problem becomes the following: compute an isogeny (an algebraic homomorphism) between the elliptic curves given. The problem seems to be hard for solving with a quantum computer. ElGamal public-key...

Abstract: In 1984, Shamir proposed the concept of the identity-based cryptosystem. Instead of generating and publishing a public key for each user, the identity-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct.This paper proposes a new identitybased c...