We show that the inadvertent use of a Carmichael number instead of a prime factor in the modulus of an RSA cryptosystem is likely to make the system fatally vulnerable, but that such numbers may be detected.

This project involves an implementation of the Rivest Shamir Adleman (RSA)[1] encryption algorithm in C. It consists of generation of two random prime numbers and a number coprime to φ(n) also called euler toitent function. These three are used to generate a public key and private key. The user has to enter a message which is encrypted by the public key. The algorithm also decrypts the generate...

For given N=pq with p and q different odd primes and natural m Banghe Li introduced the public key cryptosystem [1]. In the case m=1 the system is just the famous RSA public key cryptosystem [2]. The cryptosystem is more secure in general [2] than RSA system. But one has to solve a few problems connected with the introduced cryptosystem. The cryptosystem works with elements of the quotient ring...

In 1987, Desmedt first proposed a group oriented cryptosystem. During the past decade, group oriented cryptosystem has become one of the important cryptographical primitives. Laih and Harn proposed a generalized threshold cryptosystem with two models in 1991. In their system, each group is only assigned public key. A ciphertext can be decoded by utilizing all the secret keys owned by the users ...

New results in cryptanalysis are constantly being presented in the academic community, and this process poses no problems. Paradoxically, the discovery of a method that would allow breaking for example an RSA key in the same time as it takes to encrypt a message with it, would have serious and disturbing impacts on sectors such as finance and defence, and would in fact be impossible to publish ...

The McEliece public-key cryptosystem fails to protect any message which is sent to a recipient more than once using different random error vectors. In general, it fails to protect any messages sent to a recipient which have a known linear relation to one another. Under these conditions, which are easily detectable, the cryptosystem is subject to a devastating attack which reveals plaintext with...

We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme.

In 1998, Cai and Cusick proposed a lattice-based public-key cryptosystem based on the similar ideas of the Ajtai-Dwork cryptosystem, but with much less data expansion. However, they didn’t give any security proof. In our paper, we present an efficient ciphertext-only attack which runs in polynomial time against the cryptosystem to recover the message, so the Cai-Cusick lattice-based public-key ...

We describe a public-key cryptosystem with worst-case/average case equivalence. The cryptosystem has an amortized plaintext to ciphertext expansion of O(n), relies on the hardness of the Õ(n)-unique shortest vector problem for lattices, and requires a public key of size at most O(n) bits. The new cryptosystem generalizes a conceptually simple modification of the “Ajtai-Dwork” cryptosystem. We p...

Combinatorial problems serve as an important resource for developing practical public key cryptosystems and several combinatorial cryptosystems have been proposed in the cryptographic community. In this paper, a combinatorial public key cryptosystem is proposed. The security of the proposed cryptosystem is dependent on a combinatorial problem involving matrices. The system features fast encrypt...