相关论文: Public-key cryptography and invariant theory

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations…

This paper provides a simple variation of the basic ideas of the BB84 quantum cryptographic scheme leading to a method of key expansion. A secure random sequence (the bases sequence) determines the encoding bases in a proposed scheme. Using…

In this paper we use the nonrepresentable ring E_p(m)to introduce public key cryptosystems in noncommutative settings and based on the Semigrouop Action Problem and the Decomposition Problem respectively.

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…

In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message.…

In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…

In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented. The scheme is based on encrypting several ciphertexts with the same Goppa code and adding a burst error to them. Possible attacks are…

In this paper, we define and discuss {\phi}-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key encryption schemes, one is McEliece and Niederriter's…

I present examples of mathematical objects that are of interest for public key cryptography. Text for the Journ\'ee Annuelle 2007 of the SMF.

In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in…

Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first group signature schemes based on the conjugacy problem, decomposition problem and root problem in the braid…

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…

In 1991 the first public key protocol involving automaton groups has been proposed. In this paper we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a…

We propose modifications of known quasigroup based stream ciphers. Systems of orthogonal n-ary groupoids are used.

A Sidon space is a subspace of an extension field over a base field in which the product of any two elements can be factored uniquely, up to constants. This paper proposes a new public-key cryptosystem of the multivariate type which is…

We study cryptography based on operator theory, and propose quantum no-key (QNK) protocols from the perspective of operator theory, then present a framework of QNK protocols. The framework is expressed in two forms: trace-preserving quantum…

In this paper we generalize the definition of a multilinear map to arbitrary groups and develop a novel idea of multilinear cryptosystem using nilpotent group identities.