On a generalization of Shannon's random cipher result
On another two cryptographic identities in universal Osborn loops.
On Certain Approaches for Analysis and Design of Cryptographic Techniques
On cheating immune secret sharing.
On Distributed Oblivious Transfer
The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002This paper is about unconditionally secure distributed protocols for oblivious transfer, as proposed by Naor and Pinkas and generalized by Blundo et al. In this setting a Sender has ζ secrets and a Receiver is interested in one of them. The Sender distributes the...
On distribution functions of sequences generated by scalar and mixed product
On Graph-Based Cryptography and Symbolic Computations
We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large...
On linguistic dynamical systems, families of graphs of large girth, and cryptography.
On middle universal weak and cross inverse property loops with equal length of inverse cycles.
On minimal factorisations of sporadic groups.
On minimal length factorizations of finite groups.
On minimal logarithmic signatures of finite groups.
On Proactive Verifiable Secret Sharing Schemes
The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player's shares and we present two types of...
On real quadratic number fields suitable for cryptography.
On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...
On the invertibility of finite linear transducers
Linear finite transducers underlie a series of schemes for Public Key Cryptography (PKC) proposed in the 90s of the last century. The uninspiring and arid language then used, condemned these works to oblivion. Although some of these schemes were afterwards shown to be insecure, the promise of a new system of PKC relying on different complexity assumptions is still quite exciting. The algorithms there used depend heavily on the results of invertibility of linear transducers. In this paper we introduce...
On the joint 2-adic complexity of binary multisequences
Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences with given joint 2-adic complexity.
On the joint 2-adic complexity of binary multisequences∗
Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences...
Operations of Points on Elliptic Curve in Projective Coordinates
In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...