查看更多>>摘要：Arithmetic congruences are derived for the exponents of composite Merserute numbers. It is known that the 2(p)-1 is composite if p is a Sophie Germain prime which is congruent to 3 modulo 4. After verifying the equality of estimates of the density of these primes through refined sieve and proabablistic methods, a set of the arithmetic sequences for the exponents are listed. The coefficients in these sequences generally have a nontrivial common factor, and a shift in the number of doubling cycles for a given number of partitions is found to yield divisible Mersenne numbers. Several sequences with relatively prime coefficients have terms that are congruent to 3 modulo 4. Furthermore, a linear recursion relation for the exponents would have a non-zero density of solutions representing positive integers in the natural numbers by the Skolem-Mahler-Lech theorem, thereby predicting the infinite extent of the prime exponents of composite Mersenne numbers of this kind and the Sophie Germain primes.
Borges-Trenard, Miguel A.Borges-Quintana, MijailMonier-Columbie, Lazaro
10页
查看更多>>摘要：The genetic algorithm has been used in cryptanalysis. In this paper, we present a general attack to block ciphers by using this algorithm. This method considers the cipher as a black box and it is a known plaintext attack, whose objective is to find the key session. The crucial point of our approach is to make a partition of the key space into subsets determined by the division by a certain divisor, so that one can focus the attack in only some of these subsets. We show how this method can be successfully applied to a member of a block cipher family that contains the AES cipher.
查看更多>>摘要：The security of the Bitcoin cryptocurrency system depends on the Koblitz curve secp256k1 combined with the digital signature ECDSA and the hash function SHA-256. In this paper, we show that the security of Bitcoin with ECDSA and secp256k1 is not optimal and present a detailed study of the efficiency of Bitcoin with the digital signature algorithm Ed25519 combined with the twisted Edwards curve CurveEd25519 and the hash function SHA-512. We show that Bitcoin is more secure and more efficient with the digital signature algorithm Ed25519 and the twisted Edwards curve CurveEd2551.
查看更多>>摘要：We examine the p-ary linear codes from incidence matrix of the (n, k)-arrangement graphs for k = 2, n -2, n - 1. All the main parameters of the codes are obtained as [n(n - 1)(n - 2), n(n -1), 2(n - 2)](p), [n!/2(n - 2), n!, 2(n - 2)](p), [n!/2(n - 1), n!-1, n-1](p) respectively. We examine also the p-any linear codes from incidence matrix of graphs such as Ljubljana graph, Heawood graph and the main parameters of the codes are [168, 111, 3](p'), [21, 13, 3](p) respectively. Any transitive subgroup of automorphism groups of these graphs can be used for full permutation decoding using the corresponding codes. All the above codes can be used for full error correction by permutation decoding.
查看更多>>摘要：Let C be a code with parity-check matrix H. A stopping set S of size l <= n for H is an l-columns submatrix of H-s of H which dose not contain a row with weight one. In this paper we consider the code which parity-check matrix is incidence matrix of complete graph K-m. These codes are LDPC codes and we obtain the stopping sets for these codes.
查看更多>>摘要：In this paper, we first introduce a new class of an HV-K-algebra as a generalization of a BCK-algebra and investigate some of its properties. How can we make an HK-K-algebra? In order to answer this question, we apply the "Ends Lemma" technique on a BCK-algebra and construct the HV-K-algebra (namely an EL-K-algebra) and investigate it.
查看更多>>摘要：Let G and H be two graphs. An H-packing (resp. decomposition) of G is a family of subgraphs of G such that each edge of G belongs to at most (resp. exactly) one of the subgraphs and all subgraphs are isomorphic to H. An H-factorization of G is an H-decomposition of G if H is a factor of G. An H-packing (resp. decomposition) of G, say B, is called a (d, H)-packing (resp. decomposition) if there exists a bijection f from V(G)UE(G) onto {1,2,center dot center dot center dot,vertical bar V(G)UE(G)vertical bar} such that {w(B)vertical bar B is an element of B} = {a ,a + d,center dot center dot center dot,a +(b -1)d) , where w(B) is the sum of all vertex and edge labels on B (under f) and b = vertical bar B vertical bar. A (0, H)- and a (1, H)-packing (resp. decomposition) are said to an H-magic and an H-consecutive antimagic packing (resp. decomposition), respectively. The goal of this paper is to study an H-magic and an H-consecutive antimagic packing (resp. decomposition) of some regular graphs where H is a factor of the regular graph.
查看更多>>摘要：The complete graph K-n, for n even, has a one-factorization (proper edge coloring) with n - 1 colors. In the recent contribution [Dotan M., Linial N. (2017). ArXiv:1707.00477v2], the authors raised a conjecture on the convergence of the mild random walk on the Markov chain whose nodes are the colorings of K-n. The mild random walk consists in moving from a coloring C to a recoloring C' if and only if phi(C') <= phi(C), where phi is the potential function that takes its minimum at one-factorizations. We show the validity of such algorithm with several numerical experiments that demonstrate convergence in all cases (not just asymptotically) with polynomial cost. We prove several results on the mild random walk, we study deeply the properties of local minimum colorings, we give a detailed proof of the convergence of the algorithm for K-4 and K-6, and we raise new conjectures. We also present an alternative to the potential measure phi by consider the Shannon entropy, which has a strong parallelism with phi from the numerical standpoint.
查看更多>>摘要：We introduce in this paper the algorithmic aspect of elliptic curves together with their applications. We also recall one of the promising application in the field of zero knowledge proofs with concrete implementations.
NSTL
Taylor & Francis
Taru Publications