Abstract. We introduce a new deterministic factoring algorithm, which could be described in the fashionable term of “factoring with hints”: we show that, given the knowledge of the factorisations of O(N) terms following N = pq product of two large primes, we can recover deterministically p and q in O(N) bit operations. Although this is slower than the current best factoring algorithms, this met...

Public key cryptography has been invented to overcome some key management problems in open networks. Although nearly all aspects of public key cryptography rely on the existence of trapdoor one-way functions, only a very few candidates of this primitive have been observed yet. In this paper, we introduce a new trapdoor one-way permutation based on the hardness of factoring integers of pq-type. ...

Let (X,S) be an association scheme where X is a finite set and S is a partition of X × X. The size of X is called the order of (X,S). We define C to be the set of positive integers m such that each association scheme of order m is commutative. It is known that each prime is belonged to C and it is conjectured that each prime square is belonged to C. In this article we give a sufficient conditio...

Recall that R denotes the set of real numbers, which contains zero and also all positive or negative decimal expansions. The rational numbers, defined as Q = { pq : p, q integers, q = 0}, have repeating decimal expansions (including the terminating decimals, where 0 repeats). So, Q is a subset of R, but the two sets are definitely not equal. √ 2, π, and e are all examples of “irrationals,” real...

In this paper, we consider an RSA modulus N = pq, where the prime factors p, q are of the same size. We present an attack on RSA when the decryption exponent d is in the form d = Md1 + d0 where M is a given positive integer and d1 and d0 are two suitably small unknown integers. In 1999, Boneh and Durfee presented an attack on RSA when d < N. When d = Md1 + d0, our attack enables one to overcome...

Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in Zm, where Zm is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O((pq)...

Public key cryptography has been invented to overcome some key management problems in open networks. Although nearly all aspects of public key cryptography rely on the existence of trapdoor one-way functions, only a very few candidates of this primitive have been observed yet. In this paper, we introduce a new trapdoor one-way permutation based on the hardness of factoring integers of pq-type. ...

Let Γ be a graph with vertex set V, and let b nonnegative integers. A subset C of V is called an (a,b)-regular in if every has exactly neighbors V∖C C. In particular, (0,1)-regular sets (1,1)-regular are perfect codes total Γ, respectively. group G said to there exists Cayley which admits as set. this paper we prove that, for any generalized dihedral or order 4p pq some primes p q, nontrivial s...

A bstract We show that the strong CP problem is solved in a large class of compactifications string theory. The Peccei-Quinn mechanism solves if CP-breaking effects ultraviolet completion gravity and QCD are small compared to CP-preserving axion potential generated by low-energy instantons. characterize both classes effects. To understand quantum gravitational effects, we consider an ensemble f...

results the results reveal that pq can decrease mitochondrial viability, deplete gsh content, increase mitochondrial ros formation, and enhance lpo and mitochondrial membrane damage. the pretreatment of mitochondria with ng has the ability to reduce the toxic effects of pq in isolated mitochondria. background paraquat (pq) is a dipyridyl herbicide that sustains damage due to redox cycling. an i...