排序方式: 共有5条查询结果,搜索用时 15 毫秒
1
1.
A conjecture of P. Erdös says that the diophantine equationx+y = z has infinitely many solutions with (x,y) = 1 and suchthat if a prime p divides xyz, then p3 divides xyz. In thispaper, we give a proof of this conjecture. 相似文献
2.
Abderrahmane Nitaj Willy Susilo Joseph Tonien 《Journal of Applied Mathematics and Computing》2017,55(1-2):293-312
Boolean functions play an important role in many symmetric cryptosystems and are crucial for their security. It is important to design boolean functions with reliable cryptographic properties such as balancedness and nonlinearity. Most of these properties are based on specific structures such as Möbius transform and Algebraic Normal Form. In this paper, we introduce the notion of Dirichlet product and use it to study the arithmetical properties of boolean functions. We show that, with the Dirichlet product, the set of boolean functions is an Abelian monoid with interesting algebraic structure. In addition, we apply the Dirichlet product to the sub-family of coincident functions and exhibit many properties satisfied by such functions. 相似文献
3.
Abderrahmane Nitaj 《计算数学(英文版)》2002,20(4):337-348
AbstractAn elliptic curve is a pair (E,O), where ?is a smooth projective curve of genus 1 and O is a point of E, called the point at infinity. Every elliptic curve can be given by a Weierstrass equationE:y2 a1xy a3y = x3 a2x2 a4x a6.Let Q be the set of rationals. E is said to be dinned over Q if the coefficients ai, i = 1,2,3,4,6 are rationals and O is defined over Q.Let E/Q be an elliptic curve and let E(Q)tors be the torsion group of points of E denned over Q. The theorem of Mazur asserts that E(Q)tors is one of the following 15 groupsE(Q)tors Z/mZ, m = 1,2,..., 10,12,Z/2Z × Z/2mZ, m = 1,2,3,4.We say that an elliptic curve E'/Q is isogenous to the elliptic curve E if there is an isogeny, i.e. a morphism : E E' such that (O) = O, where O is the point at infinity.We give an explicit model of all elliptic curves for which E(Q)tors is in the form Z/mZ where m= 9,10,12 or Z/2Z × Z/2mZ where m = 4, according to Mazur's theorem. Morever, for every family of such elliptic curves, we give an explicit m 相似文献
4.
Maher Boudabra Abderrahmane Nitaj 《Journal of Applied Mathematics and Computing》2018,57(1-2):229-245
The KMOV scheme is a public key cryptosystem based on an RSA modulus \(n=pq\) where p and q are large prime numbers with \(p\equiv q\equiv 2\pmod 3\). It uses the points of an elliptic curve with equation \(y^2\equiv x^3+b\pmod n\). In this paper, we propose a generalization of the KMOV cryptosystem with a prime power modulus of the form \(n=p^{r}q^{s}\) and study its resistance to the known attacks. 相似文献
5.
Abderrahmane Nitaj 《Journal of Applied Mathematics and Computing》2013,42(1-2):309-319
Let N=pq be an RSA modulus, i.e. the product of two large unknown primes of equal bit-size. In this paper, we describe an attack on RSA in the presence of two or three exponents e i with the same modulus N and satisfying equations e i x i ??(N)y i =z i , where ?(N)=(p?1)(q?1) and x i , y i , z i are unknown parameters. The new attack is an extension of Guo’s continued fraction attack as well as the Blömer and May lattice-reduction basis attack. 相似文献
1