An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.Comment: 18 pages, 1 figur

New attacks on RSA with Moduli N = p^r q

International audienceWe present three attacks on the Prime Power RSA with mod-ulus N = p^r q. In the first attack, we consider a public exponent e satisfying an equation ex − φ(N)y = z where φ(N) = p^(r−1 )(p − 1)(q − 1). We show that one can factor N if the parameters |x| and |z| satisfy |xz| < N r(r−1) (r+1)/ 2 thereby extending the recent results of Sakar [16]. In the second attack, we consider two public exponents e1 and e2 and their corresponding private exponents d1 and d2. We show that one can factor N when d1 and d2 share a suitable amount of their most significant bits, that is |d1 − d2| < N r(r−1) (r+1) /2. The third attack enables us to factor two Prime Power RSA moduli N1 = p1^r q1 and N2 = p2^r q2 when p1 and p2 share a suitable amount of their most significant bits, namely, |p1 − p2| < p1/(2rq1 q2)

EVALUATION OF CRYPTOGRAPHIC ALGORITHMS

This article represents a synthesis of the evaluation methods for cryptographic algorithms and of their efficiency within practical applications. It approaches also the main operations carried out in cryptanalysis and the main categories and methods of attack in order to clarify the differences between evaluation concept and crypto algorithm cracking.cryptology, cryptanalysis, evaluation and cracking cryptographic algorithms

On Deterministic Polynomial-time Equivalence of Computing the CRT-RSA Secret Keys and Factoring

Let N = pq be the product of two large primes. Consider Chinese remainder theorem-Rivest, Shamir, Adleman (CRT-RSA) with the public encryption exponent e and private decryption exponents dp, dq. It is well known that given any one of dp or dq (or both) one can factorise N in probabilistic poly(log N) time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice-based deterministic poly(log N) time algorithm that uses both dp, dq (in addition to the public information e, N) to factorise N for certain ranges of dp, dq. We like to stress that proving the equivalence for all the values of dp, dq may be a nontrivial task.Defence Science Journal, 2012, 62(2), pp.122-126, DOI:http://dx.doi.org/10.14429/dsj.62.171

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

Authentication system for e-certificate by using RSA’s digital signature

Online learning and teaching become the popular channel for all participants, because they can access the courses everywhere with the high-speed internet. E-certificate is being prepared for everyone who has participated or passed the requirements of the courses. Because of many benefits frome-certificate, it may become the demand for intruders to counterfeit the certificate. In this paper, Rivest-Shamir-Adleman (RSA)’s digital signature is chosen to signe-certificate in order to avoid being counterfeited by intruders. There are two applications to managee-certificate. The first application is the signing application to sign the sub image including only participant’s name in e-certificate. In general, the file of digital signature is divided frome-certificate. That means, both of them must be selected to compare each other in checking application. In fact, the solution will be approved when each pixel of participant’s name is equal to each part from the decrypted message at the same position. In experimental session, 40 e-certificatesare chosen for the implementation. The results reveal that the accuracy is 100% and both of signing and checking processes are completed rapidly fast, especially when signing application is applied with Chinese remainder theorem (CRT) or the special technique of CRT. Therefore, the proposed method is one of the best solutions to protect e-certificate from the forgery by intruders