Public key exponent attacks on multi-prime power modulus using continued fraction expansion method

This paper proposes three public key exponent attacks of breaking the security of the prime power modulus =22 where and are distinct prime numbers of the same bit size. The first approach shows that the RSA prime power modulus =22 for q<<2q using key equation −()=1 where ()= 22(−1)(−1) can be broken by recovering the secret keys  / from the convergents of the continued fraction expansion of e/−23/4 +1/2 . The paper also reports the second and third approaches of factoring multi-prime power moduli =2 2 simultaneously through exploiting generalized system of equations −()=1 and −()=1 respectively. This can be achieved in polynomial time through utilizing Lenstra Lenstra Lovasz (LLL) algorithm and simultaneous Diophantine approximations method for =1,2,…,

Quadratic compact knapsack public-key cryptosystem

AbstractKnapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. In this paper, additive knapsack-type public-key cryptography is reconsidered. We propose a knapsack-type public-key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low-density subset-sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack

A cryptanalytic attack on the LUC cryptosystem using continued fractions

The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences. In this paper we extend the Verheul - van Tilborg and Dujella variants of the Wiener attack on RSA to the LUC cryptosystem. We describe an algorithm for finding a secret key $d$ of the form $d = r q_{m+1} pm s q_m$, for some $mgeq -1$ and nonnegative integers $r$ and $s$, using continued fractions. We derive bounds for $r$ and $s$ using results on Diophantine approximations

New vulnerability of RSA modulus type N = p2q

This paper proposes new attacks on modulus of type N = p2q. Given k moduli of the form Ni = p2iqi for k ≥ 2 and i = 1, …, k, the attack works when k public keys (Ni, ei) are such that there exist k relations of the shape eix – Niyi = zi – (ap2i + bq2i)yi or of the shape eixi – Niy = zi – (ap2i + bq2i)y where the parameters x, xi, y, yi and zi are suitably small in terms of the prime factors of the moduli. The proposed attacks utilizing the LLL algorithm enables one to factor the k moduli Ni simultaneously