New Jochemsz–May Cryptanalytic Bound for RSA System Utilizing Common Modulus N = p2q

Revisiting Fermat's Factorization for the RSA Modulus

We revisit Fermat’s factorization method for a positive integer n that is a product of two primes p and q. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of RSA relies on the hardness of factoring this modulus. As a consequence of our analysis, two variants of Fermat’s approach emerge. We also present a comparison betwee...

Improved Factoring of RSA Modulus

In 1999, the 512-bit number of 155 digits taken from the RSA Challenge list was first factored by the General Number Field Sieve. This work was done on a supercomputer and about 300 PCs or workstations by 17 experts all over the world. The calendar time for the factorization was over 6 months. Based on the open source GGNFS, we improved its algorithms and implementations. Now the 512-bit RSA mo...

Small secret exponent attack on RSA variant with modulus N=prq

We consider an RSA variant with Modulus N = p2q. This variant is known as Prime Power RSA. In PKC 2004 May proved when decryption exponent d < N0.22, one can factor N in polynomial time. In this paper, we improve this bound upto N0.395. We provide detailed experimental results to justify our claim.

Simple Backdoors on RSA Modulus by Using RSA Vulnerability

This investigation proposes two methods for embedding backdoors in the RSA modulus N = pq rather than in the public exponent e. This strategy not only permits manufacturers to embed backdoors in an RSA system, but also allows users to choose any desired public exponent, such as e = 216 +1, to ensure efficient encryption. This work utilizes lattice attack and exhaustive attack to embed backdoors...

A Further Weakness in the Common Modulus Protocol for the RSA Cryptoalgorithm