Mathematical Attacks on RSA Cryptosystem

Mathematical Attacks on RSA Cryptosystem

In this paper some of the most common attacks against Rivest, Shamir, and Adleman (RSA) cryptosystem are presented. We describe the integer factoring attacks, attacks on the underlying mathematical function, as well as attacks that exploit details in implementations of the algorithm. Algorithms for each type of attacks are developed and analyzed by their complexity, memory requirements and area...

Attacks On the RSA Cryptosystem

New Attacks on the RSA Cryptosystem

This paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix−yiφ(Ni) = zi or of the shape eixi − yφ(Ni) = zi where Ni = piqi, φ(Ni) = (pi − 1)(qi − 1) and the parameters x, xi, y, yi, zi are suitably small in terms of the prime factors of the moduli. We show that our attacks enabl...

Some Insightful Attacks on the RSA Cryptosystem

RSA has come to play a central role in electronic communications. As the first example of what is known as a public key cryptosystem, and the only one that has stood the test of nearly 30 years of attacks, RSA has become the algorithm of choice for encrypting Internet credit-card transactions, securing email, and authenticating phone calls. Like all practical cryptographic schemes, however, RSA...

The Mathematical Cryptography of the RSA Cryptosystem

Invented in 1977 by Rivest, Shamir and Adleman, the RSA cryptosystem has played a very important role in the development of modern cryptography. Its various applications in industry, Internet, banking, online shopping, cell phones, smart cards, secure information transfers and electronic signatures have made RSA a standard at the heart of modern technologies. This chapter explores the mathemati...