A New Idea for RSA Backdoors

Abstract

This article proposes a new method to inject backdoors in RSA (the public-key cryptosystem invented by Rivest, Shamir, and Adleman) and other cryptographic primitives based on the integer factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the semi-primes based on a large prime number, which acts as a “designer key” or “escrow key”. In particular, two different backdoors are proposed, one targeting a single semi-prime and the other one a pair of semi-primes. This article also describes the results of tests performed on a SageMath implementation of the backdoors.