A new idea for RSA backdoors
This addresses security vulnerabilities in cryptography for users of RSA and similar systems, but appears incremental as it builds on existing backdoor concepts.
The paper tackles the problem of injecting backdoors into RSA and other cryptographic primitives based on integer factorization, proposing a method using mathematical congruences modulo a large prime as a designer key, with tests conducted on a SageMath implementation.
This article proposes a new method to inject backdoors in RSA 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 modulo 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. The article also describes the results of tests performed on a SageMath implementation of the backdoors.