A new idea for RSA backdoors

TL;DR

This paper introduces novel RSA backdoor techniques leveraging mathematical congruences among semi-prime factors, enabling covert access through a large prime 'escrow key' with tested implementations.

Contribution

It presents new backdoor methods for RSA based on factor congruences and demonstrates their implementation and testing in SageMath.

Findings

Successful implementation of backdoors in RSA using congruences

Two distinct backdoor schemes targeting different semi-prime configurations

Empirical validation through SageMath tests

Abstract

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.