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#Key Generation

2 articles with this tag.

A visual representation of a batch GCD finding a shared prime between two RSA moduli and factoring both
Modern & Applied Cryptography Breakers Advanced

Breaking RSA with Weak Keys: Shared Primes and Pollard's p-1

RSA is unbreakable only when its primes are chosen well. If two keys share a prime, one GCD factors both in microseconds, and if a prime p has a smooth p-1, Pollard's method factors it without any search. This guide runs both real attacks against real 1024-bit keys and recovers the private keys.

11 min read

A visual representation of breaking RSA via Fermat factorization
Modern & Applied Cryptography Breakers Intermediate

Breaking RSA with Fermat Factorization

RSA's security assumes factoring n back into p and q is infeasible. That assumption quietly breaks if the key generator picks p and q too close together. Fermat's 1643 factoring method recovers them both in seconds.

13 min read

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