Tag
6 articles with this tag.
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 low public exponent like e=3 is efficient and, by itself, still safe. Broadcast the same message to three recipients using e=3 with no padding, and the Chinese Remainder Theorem recovers it with no private key at all.
10 min read
Sharing one RSA modulus across multiple key pairs looks like a harmless shortcut: skip prime generation, reuse n. If the same message ever gets encrypted under two of those keys, no private key is needed to read it back.
13 min read
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
Small private exponents make RSA decryption and signing faster. Michael Wiener showed in 1990 that a d small enough to help performance is also small enough to recover from the public key alone, via continued fractions.
12 min read
RSA made public-key cryptography practical for the world. Here's how it works, why it's secure, and where it's headed as quantum computing looms.
18 min read
