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Crypto to break

CTR mode with small counter: either huge nonce or small block size

Old SSLv2 machine, MITM the handshake, brute force the key

BEAST/CRIME attack based on compression

RSA without padding + weak public exponent, message sent to multiple people

DSA with reused k

Totally bogus: always uses same k

Kinda bogus: poor PRNG

Backdoor your own version of Dual_EC_DRBG

PRNG based on timeofday, maybe pid, other shitty entropy sources