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#Baby-Step Giant-Step

2 articles with this tag.

A visual representation of breaking Diffie-Hellman via baby-step giant-step
Modern & Applied Cryptography Breakers Intermediate

Breaking Diffie-Hellman with Baby-Step Giant-Step

Diffie-Hellman's security rests on the discrete logarithm problem being hard. For a small prime, it isn't. Baby-step giant-step trades a brute-force search of size p for one of roughly √p, and that's the whole reason real DH needs huge safe primes.

11 min read

A visual representation of breaking ElGamal via the discrete logarithm
Modern & Applied Cryptography Breakers Intermediate

Breaking ElGamal with Baby-Step Giant-Step

ElGamal's private key is just another discrete logarithm. The same baby-step giant-step technique that breaks Diffie-Hellman over a small prime recovers ElGamal's private key too, and from there decrypts any captured ciphertext directly.

11 min read

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