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4 articles with this tag.
Elliptic curve security does not come from the size of the field. It comes from one number: the largest prime factor of the group order. When that order is smooth, Pohlig-Hellman splits the discrete log into tiny subgroups and solves it in a flash. This guide runs the real attack on a toy curve and recovers the private key.
13 min read
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
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
DSA was the U.S. government's answer to a simple question: how do you prove a message came from you, without RSA's patent? Learn how the Digital Signature Algorithm works, and why a single reused number sank Sony's PS3 security.
9 min read
