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Re:How is NSA breaking so much crypto? (2015) by cesarb on Saturday December 17, 2016 @12:25PM (#13201473)
Well, curve25519 uses 256-bit keys (actually, a few bits less than 256). The parallel brute force search should take time similar to that of a 256-bit symmetric cipher.

The reason curve25519 has a security level of only 128 bits is that ECDLP takes time proportional to the square root, so half the number of bits (https://en.wikipedia.org/wiki/Elliptic_curve_cryptography#Ke...).

As for poly1305, it actually uses not one, but two separate 128-bit keys. The authentication tag computed using the first key is encrypted with the second key. For a brute force search, it should be as hard as breaking something with a single key of around 256 bits.

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