Guide to Elliptic Curve CryptographyDarrel Hankerson, Alfred J. Menezes, Scott Vanstone
Guide to Elliptic Curve Cryptography
by Darrel Hankerson, Alfred J. Menezes, Scott Vanstone · first published 2004
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It is very easy to make mistakes in ECC implementation. If you really want to code it yourself, there's a book by Menezes, Vanstone et al ("Guide to Elliptic Curve Cryptography, I think) that gives very explicit instructions about how to do everything. I used to hack on a P256 implementation. But, it is a bit out of date by now, and IIRC it doesn't say anything about Curve25519.
on “An Illustrated Guide to Elliptic Curve Cryptography Validation” ↗It's very hard to get stuff right with the secp curves. That's one of the reasons for the move to curve25519 and similar. The book "Guide to Elliptic Curve Cryptography" by Hankerson, Menezes, and Vanstone is mostly very careful step by step instruction of how to do secp* arithmetic properly. It would still be useful to have some formal verification to help the assurance…
on “We found cryptography bugs in the elliptic library using Wycheproof” ↗…RSA, where the work is all in the modular exponentiation operation, which is already carefully optimized in libraries like GMP (so just call GMP and you are done). Hankerson, Menezes, and Vanstone's "Guide to Elliptic Curve Cryptography" is very helpful if you are trying to implement ECC for some reason. Most of us are probably better off using an existing implementation.
on “Implementing RSA in Python from Scratch” ↗…see Goldreich's Foundations of Cryptography volumes. They are very dense, very dry works, but packed with information. For a specific focus on elliptic curve cryptography, Menezes et al. have published Guide to Elliptic Curve Cryptography, though elliptic curves are also treated in the above two references (Hoffstein et al. and Koblitz). Still, I appreciate the focus on ECC, which is large enough to merit entire books. For a reference…
on “Mathematical Cryptology [pdf]” ↗