mirror of
https://github.com/ipxe/ipxe
synced 2025-12-08 02:10:25 +03:00
be9ce49076
The NIST elliptic curves are Weierstrass curves and have the form y^2 = x^3 + ax + b with each curve defined by its field prime, the constants "a" and "b", and a generator base point. Implement a constant-time algorithm for point addition, based upon Algorithm 1 from "Complete addition formulas for prime order elliptic curves" (Joost Renes, Craig Costello, and Lejla Batina), and use this as a Montgomery ladder commutative operation to perform constant-time point multiplication. The code for point addition is implemented using a custom bytecode interpreter with 16-bit instructions, since this results in substantially smaller code than compiling the somewhat lengthy sequence of arithmetic operations directly. Values are calculated modulo small multiples of the field prime in order to allow for the use of relaxed Montgomery reduction. Signed-off-by: Michael Brown <mcb30@ipxe.org>
iPXE README File Quick start guide: cd src make For any more detailed instructions, see http://ipxe.org