libecdsautil

This will contain safe wrappers for libecdsautil-sys, yet currently only provides a representation of fastd public keys based on curve25519-dalek, as well as dalek-ff-group.

theory

private fastd: 282615cc09656f1f3dbe5fa24b640bfd48d8302f982477d38335c2ffab84c17e

derived public fastd: faebc966b4b255d9383f44fb2abc1b8b4d596ced9951a421af4df97f62aa1a7b

Public fastd keys (u8[32]~256bit) represent a point on the legacy curve. Points on Edwards25519 (as used in Ed25519) should share the same y-coordinate; the x-coordinate can be calculated using a multiplication as in ecc_25519_store_xy_legacy and ecc_25519_load_xy_legacy.

In Ed25519 public keys are stored in "Edwards y"-format, meaning the first 255 bits represent the y coordinate, while the high byte of the last byte gives the sign of x.

In libuecc public keys are stored in what could be called CompressedEdwardsX, as the x coordinate is packed alongside the least significant bit (lsb) of the y-coordinate.

Decompressed points are represented as a four tuple {X,Y,Z,T} with:

$x= {X \over Z}$

$y={Y \over Z}$

$ x*y={T \over Z} $

Each of the tuples segments is u32[32]~1024bit

-> But the last 24 are actually zeroes, while it's not within a calculation

Steps to verify:

• use libuecc to decompress a fastd public key
• load decompressed key as EdwardsPoint using rusts curve25519_dalek-crate
• implement compressX for EdwardsPoint which should emit the fastd public key again
• implement decompress for CompressedEdwardsX as opposing to he former
• then fastd keys could be loaded as CompressedEdwardsX and converted to Daleks representation and later fed into the verify-functions of libecdsautil

Left to do for compressed_points.rs

• implement EDWARDS_D

• implement sqrt_ratio_i()

• implement is_negative / is_odd

• implement conditional_negate

• upstream EDWARDS_D

• upstream sqrt_ratio_i() https://github.com/serai-dex/serai/pull/87

• upstream is_negative / is_odd

• upstream conditional_negate

• wait for next upstream release and strip downstream implementations