Add Ed25519
This commit is contained in:
Miguel Oliveira
parent
03c2db100f
commit
43a58ebd5e
294
ed25519.lua
Normal file
294
ed25519.lua
Normal file
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@ -0,0 +1,294 @@
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--- The Ed25519 signature scheme.
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--
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-- @module ed25519
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--
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local expect = require "cc.expect".expect
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local fp = require "ccryptolib.fp"
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local fq = require "ccryptolib.fq"
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local sha512 = require "ccryptolib.sha512"
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local random = require "ccryptolib.random"
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local util = require "ccryptolib.util"
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local unpack = unpack or table.unpack
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local D = fp.mul(fp.num(-121665), fp.invert(fp.num(121666)))
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local K = fp.kmul(D, 2)
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local O = {fp.num(0), fp.num(1), fp.num(1), fp.num(0)}
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local G = nil
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local function double(P1)
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local P1x, P1y, P1z = unpack(P1)
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local a = fp.square(P1x)
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local b = fp.square(P1y)
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local c = fp.square(P1z)
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local d = fp.kmul(c, 2)
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local e = fp.add(a, b)
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local f = fp.add(P1x, P1y)
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local g = fp.square(f)
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local h = fp.sub(g, e)
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local i = fp.sub(b, a)
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local j = fp.sub(d, i)
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local P3x = fp.mul(h, j)
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local P3y = fp.mul(i, e)
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local P3z = fp.mul(j, i)
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local P3t = fp.mul(h, e)
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return {P3x, P3y, P3z, P3t}
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end
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local function add(P1, N1)
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local P1x, P1y, P1z, P1t = unpack(P1)
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local N1p, N1m, N1z, N1t = unpack(N1)
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local a = fp.sub(P1y, P1x)
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local b = fp.mul(a, N1m)
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local c = fp.add(P1y, P1x)
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local d = fp.mul(c, N1p)
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local e = fp.mul(P1t, N1t)
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local f = fp.mul(P1z, N1z)
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local g = fp.sub(d, b)
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local h = fp.sub(f, e)
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local i = fp.add(f, e)
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local j = fp.add(d, b)
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local P3x = fp.mul(g, h)
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local P3y = fp.mul(i, j)
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local P3z = fp.mul(h, i)
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local P3t = fp.mul(g, j)
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return {P3x, P3y, P3z, P3t}
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end
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local function sub(P1, N1)
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local P1x, P1y, P1z, P1t = unpack(P1)
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local N1p, N1m, N1z, N1t = unpack(N1)
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local a = fp.sub(P1y, P1x)
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local b = fp.mul(a, N1p)
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local c = fp.add(P1y, P1x)
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local d = fp.mul(c, N1m)
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local e = fp.mul(P1t, N1t)
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local f = fp.mul(P1z, N1z)
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local g = fp.sub(d, b)
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local h = fp.add(f, e)
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local i = fp.sub(f, e)
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local j = fp.add(d, b)
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local P3x = fp.mul(g, h)
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local P3y = fp.mul(i, j)
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local P3z = fp.mul(h, i)
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local P3t = fp.mul(g, j)
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return {P3x, P3y, P3z, P3t}
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end
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local function niels(P1)
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local P1x, P1y, P1z, P1t = unpack(P1)
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local N3p = fp.add(P1y, P1x)
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local N3m = fp.sub(P1y, P1x)
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local N3z = fp.add(P1z, P1z)
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local N3t = fp.mul(P1t, K)
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return {N3p, N3m, N3z, N3t}
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end
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local function scale(P1)
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local P1x, P1y, P1z = unpack(P1)
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local zInv = fp.invert(P1z)
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local P3x = fp.mul(P1x, zInv)
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local P3y = fp.mul(P1y, zInv)
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local P3z = fp.num(1)
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local P3t = fp.mul(P3x, P3y)
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return {P3x, P3y, P3z, P3t}
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end
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local function encode(P1)
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local P1x, P1y = unpack(P1)
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local y = fp.encode(P1y)
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local xBit = fp.canonicalize(P1x)[1] % 2
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return y:sub(1, -2) .. string.char(y:byte(-1) + xBit * 128)
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end
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local function decode(str)
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local P3y = fp.decode(str)
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local a = fp.square(P3y)
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local b = fp.sub(a, fp.num(1))
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local c = fp.mul(a, D)
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local d = fp.add(c, fp.num(1))
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local P3x = fp.sqrtDiv(b, d)
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if not P3x then return nil end
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local xBit = fp.canonicalize(P3x)[1] % 2
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if xBit ~= bit32.extract(str:byte(-1), 7) then
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P3x = fp.neg(P3x)
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P3x = fp.carry(P3x)
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end
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local P3z = fp.num(1)
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local P3t = fp.mul(P3x, P3y)
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return {P3x, P3y, P3z, P3t}
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end
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G = decode("Xfffffffffffffffffffffffffffffff")
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local function signedRadixW(bits, w)
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-- TODO Find a more elegant way of doing this.
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local wPow = 2 ^ w
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local wPowh = wPow / 2
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local out = {}
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local acc = 0
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local mul = 1
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for i = 1, #bits do
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acc = acc + bits[i] * mul
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mul = mul * 2
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while i == #bits and acc > 0 or mul > wPow do
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local rem = acc % wPow
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if rem >= wPowh then rem = rem - wPow end
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acc = (acc - rem) / wPow
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mul = mul / wPow
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out[#out + 1] = rem
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end
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end
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return out
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end
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local function radixWTable(P, w)
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local out = {}
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for i = 1, 255 / w do
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local row = {niels(P)}
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for j = 2, 2 ^ w / 2 do
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P = add(P, row[1])
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row[j] = niels(P)
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end
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out[i] = row
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P = double(P)
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end
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return out
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end
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local G_W = 5
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local G_TABLE = radixWTable(G, G_W)
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local function WNAF(bits, w)
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-- TODO Find a more elegant way of doing this.
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local wPow = 2 ^ w
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local wPowh = wPow / 2
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local out = {}
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local acc = 0
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local mul = 1
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for i = 1, #bits do
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acc = acc + bits[i] * mul
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mul = mul * 2
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while i == #bits and acc > 0 or mul > wPow do
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if acc % 2 == 0 then
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acc = acc / 2
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mul = mul / 2
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out[#out + 1] = 0
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else
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local rem = acc % wPow
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if rem >= wPowh then rem = rem - wPow end
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acc = acc - rem
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out[#out + 1] = rem
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end
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end
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end
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while out[#out] == 0 do out[#out] = nil end
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return out
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end
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local function WNAFTable(P, w)
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local dP = double(P)
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local out = {niels(P)}
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for i = 3, 2 ^ w, 2 do
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out[i] = niels(add(dP, out[i - 2]))
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end
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return out
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end
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local function mulG(bits)
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local sw = signedRadixW(bits, G_W)
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local R = O
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for i = 1, #sw do
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local b = sw[i]
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if b > 0 then
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R = add(R, G_TABLE[i][b])
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elseif b < 0 then
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R = sub(R, G_TABLE[i][-b])
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end
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end
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return R
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end
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local function mul(P, bits)
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local naf = WNAF(bits, 5)
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local tbl = WNAFTable(P, 5)
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local R = O
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for i = #naf, 1, -1 do
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local b = naf[i]
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if b == 0 then
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R = double(R)
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elseif b > 0 then
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R = add(R, tbl[b])
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else
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R = sub(R, tbl[-b])
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end
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end
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return R
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end
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local function publicKey(sk)
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expect(1, sk, "string")
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assert(#sk == 32, "secret key length must be 32")
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-- FIXME SHA512 isn't constant-time.
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local h = sha512.digest(sk):sub(1, 32)
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local kBits, xkInvBits = blinding.decodeBlinded(h)
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local Y0 = mulG(xkInvBits)
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local Y1 = mul(Y0, kBits)
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return encode(scale(Y1))
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end
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local function sign(sk, pk, msg)
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expect(1, sk, "string")
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assert(#sk == 32, "secret key length must be 32")
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expect(2, pk, "string")
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assert(#pk == 32, "public key length must be 32")
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expect(3, msg, "string")
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-- Decode cwords and clamp with a mask.
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local h = sha512.digest(sk):sub(1, 32)
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local xm, m = fq.maskedDecode(h, random.random(32))
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-- Commitment.
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local k = fq.decodeWide(random.random(64))
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local kBits = fq.bits(k)
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local R = mulG(kBits)
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-- Challenge.
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local rStr = encode(scale(R))
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local e = fq.decodeWide(sha512.digest(rStr .. pk .. msg))
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-- Response.
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local exm = fq.mul(e, xm)
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local em = fq.mul(e, m)
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local s = fq.add(fq.sub(k, exm), em)
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local sStr = fq.encode(s)
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return rStr .. sStr
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end
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local function verify(pk, msg, sig)
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expect(1, pk, "string")
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assert(#pk == 32, "public key length must be 32")
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expect(2, msg, "string")
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expect(3, sig, "string")
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assert(#sig == 64, "public key length must be 32")
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local rStr = sig:sub(1, 32)
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local sStr = sig:sub(33)
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local Y = decode(pk)
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local ev = fq.decodeWide(sha512.digest(rStr .. pk .. msg))
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local evBits = fq.bits(ev)
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local sBits = util.rebaseLE({sStr:byte(1, -1)}, 256, 2)
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local Rv = add(mulG(sBits), mul(Y, evBits))
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return encode(scale(Rv)) == rStr
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end
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return {
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publicKey = publicKey,
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sign = sign,
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verify = verify,
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}
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176
sha512.lua
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176
sha512.lua
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@ -0,0 +1,176 @@
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--- The SHA512 cryptographic hash function.
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--
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-- @module sha512
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--
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local expect = require "cc.expect".expect
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local shl = bit32.lshift
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local shr = bit32.rshift
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local bxor = bit32.bxor
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local bnot = bit32.bnot
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local band = bit32.band
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local function carry64(a1, a0)
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local r0 = a0 % 2 ^ 32
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a1 = a1 + (a0 - r0) / 2 ^ 32
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return a1 % 2 ^ 32, r0
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end
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local K = {
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0x428a2f98, 0xd728ae22, 0x71374491, 0x23ef65cd, 0xb5c0fbcf, 0xec4d3b2f,
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0xe9b5dba5, 0x8189dbbc, 0x3956c25b, 0xf348b538, 0x59f111f1, 0xb605d019,
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0x923f82a4, 0xaf194f9b, 0xab1c5ed5, 0xda6d8118, 0xd807aa98, 0xa3030242,
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0x12835b01, 0x45706fbe, 0x243185be, 0x4ee4b28c, 0x550c7dc3, 0xd5ffb4e2,
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0x72be5d74, 0xf27b896f, 0x80deb1fe, 0x3b1696b1, 0x9bdc06a7, 0x25c71235,
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0xc19bf174, 0xcf692694, 0xe49b69c1, 0x9ef14ad2, 0xefbe4786, 0x384f25e3,
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0x0fc19dc6, 0x8b8cd5b5, 0x240ca1cc, 0x77ac9c65, 0x2de92c6f, 0x592b0275,
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0x4a7484aa, 0x6ea6e483, 0x5cb0a9dc, 0xbd41fbd4, 0x76f988da, 0x831153b5,
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0x983e5152, 0xee66dfab, 0xa831c66d, 0x2db43210, 0xb00327c8, 0x98fb213f,
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0xbf597fc7, 0xbeef0ee4, 0xc6e00bf3, 0x3da88fc2, 0xd5a79147, 0x930aa725,
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0x06ca6351, 0xe003826f, 0x14292967, 0x0a0e6e70, 0x27b70a85, 0x46d22ffc,
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0x2e1b2138, 0x5c26c926, 0x4d2c6dfc, 0x5ac42aed, 0x53380d13, 0x9d95b3df,
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0x650a7354, 0x8baf63de, 0x766a0abb, 0x3c77b2a8, 0x81c2c92e, 0x47edaee6,
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0x92722c85, 0x1482353b, 0xa2bfe8a1, 0x4cf10364, 0xa81a664b, 0xbc423001,
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0xc24b8b70, 0xd0f89791, 0xc76c51a3, 0x0654be30, 0xd192e819, 0xd6ef5218,
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0xd6990624, 0x5565a910, 0xf40e3585, 0x5771202a, 0x106aa070, 0x32bbd1b8,
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0x19a4c116, 0xb8d2d0c8, 0x1e376c08, 0x5141ab53, 0x2748774c, 0xdf8eeb99,
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0x34b0bcb5, 0xe19b48a8, 0x391c0cb3, 0xc5c95a63, 0x4ed8aa4a, 0xe3418acb,
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0x5b9cca4f, 0x7763e373, 0x682e6ff3, 0xd6b2b8a3, 0x748f82ee, 0x5defb2fc,
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0x78a5636f, 0x43172f60, 0x84c87814, 0xa1f0ab72, 0x8cc70208, 0x1a6439ec,
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0x90befffa, 0x23631e28, 0xa4506ceb, 0xde82bde9, 0xbef9a3f7, 0xb2c67915,
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0xc67178f2, 0xe372532b, 0xca273ece, 0xea26619c, 0xd186b8c7, 0x21c0c207,
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0xeada7dd6, 0xcde0eb1e, 0xf57d4f7f, 0xee6ed178, 0x06f067aa, 0x72176fba,
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0x0a637dc5, 0xa2c898a6, 0x113f9804, 0xbef90dae, 0x1b710b35, 0x131c471b,
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0x28db77f5, 0x23047d84, 0x32caab7b, 0x40c72493, 0x3c9ebe0a, 0x15c9bebc,
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0x431d67c4, 0x9c100d4c, 0x4cc5d4be, 0xcb3e42b6, 0x597f299c, 0xfc657e2a,
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0x5fcb6fab, 0x3ad6faec, 0x6c44198c, 0x4a475817,
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}
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--- Hashes data bytes using SHA512.
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--
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-- @tparam string data The input data.
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-- @treturn string The 64-byte hash value.
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--
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local function digest(data)
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expect(1, data, "string")
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-- Pad input.
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local bitlen = #data * 8
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local padlen = -(#data + 17) % 128
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data = data .. "\x80" .. ("\0"):rep(padlen) .. (">I16"):pack(bitlen)
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local dataWords = {(">" .. ("I4"):rep(#data / 4)):unpack(data)}
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dataWords[#dataWords] = nil
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-- Initialize state.
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local h01, h00 = 0x6a09e667, 0xf3bcc908
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local h11, h10 = 0xbb67ae85, 0x84caa73b
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local h21, h20 = 0x3c6ef372, 0xfe94f82b
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local h31, h30 = 0xa54ff53a, 0x5f1d36f1
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local h41, h40 = 0x510e527f, 0xade682d1
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local h51, h50 = 0x9b05688c, 0x2b3e6c1f
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local h61, h60 = 0x1f83d9ab, 0xfb41bd6b
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local h71, h70 = 0x5be0cd19, 0x137e2179
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-- Digest.
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local w = {}
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for i = 1, #dataWords, 32 do
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local index = i - 1
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for j = 1, 32 do
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w[j] = dataWords[index + j]
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end
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-- Message schedule.
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for j = 33, 160, 2 do
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local wf1, wf0 = w[j - 30], w[j - 29]
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local t1 = shr(wf1, 1) + shl(wf0, 31)
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local t0 = shr(wf0, 1) + shl(wf1, 31)
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local u1 = shr(wf1, 8) + shl(wf0, 24)
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local u0 = shr(wf0, 8) + shl(wf1, 24)
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local v1 = shr(wf1, 7)
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local v0 = shr(wf0, 7) + shl(wf1, 25)
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local w21, w20 = w[j - 4], w[j - 3]
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local w1 = shr(w21, 19) + shl(w20, 13)
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local w0 = shr(w20, 19) + shl(w21, 13)
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local x0 = shr(w21, 29) + shl(w20, 3)
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local x1 = shr(w20, 29) + shl(w21, 3)
|
||||
local y1 = shr(w21, 6)
|
||||
local y0 = shr(w20, 6) + shl(w21, 26)
|
||||
|
||||
local r1, r0 =
|
||||
w[j - 32] + bxor(t1, u1, v1) + w[j - 14] + bxor(w1, x1, y1),
|
||||
w[j - 31] + bxor(t0, u0, v0) + w[j - 13] + bxor(w0, x0, y0)
|
||||
|
||||
w[j], w[j + 1] = carry64(r1, r0)
|
||||
end
|
||||
|
||||
-- Block function.
|
||||
local a1, a0 = h01, h00
|
||||
local b1, b0 = h11, h10
|
||||
local c1, c0 = h21, h20
|
||||
local d1, d0 = h31, h30
|
||||
local e1, e0 = h41, h40
|
||||
local f1, f0 = h51, h50
|
||||
local g1, g0 = h61, h60
|
||||
local h1, h0 = h71, h70
|
||||
for j = 1, 160, 2 do
|
||||
local t1 = shr(e1, 14) + shl(e0, 18)
|
||||
local t0 = shr(e0, 14) + shl(e1, 18)
|
||||
local u1 = shr(e1, 18) + shl(e0, 14)
|
||||
local u0 = shr(e0, 18) + shl(e1, 14)
|
||||
local v0 = shr(e1, 9) + shl(e0, 23)
|
||||
local v1 = shr(e0, 9) + shl(e1, 23)
|
||||
local s11 = bxor(t1, u1, v1)
|
||||
local s10 = bxor(t0, u0, v0)
|
||||
|
||||
local ch1 = bxor(band(e1, f1), band(bnot(e1), g1))
|
||||
local ch0 = bxor(band(e0, f0), band(bnot(e0), g0))
|
||||
|
||||
local temp11 = h1 + s11 + ch1 + K[j] + w[j]
|
||||
local temp10 = h0 + s10 + ch0 + K[j + 1] + w[j + 1]
|
||||
|
||||
local w1 = shr(a1, 28) + shl(a0, 4)
|
||||
local w0 = shr(a0, 28) + shl(a1, 4)
|
||||
local x0 = shr(a1, 2) + shl(a0, 30)
|
||||
local x1 = shr(a0, 2) + shl(a1, 30)
|
||||
local y0 = shr(a1, 7) + shl(a0, 25)
|
||||
local y1 = shr(a0, 7) + shl(a1, 25)
|
||||
local s01 = bxor(w1, x1, y1)
|
||||
local s00 = bxor(w0, x0, y0)
|
||||
|
||||
local maj1 = bxor(band(a1, b1), band(a1, c1), band(b1, c1))
|
||||
local maj0 = bxor(band(a0, b0), band(a0, c0), band(b0, c0))
|
||||
|
||||
local temp21 = s01 + maj1
|
||||
local temp20 = s00 + maj0
|
||||
|
||||
h1 = g1 h0 = g0
|
||||
g1 = f1 g0 = f0
|
||||
f1 = e1 f0 = e0
|
||||
e1, e0 = carry64(d1 + temp11, d0 + temp10)
|
||||
d1 = c1 d0 = c0
|
||||
c1 = b1 c0 = b0
|
||||
b1 = a1 b0 = a0
|
||||
a1, a0 = carry64(temp11 + temp21, temp10 + temp20)
|
||||
end
|
||||
|
||||
h01, h00 = carry64(h01 + a1, h00 + a0)
|
||||
h11, h10 = carry64(h11 + b1, h10 + b0)
|
||||
h21, h20 = carry64(h21 + c1, h20 + c0)
|
||||
h31, h30 = carry64(h31 + d1, h30 + d0)
|
||||
h41, h40 = carry64(h41 + e1, h40 + e0)
|
||||
h51, h50 = carry64(h51 + f1, h50 + f0)
|
||||
h61, h60 = carry64(h61 + g1, h60 + g0)
|
||||
h71, h70 = carry64(h71 + h1, h70 + h0)
|
||||
end
|
||||
|
||||
return (">I4I4I4I4I4I4I4I4I4I4I4I4I4I4I4I4"):pack(
|
||||
h01, h00, h11, h10, h21, h20, h31, h30,
|
||||
h41, h40, h51, h50, h61, h60, h71, h70
|
||||
)
|
||||
end
|
||||
|
||||
return {
|
||||
digest = digest,
|
||||
}
|
||||
Loading…
Reference in a new issue