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Save a multiplication on X25519 ladder step over G

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Miguel Oliveira 2022-03-24 18:17:07 -03:00
parent c180d31001
commit 4491ac4029
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GPG key ID: 2C2BE789E1377025
1 changed files with 8 additions and 9 deletions
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17
x25519.lua
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@ -20,8 +20,7 @@ local function double(x1, z1)
return x3, z3 return x3, z3
end end
-- TODO We can save a multiplication when stepping over G, since dx = 9. local function step(dxmul, dx, x1, z1, x2, z2)
local function step(dx, x1, z1, x2, z2)
local a = fp.add(x1, z1) local a = fp.add(x1, z1)
local aa = fp.square(a) local aa = fp.square(a)
local b = fp.sub(x1, z1) local b = fp.sub(x1, z1)
@ -32,7 +31,7 @@ local function step(dx, x1, z1, x2, z2)
local da = fp.mul(d, a) local da = fp.mul(d, a)
local cb = fp.mul(c, b) local cb = fp.mul(c, b)
local x4 = fp.square(fp.add(da, cb)) local x4 = fp.square(fp.add(da, cb))
local z4 = fp.mul(dx, fp.square(fp.sub(da, cb))) local z4 = dxmul(fp.square(fp.sub(da, cb)), dx)
local x3 = fp.mul(aa, bb) local x3 = fp.mul(aa, bb)
local z3 = fp.mul(e, fp.add(bb, fp.kmul(e, 121666))) local z3 = fp.mul(e, fp.add(bb, fp.kmul(e, 121666)))
return x3, z3, x4, z4 return x3, z3, x4, z4
@ -59,19 +58,19 @@ local function bits(str)
return {unpack(out, 4)} return {unpack(out, 4)}
end end
local function ladder8(dx, bits) local function ladder8(dxmul, dx, bits)
local x1 = fp.num(1) local x1 = fp.num(1)
local z1 = fp.num(0) local z1 = fp.num(0)
local z2 = fp.decode(random.random(32)) local z2 = fp.decode(random.random(32))
local x2 = fp.mul(dx, z2) local x2 = dxmul(z2, dx)
-- Standard ladder. -- Standard ladder.
for i = #bits, 1, -1 do for i = #bits, 1, -1 do
if bits[i] == 0 then if bits[i] == 0 then
x1, z1, x2, z2 = step(dx, x1, z1, x2, z2) x1, z1, x2, z2 = step(dxmul, dx, x1, z1, x2, z2)
else else
x2, z2, x1, z1 = step(dx, x2, z2, x1, z1) x2, z2, x1, z1 = step(dxmul, dx, x2, z2, x1, z1)
end end
end end
@ -93,7 +92,7 @@ local mod = {}
function mod.publicKey(sk) function mod.publicKey(sk)
expect(1, sk, "string") expect(1, sk, "string")
assert(#sk == 32, "secret key length must be 32") assert(#sk == 32, "secret key length must be 32")
return fp.encode(ladder8(fp.num(9), bits(sk))) return fp.encode(ladder8(fp.kmul, 9, bits(sk)))
end end
--- Performs the key exchange. --- Performs the key exchange.
@ -107,7 +106,7 @@ function mod.exchange(sk, pk)
assert(#sk == 32, "secret key length must be 32") assert(#sk == 32, "secret key length must be 32")
expect(2, pk, "string") expect(2, pk, "string")
assert(#pk == 32, "public key length must be 32") assert(#pk == 32, "public key length must be 32")
return fp.encode(ladder8(fp.decode(pk), bits(sk))) return fp.encode(ladder8(fp.mul, fp.decode(pk), bits(sk)))
end end
return mod return mod