126 lines
2.9 KiB
Lua
126 lines
2.9 KiB
Lua
local expect = require "cc.expect".expect
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local fp = require "ccryptolib.internal.fp"
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local fq = require "ccryptolib.internal.fq"
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local x25519 = require "ccryptolib.internal.x25519"
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local random = require "ccryptolib.random"
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local ORDER = 4
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--- The inverse of 8 modulo q (in montgomery form).
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local INV8Q = {
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5110253,
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3039345,
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2503500,
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11779568,
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15416472,
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16766550,
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16777215,
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16777215,
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16777215,
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16777215,
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4095,
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}
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local function fqRandom()
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return fq.decodeWide(random.random(64))
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end
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local function ladder8(dx, bits)
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local x1 = fp.num(1)
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local z1 = fp.num(0)
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-- Compute a randomization factor for randomized projective coordinates.
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-- Biased but good enough.
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local rf = fp.decode(random.random(32))
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local x2 = fp.mul(rf, dx)
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local z2 = rf
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-- Standard ladder.
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for i = #bits, 1, -1 do
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if bits[i] == 0 then
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x1, z1, x2, z2 = x25519.step(dx, x1, z1, x2, z2)
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else
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x2, z2, x1, z1 = x25519.step(dx, x2, z2, x1, z1)
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end
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end
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-- Multiply by 8 (double 3 times).
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for _ = 1, 3 do
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x1, z1 = x25519.double(x1, z1)
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end
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return fp.mul(x1, fp.invert(z1))
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end
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local mod = {}
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function mod.secretKeyInit(sk)
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sk = fq.decodeClamped(sk)
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-- Set up the mask.
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local sks = {}
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local sum = fq.num(0)
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for i = 1, ORDER - 1 do
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sks[i] = fqRandom()
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sum = fq.add(sum, sks[i])
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end
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sks[ORDER] = fq.add(sk, fq.neg(sum))
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return sks
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end
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function mod.secretKeyEncode(sks)
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local out = {}
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for i = 1, ORDER do out[i] = fq.encode(sks[i]) end
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return table.concat(out)
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end
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function mod.secretKeyDecode(str)
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expect(1, str, "string")
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assert(#str == ORDER * 32, ("secret key length must be %d"):format(ORDER * 32))
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local out = {}
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for i = 1, ORDER do out[i] = fq.decode(str:sub(i * 32 - 31, i * 32)) end
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return out
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end
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function mod.secretKeyRemask(sks)
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local sum = fq.num(0)
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local out = {}
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for i = 1, ORDER - 1 do
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local element = fqRandom()
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out[i] = fq.add(sks[i], element)
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sum = fq.add(sum, element)
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end
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out[ORDER] = fq.add(sks[ORDER], fq.neg(sum))
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return out
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end
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function mod.exchange(sks, pk, mc)
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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, mc, "string")
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assert(#mc == 32, "multiplier length must be 32")
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-- Get the multiplier in Fq.
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mc = fq.decodeClamped(mc)
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-- Multiply secret key members and add them together.
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-- This unwraps into the "true" secret key times the multiplier (mod q).
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local skmt = fq.num(0)
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for i = 1, #sks do skmt = fq.add(skmt, fq.mul(sks[i], mc)) end
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-- Get bits.
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-- We have our exponent modulo q. We also know that its value is 0 modulo 8.
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-- Use the Chinese Remainder Theorem to find its value modulo 8q.
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local bits = fq.bits(fq.mul(skmt, INV8Q))
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return fp.encode(ladder8(fp.decode(pk), bits))
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end
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return mod
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