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wireguard-android/tunnel/src/main/java/com/wireguard/crypto/Curve25519.java

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/*
* Copyright © 2016 Southern Storm Software, Pty Ltd.
* Copyright © 2017-2019 WireGuard LLC. All Rights Reserved.
* SPDX-License-Identifier: Apache-2.0
*/
package com.wireguard.crypto;
import androidx.annotation.Nullable;
import java.util.Arrays;
/**
* Implementation of the Curve25519 elliptic curve algorithm.
* <p>
* This implementation was imported to WireGuard from noise-java:
* https://github.com/rweather/noise-java
* <p>
* This implementation is based on that from arduinolibs:
* https://github.com/rweather/arduinolibs
* <p>
* Differences in this version are due to using 26-bit limbs for the
* representation instead of the 8/16/32-bit limbs in the original.
* <p>
* References: http://cr.yp.to/ecdh.html, RFC 7748
*/
@SuppressWarnings({"MagicNumber", "NonConstantFieldWithUpperCaseName", "SuspiciousNameCombination"})
public final class Curve25519 {
// Numbers modulo 2^255 - 19 are broken up into ten 26-bit words.
private static final int NUM_LIMBS_255BIT = 10;
private static final int NUM_LIMBS_510BIT = 20;
private final int[] A;
private final int[] AA;
private final int[] B;
private final int[] BB;
private final int[] C;
private final int[] CB;
private final int[] D;
private final int[] DA;
private final int[] E;
private final long[] t1;
private final int[] t2;
private final int[] x_1;
private final int[] x_2;
private final int[] x_3;
private final int[] z_2;
private final int[] z_3;
/**
* Constructs the temporary state holder for Curve25519 evaluation.
*/
private Curve25519() {
// Allocate memory for all of the temporary variables we will need.
x_1 = new int[NUM_LIMBS_255BIT];
x_2 = new int[NUM_LIMBS_255BIT];
x_3 = new int[NUM_LIMBS_255BIT];
z_2 = new int[NUM_LIMBS_255BIT];
z_3 = new int[NUM_LIMBS_255BIT];
A = new int[NUM_LIMBS_255BIT];
B = new int[NUM_LIMBS_255BIT];
C = new int[NUM_LIMBS_255BIT];
D = new int[NUM_LIMBS_255BIT];
E = new int[NUM_LIMBS_255BIT];
AA = new int[NUM_LIMBS_255BIT];
BB = new int[NUM_LIMBS_255BIT];
DA = new int[NUM_LIMBS_255BIT];
CB = new int[NUM_LIMBS_255BIT];
t1 = new long[NUM_LIMBS_510BIT];
t2 = new int[NUM_LIMBS_510BIT];
}
/**
* Conditional swap of two values.
*
* @param select Set to 1 to swap, 0 to leave as-is.
* @param x The first value.
* @param y The second value.
*/
private static void cswap(int select, final int[] x, final int[] y) {
select = -select;
for (int index = 0; index < NUM_LIMBS_255BIT; ++index) {
final int dummy = select & (x[index] ^ y[index]);
x[index] ^= dummy;
y[index] ^= dummy;
}
}
/**
* Evaluates the Curve25519 curve.
*
* @param result Buffer to place the result of the evaluation into.
* @param offset Offset into the result buffer.
* @param privateKey The private key to use in the evaluation.
* @param publicKey The public key to use in the evaluation, or null
* if the base point of the curve should be used.
*/
public static void eval(final byte[] result, final int offset,
final byte[] privateKey, @Nullable final byte[] publicKey) {
final Curve25519 state = new Curve25519();
try {
// Unpack the public key value. If null, use 9 as the base point.
Arrays.fill(state.x_1, 0);
if (publicKey != null) {
// Convert the input value from little-endian into 26-bit limbs.
for (int index = 0; index < 32; ++index) {
final int bit = (index * 8) % 26;
final int word = (index * 8) / 26;
final int value = publicKey[index] & 0xFF;
if (bit <= (26 - 8)) {
state.x_1[word] |= value << bit;
} else {
state.x_1[word] |= value << bit;
state.x_1[word] &= 0x03FFFFFF;
state.x_1[word + 1] |= value >> (26 - bit);
}
}
// Just in case, we reduce the number modulo 2^255 - 19 to
// make sure that it is in range of the field before we start.
// This eliminates values between 2^255 - 19 and 2^256 - 1.
state.reduceQuick(state.x_1);
state.reduceQuick(state.x_1);
} else {
state.x_1[0] = 9;
}
// Initialize the other temporary variables.
Arrays.fill(state.x_2, 0); // x_2 = 1
state.x_2[0] = 1;
Arrays.fill(state.z_2, 0); // z_2 = 0
System.arraycopy(state.x_1, 0, state.x_3, 0, state.x_1.length); // x_3 = x_1
Arrays.fill(state.z_3, 0); // z_3 = 1
state.z_3[0] = 1;
// Evaluate the curve for every bit of the private key.
state.evalCurve(privateKey);
// Compute x_2 * (z_2 ^ (p - 2)) where p = 2^255 - 19.
state.recip(state.z_3, state.z_2);
state.mul(state.x_2, state.x_2, state.z_3);
// Convert x_2 into little-endian in the result buffer.
for (int index = 0; index < 32; ++index) {
final int bit = (index * 8) % 26;
final int word = (index * 8) / 26;
if (bit <= (26 - 8))
result[offset + index] = (byte) (state.x_2[word] >> bit);
else
result[offset + index] = (byte) ((state.x_2[word] >> bit) | (state.x_2[word + 1] << (26 - bit)));
}
} finally {
// Clean up all temporary state before we exit.
state.destroy();
}
}
/**
* Subtracts two numbers modulo 2^255 - 19.
*
* @param result The result.
* @param x The first number to subtract.
* @param y The second number to subtract.
*/
private static void sub(final int[] result, final int[] x, final int[] y) {
int index;
int borrow;
// Subtract y from x to generate the intermediate result.
borrow = 0;
for (index = 0; index < NUM_LIMBS_255BIT; ++index) {
borrow = x[index] - y[index] - ((borrow >> 26) & 0x01);
result[index] = borrow & 0x03FFFFFF;
}
// If we had a borrow, then the result has gone negative and we
// have to add 2^255 - 19 to the result to make it positive again.
// The top bits of "borrow" will be all 1's if there is a borrow
// or it will be all 0's if there was no borrow. Easiest is to
// conditionally subtract 19 and then mask off the high bits.
borrow = result[0] - ((-((borrow >> 26) & 0x01)) & 19);
result[0] = borrow & 0x03FFFFFF;
for (index = 1; index < NUM_LIMBS_255BIT; ++index) {
borrow = result[index] - ((borrow >> 26) & 0x01);
result[index] = borrow & 0x03FFFFFF;
}
result[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
}
/**
* Adds two numbers modulo 2^255 - 19.
*
* @param result The result.
* @param x The first number to add.
* @param y The second number to add.
*/
private void add(final int[] result, final int[] x, final int[] y) {
int carry = x[0] + y[0];
result[0] = carry & 0x03FFFFFF;
for (int index = 1; index < NUM_LIMBS_255BIT; ++index) {
carry = (carry >> 26) + x[index] + y[index];
result[index] = carry & 0x03FFFFFF;
}
reduceQuick(result);
}
/**
* Destroy all sensitive data in this object.
*/
private void destroy() {
// Destroy all temporary variables.
Arrays.fill(x_1, 0);
Arrays.fill(x_2, 0);
Arrays.fill(x_3, 0);
Arrays.fill(z_2, 0);
Arrays.fill(z_3, 0);
Arrays.fill(A, 0);
Arrays.fill(B, 0);
Arrays.fill(C, 0);
Arrays.fill(D, 0);
Arrays.fill(E, 0);
Arrays.fill(AA, 0);
Arrays.fill(BB, 0);
Arrays.fill(DA, 0);
Arrays.fill(CB, 0);
Arrays.fill(t1, 0L);
Arrays.fill(t2, 0);
}
/**
* Evaluates the curve for every bit in a secret key.
*
* @param s The 32-byte secret key.
*/
private void evalCurve(final byte[] s) {
int sposn = 31;
int sbit = 6;
int svalue = s[sposn] | 0x40;
int swap = 0;
// Iterate over all 255 bits of "s" from the highest to the lowest.
// We ignore the high bit of the 256-bit representation of "s".
while (true) {
// Conditional swaps on entry to this bit but only if we
// didn't swap on the previous bit.
final int select = (svalue >> sbit) & 0x01;
swap ^= select;
cswap(swap, x_2, x_3);
cswap(swap, z_2, z_3);
swap = select;
// Evaluate the curve.
add(A, x_2, z_2); // A = x_2 + z_2
square(AA, A); // AA = A^2
sub(B, x_2, z_2); // B = x_2 - z_2
square(BB, B); // BB = B^2
sub(E, AA, BB); // E = AA - BB
add(C, x_3, z_3); // C = x_3 + z_3
sub(D, x_3, z_3); // D = x_3 - z_3
mul(DA, D, A); // DA = D * A
mul(CB, C, B); // CB = C * B
add(x_3, DA, CB); // x_3 = (DA + CB)^2
square(x_3, x_3);
sub(z_3, DA, CB); // z_3 = x_1 * (DA - CB)^2
square(z_3, z_3);
mul(z_3, z_3, x_1);
mul(x_2, AA, BB); // x_2 = AA * BB
mulA24(z_2, E); // z_2 = E * (AA + a24 * E)
add(z_2, z_2, AA);
mul(z_2, z_2, E);
// Move onto the next lower bit of "s".
if (sbit > 0) {
--sbit;
} else if (sposn == 0) {
break;
} else if (sposn == 1) {
--sposn;
svalue = s[sposn] & 0xF8;
sbit = 7;
} else {
--sposn;
svalue = s[sposn];
sbit = 7;
}
}
// Final conditional swaps.
cswap(swap, x_2, x_3);
cswap(swap, z_2, z_3);
}
/**
* Multiplies two numbers modulo 2^255 - 19.
*
* @param result The result.
* @param x The first number to multiply.
* @param y The second number to multiply.
*/
private void mul(final int[] result, final int[] x, final int[] y) {
// Multiply the two numbers to create the intermediate result.
long v = x[0];
for (int i = 0; i < NUM_LIMBS_255BIT; ++i) {
t1[i] = v * y[i];
}
for (int i = 1; i < NUM_LIMBS_255BIT; ++i) {
v = x[i];
for (int j = 0; j < (NUM_LIMBS_255BIT - 1); ++j) {
t1[i + j] += v * y[j];
}
t1[i + NUM_LIMBS_255BIT - 1] = v * y[NUM_LIMBS_255BIT - 1];
}
// Propagate carries and convert back into 26-bit words.
v = t1[0];
t2[0] = ((int) v) & 0x03FFFFFF;
for (int i = 1; i < NUM_LIMBS_510BIT; ++i) {
v = (v >> 26) + t1[i];
t2[i] = ((int) v) & 0x03FFFFFF;
}
// Reduce the result modulo 2^255 - 19.
reduce(result, t2, NUM_LIMBS_255BIT);
}
/**
* Multiplies a number by the a24 constant, modulo 2^255 - 19.
*
* @param result The result.
* @param x The number to multiply by a24.
*/
private void mulA24(final int[] result, final int[] x) {
final long a24 = 121665;
long carry = 0;
for (int index = 0; index < NUM_LIMBS_255BIT; ++index) {
carry += a24 * x[index];
t2[index] = ((int) carry) & 0x03FFFFFF;
carry >>= 26;
}
t2[NUM_LIMBS_255BIT] = ((int) carry) & 0x03FFFFFF;
reduce(result, t2, 1);
}
/**
* Raise x to the power of (2^250 - 1).
*
* @param result The result. Must not overlap with x.
* @param x The argument.
*/
private void pow250(final int[] result, final int[] x) {
// The big-endian hexadecimal expansion of (2^250 - 1) is:
// 03FFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
//
// The naive implementation needs to do 2 multiplications per 1 bit and
// 1 multiplication per 0 bit. We can improve upon this by creating a
// pattern 0000000001 ... 0000000001. If we square and multiply the
// pattern by itself we can turn the pattern into the partial results
// 0000000011 ... 0000000011, 0000000111 ... 0000000111, etc.
// This averages out to about 1.1 multiplications per 1 bit instead of 2.
// Build a pattern of 250 bits in length of repeated copies of 0000000001.
square(A, x);
for (int j = 0; j < 9; ++j)
square(A, A);
mul(result, A, x);
for (int i = 0; i < 23; ++i) {
for (int j = 0; j < 10; ++j)
square(A, A);
mul(result, result, A);
}
// Multiply bit-shifted versions of the 0000000001 pattern into
// the result to "fill in" the gaps in the pattern.
square(A, result);
mul(result, result, A);
for (int j = 0; j < 8; ++j) {
square(A, A);
mul(result, result, A);
}
}
/**
* Computes the reciprocal of a number modulo 2^255 - 19.
*
* @param result The result. Must not overlap with x.
* @param x The argument.
*/
private void recip(final int[] result, final int[] x) {
// The reciprocal is the same as x ^ (p - 2) where p = 2^255 - 19.
// The big-endian hexadecimal expansion of (p - 2) is:
// 7FFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFEB
// Start with the 250 upper bits of the expansion of (p - 2).
pow250(result, x);
// Deal with the 5 lowest bits of (p - 2), 01011, from highest to lowest.
square(result, result);
square(result, result);
mul(result, result, x);
square(result, result);
square(result, result);
mul(result, result, x);
square(result, result);
mul(result, result, x);
}
/**
* Reduce a number modulo 2^255 - 19.
*
* @param result The result.
* @param x The value to be reduced. This array will be
* modified during the reduction.
* @param size The number of limbs in the high order half of x.
*/
private void reduce(final int[] result, final int[] x, final int size) {
// Calculate (x mod 2^255) + ((x / 2^255) * 19) which will
// either produce the answer we want or it will produce a
// value of the form "answer + j * (2^255 - 19)". There are
// 5 left-over bits in the top-most limb of the bottom half.
int carry = 0;
int limb = x[NUM_LIMBS_255BIT - 1] >> 21;
x[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
for (int index = 0; index < size; ++index) {
limb += x[NUM_LIMBS_255BIT + index] << 5;
carry += (limb & 0x03FFFFFF) * 19 + x[index];
x[index] = carry & 0x03FFFFFF;
limb >>= 26;
carry >>= 26;
}
if (size < NUM_LIMBS_255BIT) {
// The high order half of the number is short; e.g. for mulA24().
// Propagate the carry through the rest of the low order part.
for (int index = size; index < NUM_LIMBS_255BIT; ++index) {
carry += x[index];
x[index] = carry & 0x03FFFFFF;
carry >>= 26;
}
}
// The "j" value may still be too large due to the final carry-out.
// We must repeat the reduction. If we already have the answer,
// then this won't do any harm but we must still do the calculation
// to preserve the overall timing. The "j" value will be between
// 0 and 19, which means that the carry we care about is in the
// top 5 bits of the highest limb of the bottom half.
carry = (x[NUM_LIMBS_255BIT - 1] >> 21) * 19;
x[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
for (int index = 0; index < NUM_LIMBS_255BIT; ++index) {
carry += x[index];
result[index] = carry & 0x03FFFFFF;
carry >>= 26;
}
// At this point "x" will either be the answer or it will be the
// answer plus (2^255 - 19). Perform a trial subtraction to
// complete the reduction process.
reduceQuick(result);
}
/**
* Reduces a number modulo 2^255 - 19 where it is known that the
* number can be reduced with only 1 trial subtraction.
*
* @param x The number to reduce, and the result.
*/
private void reduceQuick(final int[] x) {
// Perform a trial subtraction of (2^255 - 19) from "x" which is
// equivalent to adding 19 and subtracting 2^255. We add 19 here;
// the subtraction of 2^255 occurs in the next step.
int carry = 19;
for (int index = 0; index < NUM_LIMBS_255BIT; ++index) {
carry += x[index];
t2[index] = carry & 0x03FFFFFF;
carry >>= 26;
}
// If there was a borrow, then the original "x" is the correct answer.
// If there was no borrow, then "t2" is the correct answer. Select the
// correct answer but do it in a way that instruction timing will not
// reveal which value was selected. Borrow will occur if bit 21 of
// "t2" is zero. Turn the bit into a selection mask.
final int mask = -((t2[NUM_LIMBS_255BIT - 1] >> 21) & 0x01);
final int nmask = ~mask;
t2[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
for (int index = 0; index < NUM_LIMBS_255BIT; ++index)
x[index] = (x[index] & nmask) | (t2[index] & mask);
}
/**
* Squares a number modulo 2^255 - 19.
*
* @param result The result.
* @param x The number to square.
*/
private void square(final int[] result, final int[] x) {
mul(result, x, x);
}
}
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