Curve25519: Import class from noise-java

Signed-off-by: Jason A. Donenfeld <Jason@zx2c4.com>

1 files changed, 534 insertions, 0 deletions

diff --git a/app/src/main/java/com/wireguard/crypto/Curve25519.java b/app/src/main/java/com/wireguard/crypto/Curve25519.java
new file mode 100644
index 00000000..17f1b3d7
--- /dev/null
+++ b/app/src/main/java/com/wireguard/crypto/Curve25519.java
@@ -0,0 +1,534 @@
+/*
+ * Copyright (C) 2016 Southern Storm Software, Pty Ltd.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+package com.wireguard.crypto;
+
+import java.util.Arrays;
+
+/**
+ * Implementation of the Curve25519 elliptic curve algorithm.
+ *
+ * This implementation is based on that from arduinolibs:
+ * https://github.com/rweather/arduinolibs
+ *
+ * This implementation is copied verbatim from noise-java:
+ * https://github.com/rweather/noise-java
+ *
+ * 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.
+ *
+ * References: http://cr.yp.to/ecdh.html, RFC 7748
+ */
+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 int[] x_1;
+	private int[] x_2;
+	private int[] x_3;
+	private int[] z_2;
+	private int[] z_3;
+	private int[] A;
+	private int[] B;
+	private int[] C;
+	private int[] D;
+	private int[] E;
+	private int[] AA;
+	private int[] BB;
+	private int[] DA;
+	private int[] CB;
+	private long[] t1;
+	private int[] t2;
+
+	/**
+	 * 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];
+	}
+
+
+	/**
+	 * 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);
+	}
+
+	/**
+	 * 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(int[] x)
+	{
+		int index, carry;
+
+	    // 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.
+		carry = 19;
+		for (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.
+		int mask = -((t2[NUM_LIMBS_255BIT - 1] >> 21) & 0x01);
+		int nmask = ~mask;
+		t2[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
+		for (index = 0; index < NUM_LIMBS_255BIT; ++index)
+			x[index] = (x[index] & nmask) | (t2[index] & mask);
+	}
+
+	/**
+	 * 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(int[] result, int[] x, int size)
+	{
+		int index, limb, carry;
+
+	    // 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.
+		carry = 0;
+		limb = x[NUM_LIMBS_255BIT - 1] >> 21;
+		x[NUM_LIMBS_255BIT - 1] &= 0x001FFFFF;
+		for (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 (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 (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);
+	}
+
+	/**
+	 * 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(int[] result, int[] x, int[] y)
+	{
+		int i, j;
+
+		// Multiply the two numbers to create the intermediate result.
+		long v = x[0];
+		for (i = 0; i < NUM_LIMBS_255BIT; ++i) {
+			t1[i] = v * y[i];
+		}
+		for (i = 1; i < NUM_LIMBS_255BIT; ++i) {
+			v = x[i];
+			for (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 (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);
+	}
+
+	/**
+	 * Squares a number modulo 2^255 - 19.
+	 *
+	 * @param result The result.
+	 * @param x The number to square.
+	 */
+	private void square(int[] result, int[] x)
+	{
+		mul(result, x, x);
+	}
+
+	/**
+	 * 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(int[] result, int[] x)
+	{
+		long a24 = 121665;
+		long carry = 0;
+		int index;
+		for (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);
+	}
+
+	/**
+	 * 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(int[] result, int[] x, int[] y)
+	{
+		int index, carry;
+		carry = x[0] + y[0];
+		result[0] = carry & 0x03FFFFFF;
+		for (index = 1; index < NUM_LIMBS_255BIT; ++index) {
+			carry = (carry >> 26) + x[index] + y[index];
+			result[index] = carry & 0x03FFFFFF;
+		}
+		reduceQuick(result);
+	}
+
+	/**
+	 * 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 void sub(int[] result, int[] x, int[] y)
+	{
+		int index, 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;
+	}
+
+	/**
+	 * 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, int[] x, int[] y)
+	{
+		int dummy;
+		select = -select;
+		for (int index = 0; index < NUM_LIMBS_255BIT; ++index) {
+			dummy = select & (x[index] ^ y[index]);
+			x[index] ^= dummy;
+			y[index] ^= dummy;
+		}
+	}
+
+	/**
+	 * 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(int[] result, int[] x)
+	{
+		int i, j;
+
+	    // 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 (j = 0; j < 9; ++j)
+			square(A, A);
+		mul(result, A, x);
+		for (i = 0; i < 23; ++i) {
+			for (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 (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(int[] result, 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);
+	}
+
+	/**
+	 * Evaluates the curve for every bit in a secret key.
+	 *
+	 * @param s The 32-byte secret key.
+	 */
+	private void evalCurve(byte[] s)
+	{
+		int sposn = 31;
+		int sbit = 6;
+		int svalue = s[sposn] | 0x40;
+		int swap = 0;
+		int select;
+
+	    // 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".
+		for (;;) {
+	        // Conditional swaps on entry to this bit but only if we
+	        // didn't swap on the previous bit.
+			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);
+	}
+
+	/**
+	 * 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(byte[] result, int offset, byte[] privateKey, byte[] publicKey)
+	{
+		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) {
+			    	int bit = (index * 8) % 26;
+			    	int word = (index * 8) / 26;
+			    	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) {
+		    	int bit = (index * 8) % 26;
+		    	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();
+		}
+	}
+}