Curve25519: fix up spacing

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

1 files changed, 491 insertions, 491 deletions

diff --git a/app/src/main/java/com/wireguard/crypto/Curve25519.java b/app/src/main/java/com/wireguard/crypto/Curve25519.java
index fdc89635..5d27c3e3 100644
--- a/app/src/main/java/com/wireguard/crypto/Curve25519.java
+++ b/app/src/main/java/com/wireguard/crypto/Curve25519.java
@@ -41,495 +41,495 @@ import java.util.Arrays;
 @SuppressWarnings("ALL")
 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();
-		}
-	}
+    // 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();
+        }
+    }
 }