/*
 * 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.southernstorm.noise.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
 *
 * 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();
		}
	}
}
