src/java.base/share/classes/java/math/BigInteger.java

rev 12150 : 8046943: Leverage CPU Instructions for GHASH and RSA
Summary: Add montgomeryMultiply intrinsics
Reviewed-by: kvn

@@ -2602,10 +2602,22 @@
     }
 
     static int[] bnExpModThreshTable = {7, 25, 81, 241, 673, 1793,
                                                 Integer.MAX_VALUE}; // Sentinel
 
+    private int[] montgomeryMultiply(int[] a, int[] b, int[] n, int len, long inv,
+                                     int[] product) {
+        product = multiplyToLen(a, len, b, len, product);
+        return montReduce(product, n, len, (int)inv);
+    }
+
+    private int[] montgomerySquare(int[] a, int[] n, int len, long inv,
+                                     int[] product) {
+        product = squareToLen(a, len, product);
+        return montReduce(product, n, len, (int)inv);
+    }
+
     /**
      * Returns a BigInteger whose value is x to the power of y mod z.
      * Assumes: z is odd && x < z.
      */
     private BigInteger oddModPow(BigInteger y, BigInteger z) {

@@ -2677,10 +2689,21 @@
         int[] base = mag.clone();
         int[] exp = y.mag;
         int[] mod = z.mag;
         int modLen = mod.length;
 
+        // Make modLen even. It is conventional to use a cryptographic
+        // modulus that is 512, 768, 1024, or 2048 bits, so this code
+        // will not normally be executed. However, it is necessary for
+        // the correct functioning of the HotSpot intrinsics.
+        if ((modLen & 1) != 0) {
+            int[] x = new int[modLen + 1];
+            System.arraycopy(mod, 0, x, 1, modLen);
+            mod = x;
+            modLen++;
+        }
+                
         // Select an appropriate window size
         int wbits = 0;
         int ebits = bitLength(exp, exp.length);
         // if exponent is 65537 (0x10001), use minimum window size
         if ((ebits != 17) || (exp[0] != 65537)) {

@@ -2695,43 +2718,44 @@
         // Allocate table for precomputed odd powers of base in Montgomery form
         int[][] table = new int[tblmask][];
         for (int i=0; i < tblmask; i++)
             table[i] = new int[modLen];
 
-        // Compute the modular inverse
-        int inv = -MutableBigInteger.inverseMod32(mod[modLen-1]);
+        // Compute the modular inverse of the least significant 64-bit
+        // digit of the modulus
+        long n0 = (mod[modLen-1] & LONG_MASK) + ((mod[modLen-2] & LONG_MASK) << 32);
+        long inv = -MutableBigInteger.inverseMod64(n0);
 
         // Convert base to Montgomery form
         int[] a = leftShift(base, base.length, modLen << 5);
 
         MutableBigInteger q = new MutableBigInteger(),
                           a2 = new MutableBigInteger(a),
                           b2 = new MutableBigInteger(mod);
+        b2.normalize(); // MutableBigInteger.divide() assumes that its
+                        // divisor is in normal form.
 
         MutableBigInteger r= a2.divide(b2, q);
         table[0] = r.toIntArray();
 
         // Pad table[0] with leading zeros so its length is at least modLen
         if (table[0].length < modLen) {
            int offset = modLen - table[0].length;
            int[] t2 = new int[modLen];
-           for (int i=0; i < table[0].length; i++)
-               t2[i+offset] = table[0][i];
+           System.arraycopy(table[0], 0, t2, offset, table[0].length);
            table[0] = t2;
         }
 
         // Set b to the square of the base
-        int[] b = squareToLen(table[0], modLen, null);
-        b = montReduce(b, mod, modLen, inv);
+        int[] b = montgomerySquare(table[0], mod, modLen, inv, null);
 
         // Set t to high half of b
         int[] t = Arrays.copyOf(b, modLen);
 
         // Fill in the table with odd powers of the base
         for (int i=1; i < tblmask; i++) {
-            int[] prod = multiplyToLen(t, modLen, table[i-1], modLen, null);
-            table[i] = montReduce(prod, mod, modLen, inv);
+            table[i] = montgomeryMultiply(t, table[i-1], mod, modLen, inv, null);
         }
 
         // Pre load the window that slides over the exponent
         int bitpos = 1 << ((ebits-1) & (32-1));
 

@@ -2798,12 +2822,11 @@
                 if (isone) {
                     b = mult.clone();
                     isone = false;
                 } else {
                     t = b;
-                    a = multiplyToLen(t, modLen, mult, modLen, a);
-                    a = montReduce(a, mod, modLen, inv);
+                    a = montgomeryMultiply(t, mult, mod, modLen, inv, a);
                     t = a; a = b; b = t;
                 }
             }
 
             // Check if done

@@ -2811,21 +2834,20 @@
                 break;
 
             // Square the input
             if (!isone) {
                 t = b;
-                a = squareToLen(t, modLen, a);
-                a = montReduce(a, mod, modLen, inv);
+                a = montgomerySquare(t, mod, modLen, inv, a);
                 t = a; a = b; b = t;
             }
         }
 
         // Convert result out of Montgomery form and return
         int[] t2 = new int[2*modLen];
         System.arraycopy(b, 0, t2, modLen, modLen);
 
-        b = montReduce(t2, mod, modLen, inv);
+        b = montReduce(t2, mod, modLen, (int)inv);
 
         t2 = Arrays.copyOf(b, modLen);
 
         return new BigInteger(1, t2);
     }