Francois Berder / BigInt

This library provides a way to easily handle arbitrary large integers.

This library provides the following operations :

  • addition, substraction, multiplication, division and modulo
  • bits operators (AND, OR, XOR, left and right shifts)
  • boolean operators
  • modular exponentiation (using montgomery algorithm)
  • modular inverse

Example

In this example, we use a 1024 bits long RSA key to encrypt and decrypt a message. We first encrypt the value 0x41 (65 in decimal) and then decrypt it. At the end, m should be equal to 0x41. The encryption is fast (0, 4 second) while the decryption is really slow. This code will take between 30 seconds and 2 minutes to execute depending on the compiler and optimization flags.

main.cpp

#include "mbed.h"
#include "BigInt.h"
#include <stdlib.h>
#include <stdio.h>

uint8_t modbits[] = {
0xd9, 0x4d, 0x88, 0x9e, 0x88, 0x85, 0x3d, 0xd8, 0x97, 0x69, 0xa1, 0x80, 0x15, 0xa0, 0xa2, 0xe6,
0xbf, 0x82, 0xbf, 0x35, 0x6f, 0xe1, 0x4f, 0x25, 0x1f, 0xb4, 0xf5, 0xe2, 0xdf, 0x0d, 0x9f, 0x9a,
0x94, 0xa6, 0x8a, 0x30, 0xc4, 0x28, 0xb3, 0x9e, 0x33, 0x62, 0xfb, 0x37, 0x79, 0xa4, 0x97, 0xec,
0xea, 0xea, 0x37, 0x10, 0x0f, 0x26, 0x4d, 0x7f, 0xb9, 0xfb, 0x1a, 0x97, 0xfb, 0xf6, 0x21, 0x13,
0x3d, 0xe5, 0x5f, 0xdc, 0xb9, 0xb1, 0xad, 0x0d, 0x7a, 0x31, 0xb3, 0x79, 0x21, 0x6d, 0x79, 0x25,
0x2f, 0x5c, 0x52, 0x7b, 0x9b, 0xc6, 0x3d, 0x83, 0xd4, 0xec, 0xf4, 0xd1, 0xd4, 0x5c, 0xbf, 0x84,
0x3e, 0x84, 0x74, 0xba, 0xbc, 0x65, 0x5e, 0x9b, 0xb6, 0x79, 0x9c, 0xba, 0x77, 0xa4, 0x7e, 0xaf,
0xa8, 0x38, 0x29, 0x64, 0x74, 0xaf, 0xc2, 0x4b, 0xeb, 0x9c, 0x82, 0x5b, 0x73, 0xeb, 0xf5, 0x49
};

uint8_t dbits[] = {
0x04, 0x7b, 0x9c, 0xfd, 0xe8, 0x43, 0x17, 0x6b, 0x88, 0x74, 0x1d, 0x68, 0xcf, 0x09, 0x69, 0x52,
0xe9, 0x50, 0x81, 0x31, 0x51, 0x05, 0x8c, 0xe4, 0x6f, 0x2b, 0x04, 0x87, 0x91, 0xa2, 0x6e, 0x50,
0x7a, 0x10, 0x95, 0x79, 0x3c, 0x12, 0xba, 0xe1, 0xe0, 0x9d, 0x82, 0x21, 0x3a, 0xd9, 0x32, 0x69,
0x28, 0xcf, 0x7c, 0x23, 0x50, 0xac, 0xb1, 0x9c, 0x98, 0xf1, 0x9d, 0x32, 0xd5, 0x77, 0xd6, 0x66,
0xcd, 0x7b, 0xb8, 0xb2, 0xb5, 0xba, 0x62, 0x9d, 0x25, 0xcc, 0xf7, 0x2a, 0x5c, 0xeb, 0x8a, 0x8d,
0xa0, 0x38, 0x90, 0x6c, 0x84, 0xdc, 0xdb, 0x1f, 0xe6, 0x77, 0xdf, 0xfb, 0x2c, 0x02, 0x9f, 0xd8,
0x92, 0x63, 0x18, 0xee, 0xde, 0x1b, 0x58, 0x27, 0x2a, 0xf2, 0x2b, 0xda, 0x5c, 0x52, 0x32, 0xbe,
0x06, 0x68, 0x39, 0x39, 0x8e, 0x42, 0xf5, 0x35, 0x2d, 0xf5, 0x88, 0x48, 0xad, 0xad, 0x11, 0xa1
};

int main() 
{
    BigInt e = 65537, mod, d;
    mod.importData(modbits, sizeof(modbits));
    d.importData(dbits, sizeof(dbits));

    BigInt c = modPow(0x41,e,mod);
    c.print();
    BigInt m = modPow(c,d,mod);
    m.print();
    printf("done\n");
    
    return 0;
}

Diff: BigInt.cpp

Revision:
24:a3453a18388c
Parent:
23:002f471a973e
Child:
25:3d5c1f299da2
--- a/BigInt.cpp	Mon Mar 10 21:59:19 2014 +0000
+++ b/BigInt.cpp	Sun Apr 06 08:12:52 2014 +0000
@@ -15,7 +15,12 @@
     0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000, 0x20000000, 0x40000000, 0x80000000
 };
 
-static uint32_t num(const uint32_t a)
+static uint32_t BITS2[] =
+{
+    0x00FFFFFF, 0x0000FFFF, 0x00FFFFFF
+};
+
+static inline uint32_t num(const uint32_t a)
 {
     return a/4 + (a%4 ? 1:0); 
 }
@@ -539,14 +544,14 @@
     while(r > 0)
     {
         if(a.bits[j/32] & BITS[j%32])
-            result += b;
+            result.add(b);
         
         if(result.bits[0] & BITS[0])
-            result += m;
+            result.add(m);
      
         ++j; 
         --r;
-        result >>= 1;
+        result.shr();
     }
     
     if(result >= m)
@@ -579,6 +584,7 @@
     uint32_t j = 0; 
     while(j <= n)
     {
+        
         if(expn.bits[j/32] & BITS[j%32])
         {
             if(tmp.isValid())
@@ -589,6 +595,7 @@
         ++j;
         if(j <= n)  
             montA = montgomeryStep(montA, montA, modulus, r);
+        
     }
     
     // convert tmp to normal world
@@ -613,6 +620,50 @@
     printf("\n");
 }
 
+void BigInt::add(const BigInt &b)
+{
+    uint32_t al = num(size);
+    uint32_t bl = num(b.size);
+    uint32_t rsize = std::max(size, b.size) + 1;
+    size_t l = num(rsize);
+    
+    if(l > al)
+    {
+        bits = (uint32_t*)realloc(bits, sizeof(uint32_t)*l);
+        memset(&bits[al], 0, (l-al)*sizeof(uint32_t));
+        size = rsize;
+    }
+
+    uint32_t carry = 0;
+    for(int i = 0; i < l; ++i)
+    {
+        uint32_t tmpA = 0, tmpB = 0;
+        if(i < al)
+            tmpA = bits[i];
+        if(i < bl)
+            tmpB = b.bits[i];
+        bits[i] = tmpA + tmpB + carry;
+        carry = bits[i] < std::max(tmpA, tmpB);
+    }
+
+    trim();
+}
+
+void BigInt::shr()
+{
+    uint32_t lastBit = 0;
+    uint32_t tmp;
+    for(int i = num(size)-1; i >= 0; --i)
+    {
+        tmp = bits[i] & BITS[0];
+        bits[i] >>= 1;
+        bits[i] |= (lastBit ? BITS[31] : 0);
+        lastBit = tmp;
+    }
+
+    trim();
+}
+
 void BigInt::trim()
 {
     assert(isValid());
@@ -623,15 +674,12 @@
         newSize--;
     if(newSize == 0)
         newSize = 1;
-    if(num(newSize) < num(size))
+    uint32_t n = num(newSize);
+    if(n < num(size))
     {
-        uint32_t *tmp = new uint32_t[num(size)];
-        memcpy(tmp, bits, num(size)*sizeof(uint32_t));
-        delete[] bits;
-        bits = new uint32_t[num(newSize)];
-        memset(bits, 0, sizeof(uint32_t)*num(newSize));
-        memcpy(bits, tmp, newSize);
-        delete[] tmp;
+        bits = (uint32_t*)realloc(bits, n*sizeof(uint32_t));
+        if(newSize % 4 != 0)
+            bits[n-1] &= BITS2[newSize%4];
     }
     size = newSize; 
 }
@@ -651,4 +699,4 @@
     n += tmp2;
 
     return n;
-}
+}
\ No newline at end of file