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:
1:00f2c40d46ed
Parent:
0:9d554894785b
Child:
2:1001793a090d
--- a/BigInt.cpp	Fri Sep 20 13:29:23 2013 +0000
+++ b/BigInt.cpp	Fri Sep 20 15:45:22 2013 +0000
@@ -217,6 +217,106 @@
     this->operator-=(a);
     return t;
 }
+/*
+BigInt operator*(const BigInt &a, const BigInt& b)
+{
+    BigInt result;   
+    
+    // if a == 0 or b == 0 then result = 0
+    if(!a || !b)
+    {
+        uint8_t tmp = 0;
+        result.import(&tmp, 1);
+        return result;
+    }
+    
+    uint8_t tmp = 1;
+    BigInt one;
+    one.import(&tmp, 1);
+    // if a == 1, then result = b
+    if(a == one)
+        return (result = b);
+    
+    // if b == 1, then result = a
+    if(b == one)
+        return (result = a);
+        
+        
+    
+    return result;
+}
+
+BigInt& BigInt::operator*=(const BigInt &b)
+{
+    return (*this = (*this) * b);
+}
+
+*/
+BigInt operator>>(const BigInt &a, const uint32_t m)
+{
+    BigInt result;
+    if(m == 0)
+        return result = a;
+    if(m/8 >= a.size)
+    {
+        uint8_t tmp = 0;
+        result.import(&tmp, 0);
+        return result;
+    }
+    
+    result.size = a.size - m/8;
+    result.bits = new uint32_t[num(result.size)];
+    uint8_t s = m%32;
+    for(uint32_t i = 0; i < num(result.size); ++i)
+    {
+        if(m/32+i+1 < num(a.size))
+            result.bits[i] =  (a.bits[m/32+i+1] << (32-s)) |  (a.bits[m/32+i] >> s);
+        else
+            result.bits[i] = (a.bits[m/32+i] >> s);
+    }
+    
+    
+    return result;
+}
+
+BigInt& BigInt::operator>>=(const uint32_t m)
+{
+    return *this = *this >> m;
+}
+ 
+BigInt operator<<(const BigInt &a, const uint32_t m)
+{
+    BigInt result;
+
+    if(m == 0)
+        return result = a;
+
+    result.size = m/8 + a.size;
+    uint32_t h = a.bits[num(a.size)-1];
+    if((h << (m%32)) < h)
+        ++result.size;
+    uint32_t l = num(result.size);
+    result.bits = new uint32_t[l];
+    memset(result.bits, 0, sizeof(uint32_t)*l);
+    uint32_t s = m % 32;
+    for(uint32_t i = 0; i < num(a.size); ++i)
+    {
+        if(i == 0)
+            result.bits[m/32+i] = a.bits[i] << s;
+        else
+            result.bits[m/32+i] = (a.bits[i] << s) | (a.bits[i-1] >> (32-s));
+    }
+    if(a.bits[num(a.size)-1] << s < a.bits[num(a.size)-1])
+        result.bits[num(result.size)-1] = a.bits[num(a.size)-1] >> (32-s);
+
+    
+    return result;
+}
+
+BigInt& BigInt::operator<<=(const uint32_t m)
+{
+    return (*this = *this << m);
+}
 
 bool operator==(const BigInt &a, const BigInt &b)
 {
@@ -271,11 +371,11 @@
     return (a > b) || (a == b);
 }
 
-bool BigInt::operator!()
+bool operator!(const BigInt &a)
 {
-    if(size != 1)
+    if(a.size != 1)
         return false;
-    return bits[0] == 0;
+    return a.bits[0] == 0;
 }
  
 void BigInt::print()
@@ -284,7 +384,7 @@
     uint32_t n = num(size);
     for(int i = n-1; i >= 0; --i)
     {
-        printf("%08x", bits[i]);
+        printf("%08x ", bits[i]);
     }
     printf("\n");
 }