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;
}

Files at this revision

API Documentation at this revision

Revision 21:cfa04e0e6b59, committed 2014-03-10

Comitter:
feb11
Date:
Mon Mar 10 13:25:33 2014 +0000
Parent:
20:d747159d77c4
Child:
22:9d5f18b86753
Commit message:
minor changes in operator& | ^

Changed in this revision

BigInt.cpp Show annotated file Show diff for this revision Revisions of this file 
--- a/BigInt.cpp	Mon Mar 10 12:51:47 2014 +0000
+++ b/BigInt.cpp	Mon Mar 10 13:25:33 2014 +0000
@@ -81,8 +81,8 @@
         delete[] bits;
     bits = new uint32_t[l];
     memset(bits, 0, sizeof(uint32_t)*l);
-    for(int i = length-1; i >=0; --i)
-        bits[i/4] |= data[i] << ((i%4)*8);
+    for(int i = 0; i < length; ++i)
+        bits[(length-i-1)/4] |= data[i] << ((3-i%4)*8);
         
     trim();
 }
@@ -452,11 +452,10 @@
 
     BigInt result;
 
-    result.size = a.size < b.size ? a.size : b.size;
+    result.size = std::min(a.size, b.size);
     uint32_t l = num(result.size);
     result.bits = new uint32_t[l];
-    memset(result.bits, 0, l);
-    
+    memset(result.bits, 0, l*sizeof(uint32_t));
     for(uint32_t i = 0; i < l; ++i)
         result.bits[i] = a.bits[i] & b.bits[i];
 
@@ -480,8 +479,8 @@
     uint32_t nb = num(b.size);
     uint32_t l = std::max(na,nb);
     result.size = std::max(a.size, b.size);
-    result.bits = new uint32_t[l];
-    memset(result.bits, 0, l);
+    result.bits = new uint32_t[num(result.size)];
+    memset(result.bits, 0, num(result.size)*sizeof(uint32_t));
     
     for(uint32_t i = 0; i < l; ++i)
     {
@@ -511,11 +510,10 @@
 
     uint32_t na = num(a.size);
     uint32_t nb = num(b.size);
-    uint32_t l = std::max(na,nb);
     result.size = std::max(a.size, b.size);
+    uint32_t l = num(result.size);
     result.bits = new uint32_t[l];
-    memset(result.bits, 0, l);
-    
+    memset(result.bits, 0, l*sizeof(uint32_t));
     for(uint32_t i = 0; i < l; ++i)
     {
         if(i < na && i < nb)