Francois Berder
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;
}
Revision 8:2a361f1b41da, committed 2013-10-04
- Comitter:
- feb11
- Date:
- Fri Oct 04 15:16:06 2013 +0000
- Parent:
- 7:1aad58757705
- Child:
- 9:3c191fa04f6e
- Commit message:
- implemented XOR
Changed in this revision
| BigInt.cpp | Show annotated file Show diff for this revision Revisions of this file |
| BigInt.h | Show annotated file Show diff for this revision Revisions of this file |
--- a/BigInt.cpp Fri Oct 04 15:10:31 2013 +0000
+++ b/BigInt.cpp Fri Oct 04 15:16:06 2013 +0000
@@ -472,7 +472,36 @@
{
return (*this = *this | a);
}
+
+BigInt operator^(const BigInt &a, const BigInt &b)
+{
+ BigInt result;
+
+ uint32_t na = num(a.size);
+ uint32_t nb = num(b.size);
+ uint32_t l = max(na,nb);
+ result.size = max(a.size, b.size);
+ result.bits = new uint32_t[l];
+ memset(result.bits, 0, l);
+ for(uint32_t i = 0; i < l; ++i)
+ {
+ if(i < na && i < nb)
+ result.bits[i] = a.bits[i] ^ b.bits[i];
+ else if(i < na)
+ result.bits[i] = a.bits[i];
+ else
+ result.bits[i] = b.bits[i];
+ }
+
+ return result;
+}
+
+BigInt& BigInt::operator^=(const BigInt &a)
+{
+ return (*this = *this ^ a);
+}
+
void BigInt::print()
{
printf("size: %d bytes\n", size);
--- a/BigInt.h Fri Oct 04 15:10:31 2013 +0000
+++ b/BigInt.h Fri Oct 04 15:16:06 2013 +0000
@@ -51,7 +51,9 @@
BigInt& operator&=(const BigInt &a);
friend BigInt operator|(const BigInt &a, const BigInt &b);
BigInt& operator|=(const BigInt &a);
-
+ friend BigInt operator^(const BigInt &a, const BigInt &b);
+ BigInt& operator^=(const BigInt &a);
+
// debug
void print();