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 24:a3453a18388c, committed 2014-04-06
- Comitter:
- feb11
- Date:
- Sun Apr 06 08:12:52 2014 +0000
- Parent:
- 23:002f471a973e
- Child:
- 25:3d5c1f299da2
- Commit message:
- improved speed of modPow
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 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
--- a/BigInt.h Mon Mar 10 21:59:19 2014 +0000
+++ b/BigInt.h Sun Apr 06 08:12:52 2014 +0000
@@ -68,6 +68,10 @@
private :
+ // fast operations
+ void add(const BigInt &b);
+ void shr();
+
void trim();
uint32_t numBits() const;
@@ -79,4 +83,4 @@
};
-#endif
+#endif
\ No newline at end of file