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elgamal.h File Reference

ElGamal algorithm. More...

#include "mpbarrett.h"

Go to the source code of this file.

Functions

int elgv1sign (const mpbarrett *p, const mpbarrett *n, const mpnumber *g, randomGeneratorContext *, const mpnumber *hm, const mpnumber *x, mpnumber *r, mpnumber *s)
 This function performs raw ElGamal signing, variant 1.

int elgv3sign (const mpbarrett *p, const mpbarrett *n, const mpnumber *g, randomGeneratorContext *, const mpnumber *hm, const mpnumber *x, mpnumber *r, mpnumber *s)
 This function performs raw ElGamal signing, variant 3.

int elgv1vrfy (const mpbarrett *p, const mpbarrett *n, const mpnumber *g, const mpnumber *hm, const mpnumber *y, const mpnumber *r, const mpnumber *s)
 This function performs raw ElGamal verification, variant 1.

int elgv3vrfy (const mpbarrett *p, const mpbarrett *n, const mpnumber *g, const mpnumber *hm, const mpnumber *y, const mpnumber *r, const mpnumber *s)
 This function performs raw ElGamal verification, variant 3.

Detailed Description

ElGamal algorithm.

For more information on this algorithm, see: "Handbook of Applied Cryptography", 11.5.2: "The ElGamal signature scheme", p. 454-459

Two of the signature variants in Note 11.70 are implemented.

Todo:
Implement ElGamal encryption and decryption.

Explore the possibility of using simultaneous multiple exponentiation, as described in HAC, 14.87 (iii).

Author:
Bob Deblier <bob.deblier@pandora.be>

Definition in file elgamal.h.

Function Documentation

int elgv1sign (  const mpbarrett *  p,
const mpbarrett *  n,
const mpnumber *  g,
randomGeneratorContext *  rgc,
const mpnumber *  hm,
const mpnumber *  x,
mpnumber *  r,
mpnumber *  s
) 
 

This function performs raw ElGamal signing, variant 1.

Signing equations:

  • $r=g^{k}\ \textrm{mod}\ p$
  • $s=k^{-1}(h(m)-xr)\ \textrm{mod}\ (p-1)$
Parameters:
p The prime.
n The reducer mod (p-1).
g The generator.
rgc The pseudo-random generat
hm The hash to be signed.
x The private key value.
r The signature's r value.
s The signature's s value.
Return values:
0 on success.
-1 on failure.

int elgv1vrfy (  const mpbarrett *  p,
const mpbarrett *  n,
const mpnumber *  g,
const mpnumber *  hm,
const mpnumber *  y,
const mpnumber *  r,
const mpnumber *  s
) 
 

This function performs raw ElGamal verification, variant 1.

Verifying equations:

  • Check $0<r<p$ and $0<s<(p-1)$
  • $v_1=y^{r}r^{s}\ \textrm{mod}\ p$
  • $v_2=g^{h(m)}\ \textrm{mod}\ p$
  • Check $v_1=v_2$
Parameters:
p The prime.
n The reducer mod (p-1).
g The generator.
hm The hash to be signed.
y The public key value.
r The signature's r value.
s The signature's s value.
Return values:
1 on success.
0 on failure.

int elgv3sign (  const mpbarrett *  p,
const mpbarrett *  n,
const mpnumber *  g,
randomGeneratorContext *  rgc,
const mpnumber *  hm,
const mpnumber *  x,
mpnumber *  r,
mpnumber *  s
) 
 

This function performs raw ElGamal signing, variant 3.

Signing equations:

  • $r=g^{k}\ \textrm{mod}\ p$
  • $s=xr+kh(m)\ \textrm{mod}\ (p-1)$
Parameters:
p The prime.
n The reducer mod (p-1).
g The generator.
rgc The pseudo-random generat
hm The hash to be signed.
x The private key value.
r The signature's r value.
s The signature's s value.
Return values:
0 on success.
-1 on failure.

int elgv3vrfy (  const mpbarrett *  p,
const mpbarrett *  n,
const mpnumber *  g,
const mpnumber *  hm,
const mpnumber *  y,
const mpnumber *  r,
const mpnumber *  s
) 
 

This function performs raw ElGamal verification, variant 3.

Verifying equations:

  • Check $0<r<p$ and $0<s<(p-1)$
  • $v_1=g^{s}\ \textrm{mod}\ p$
  • $v_2=y^{r}r^{h(m)}\ \textrm{mod}\ p$
  • Check $v_1=v_2$
Parameters:
p The prime.
n The reducer mod (p-1).
g The generator.
hm The hash to be signed.
y The public key value.
r The signature's r value.
s The signature's s value.
Return values:
1 on success.
0 on failure.

Generated on Wed Mar 24 13:56:53 2004 for BeeCrypt by doxygen 1.3.6