Abstract
With the emergence of the 3G (third-generation) networks for mobile communications, data security becomes even more important. Designing cryptosystems that meet both the power contraints and computing constraints of mobile units is very challenging. The GH-PKC reduces the size of the modulus and speeds up the computations of the same degree of security as existing cryptosystems. Our research focus is on software implementation of the GH-PKC and analysis on its performance over the existing cryptosystems.
Introduction
The
GH
Public-key
Cryptosystem
(GH-PKC)
was
developed
by
G.
Gong
and
L.
Harn
in
1999.
This
cryptosystem
is
based
on
the
third-order
linear
feedback
shift
register
(LFSR)
sequences
with
a
particular
phase.
Such
a
particular
LSFR
sequences
are
called
a
characteristic
sequence.
The
elements
of
the
sequences
are
taken
from
a
finite
field
GF(q).
The
security
of
GH-PKS
is
based
on
the
difficult
of
the
solving
discrete
logrithm
in
the
extension
GF(q3)
of
GF(q).
The
part
of
the
GH
Diffie-Hellman
(GH-DH)
key
agreement
protocol
was
published
in
the
proceddings
of
ChinaCrypto'1998
and
the
GH-DH
together
with
the
GH-RSA
type
was
published
in
the
November
1999
issue
of
IEEE
Transactions
on
Information
Theory.
Two
important
features
of
the
GH-PKC:
- GH-PKC has the same modular size as the elliptic curve public-key system while achieving the same 1024 bit security level for q = p2 .
- GH-PKC can be resistant to power analysis attack and timer analysis attack without increasing cost of computation.
The XTR, presented at Crypto'2000 by Lenstra and Verheul, is a special case of the special type of characteristic sequences when q = p2.
Some papers and slides on the GH-PKCS
- S. Sin, Software Implementation of Gong-Harn Public-key Cryptosystem and Analysis, Master's Thesis, April 2004, Waterloo, University of Waterloo, supervised by G. Gong, Thesis (PDF) (Appendices are removed).
- S. Sin, The GH-DSA, RIM-Seminar, October 2003, Slides on GH-DSA (PDF).
- S.Sin, Gong-Harn Public-key Cryptosystems, Poster (PDF).
- G. Gong and L. Harn, A new approach for public key distribution, Proceedings of China-Crypto'98, May 1998, Chengdu, China (PS).
- G. Gong and L. Harn, Public-key cryptosystems based on cubic finite field extensions, IEEE Trans. on Inform. Theory, vol. 45, No.7, November 1999, pp. 2601-2605, PS, Public-key cryptosystems based on cubic finite field extensions (PDF).
- Slides of the talk on the GH public-key cryptosystems at Queens University [PS], October 2000.
- G. Gong, L. Harn and H.P. Wu, The GH public-key cryptosystems, the Proceedings of the Eighth Annual Workshop on Selected Areas in Cryptography, Toronto, August 16-18, 2001. CORR 2001-35 [PS, slides].
- K. J. Giuliani, Generating large instances of the Gong-Harn cryptosystems, to be presented at the Conference on Cryptography and Coding, Dec. 17-19, 2001, Cirencester, UK, [PS].
- Roy Krischer, An implementation of the Gong-Harn Diffie Hellman key agreement protocol [PS], supervised Undergraduate Research Assistant, Spring 2001, Research Project Report.