Generating Keys in Elliptic Curve Cryptosystems

Dragan Vidakovic

Abstract


In this paper, we will present how to find keys elliptic curve cryptosystems  (ECC) with simple tools of Delphi 7 console application, using the software problem solving of the scalar point multiplication in the field GF(p), where p is an arbitrary prime number.


Keywords


Cryptography, ECC, Point multiplication, Public key, Open source software

Full Text:

PDF

References


Vidakovic D., Simic D., “A Novel Approach To Building Secure Systems“, ARES 2007, Vienna, Austria, pp 1074-1084.

Johnson D., Menezes A. and Vanstone S., “The Elliptic Curve Digital Signature Algorithm (ECDSA)â€, Certicom Research, Canada,

Vidakovic D., Nikolic O., Parezanovic D., “Acceleration Detection of Large (Probably) Prime Numbersâ€, International Journal of UbiComp (IJU), Vol.4, No.1, January 2013

Vidakovic D., Parezanovic D., Nikolic O. and Kaljevic J., “Rsa Signature: Behind The Scenesâ€, Advanced Computing: An International Journal ( ACIJ ), Vol.4, No.2, March 2013.

Vidakovic D., Nikolic O, Kaljevic J. and Parezanovic D., “Joint Operation in Public Key Cryptographyâ€, (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 4, No.3, 2013

R. Lidl and H. Niederreitter, Introduction to Finite Fields and their Applications, Cambridge University Press, 1984.

R. Lercier and F. Morain, “Counting the number of points on elliptic curves over finite fields: strategies and performancesâ€, Advances in Cryptology – Eurocrypt ’95, Lecture Notes in Computer

Avinash Kak, “ Lecture and Notes on Computer and Network Securityâ€, https://engineering.purdue.edu/kak/compsec/, accesed 15.05.2013.

Schoof R., “Elliptic curves over finite fields and the computation of square roots mod pâ€, Mathematics of Computation, 44 (1985), 483-494.

Koblitz N., “Elliptic Curve Cryptosystemsâ€, Mathematics of Computation, 48, pp. 203-209,1987.

Miller V., “Uses of elliptic curves in cryptographyâ€, Advances in Cryptology: proceedings of Crypto ‘85, Lecture Notes in Computer Science, vol. 218. New York: Springer-Verlag, 1986., pp 417-426.

Blake I., Seroussi G. and Smart N., Elliptic Curves in Cryptography, Cambridge University Press,1999.

A. Enge, Elliptic Curves and Their Applications to Cryptography— An Introduction, Kluwer Academic Publishers, 1999.

Hasegawa, J. Nakajima and M. Matsui, “A practical implementation of elliptic curve cryptosystems

A. Menezes, Elliptic Curve Public Key Cryptosystems, Kluwer Academic Publishers, Boston, 1993

A. Menezes and S. Vanstone. “Elliptic curve cryptosystems and their implementationâ€. Journal of Cryptology, 1993.

D. R. Stinson, Cryptography, theory and practice, Third Edition, Chapman & Hall/CRC, 2006.

J. H. Silverman, The arithmetic of elliptic, Springer Verlag, Berlin, 1986.

R. Lercier and F. Morain, “Counting the number of points on elliptic curves over finite fields: strategies and performancesâ€, Advances in Cryptology – Eurocrypt ’95, Lecture Notes in Computer Science, 921 (1995), Springer-Verlag, 79-94.

Lopez J. and Dahab R., “Fast multiplication on elliptic curves over GF(2m) without precomputationâ€, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.4712, Accessed May 2013.

Vidakovic D., “Analysis and implementation of asymmetric algorithms for data secrecy and integrity protectionâ€, Master Thesis (mentor Jovan Golic), Faculty of Electrical Engineering, Belgrade,Serbia, 1999.

Menezes A., van Oorschot P. C.,Vanstone S., Handbook of Applied Cryptography, CRC Press, New York, 1997.

T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithm problem, IEEE Trans. Info. Theory, IT-31, (1985), pp. 469-472

J. Silverman and J. Suzuki, “Elliptic curve discrete logarithms and the index calculusâ€, Advancesin Cryptology – Asiacrypt ’98, Lecture Notes in Computer Science, 1514 (1999), Springer-Verlag,110-125.

M. Jacobson, A. Menezes and A. Stein. Solving elliptic curve discrete logarithm problems using Weil descent. Preprint, 2001.

Koblitz N., “Cryptography As a Teaching Toolâ€, Cryptologia, Vol. 21, No. 4 (1997)., “Cryptography As a Teaching Toolâ€, Cryptologia, Vol. 21, No. 4 (1997).

D. Vidakovic, D. Parezanovic, J. Kaljevic, “Addition and doubling of pointsâ€, Journal of theoretical physics & Cryptography (IJTPC), Vol. 3, July 2013.


Refbacks

  • There are currently no refbacks.


ISSN: 1694-2507 (Print)

ISSN: 1694-2108 (Online)