The week's pick
Reseach Article
Cryptography by Karatsuba Multiplier with ASCII Codes
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 1 - Number 12 |
| Year of Publication: 2010 |
| Authors: Tarun Narayan Shankar, G.Sahoo |
10.5120/262-421
|
Tarun Narayan Shankar, G.Sahoo . Cryptography by Karatsuba Multiplier with ASCII Codes. International Journal of Computer Applications. 1, 12 ( February 2010), 53-60. DOI=10.5120/262-421
Abstract
In this paper we describe Cryptography by using Karatsuba multipliers and ASCII codes implementing through coordinate geometry for data encryption and decryption with its code in matlab. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation on the elliptic curve and its declaration for data encryption and (ii) private key generation and its use in data decryption depended on the points on two dimensional elliptical curve. We also discuss the implementation of ECC on binary field. An overview of ECC implementation on two dimensional representation of ASCII codes with coordinate systems and data encryption through Elgamal Encryption technique has been discussed. Karatsuba multiplier is a fast process to solve the Elliptic curve cryptography problems. Here we have applied Karatsuba multiplier for point multiplication. Much attention has been given on the mathematical implementation of elliptic curves through Karatsuba multiplier. For cryptographic purposes, specifically results of the group formed by an elliptic curve over a finite field E(F2m), and showing how this can form public key cryptographic systems for use in both encryption and key exchange. Finally we describe how to encrypt and decrypt the data with the ASCII codes through Karatsuba multiplier and its implimentation through matlab.
References
- Koblitz N., Menezes A.J., and Vanstone S.A. The state of elliptic curve cryptography. Design, Codes, and Cryptography. Vol 19, Issue 2-3, 2000, page 173-193.
- A. Karatsuba and Y. Ofman, Multiplication of multidigitnumbers on automata, Sov. Phys. Dokl., Vol.7, 1963, 595-596.
- Nedjah, N. and Mourelle, L.M. (Eds.), Embedded Cryptographic Hardware:Methodologies andApplications, Nova Science Publishers, Hauppauge,NY, USA, 2004.
- S. Bajracharya, C. Shu, K. Gaj, and T. El-Ghazawi, Implementation of Elliptic Curve Cryptosystems over GF(2n) in Optimal Normal Basis on a Reconfigurable Computer.
- Menezes A.J., Teske E., and Weng A. Weak fields for ECC.CORR 2003-15, Technical Report, University of Waterloo, 2003..
- Rivest R., Schamir A. and Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21, 1978, 120-126.
- C. Shu, S. Kwon, and K. Gaj, Reconfigurable Computing Approach for Tate Pairing Cryptosystems over Binary Fields submitted to IEEE Transactions on Computers.
- Certicom. Information on the Certicom ECCchallenge, http://www.certicom.com/research/ecc hallenge.html
- ElGamal, T., A public key cryptosystem and a signature scheme based on discrete logarithm,IEEE Trans. Inform, Theory, IT-31, no.4, pp469-472, July 1985.
- T.N.Shankar,G.Sahoo,Cryptography with ellipitic curves ,International Journal of Computer Science And Applications ,page 38-42,Vol.2 No.1.
- T.N.Shankar,G.Sahoo,Cryptography with ASCII codes ,International Journal of Secure Digital Age Information Vol.1 No.2.
- Computer organization by Moris Mano,PHI publications.
Index Terms
Keywords