Volume 6, no. 2Pages 120 - 127

Development, Implementation and Analysis of Cryptographic Protocol for Digital Signatures Based on Elliptic Curves

S.G. Chekanov
Cryptographic primitives based on elliptic curves have become very popular recently. The main reason is that elliptic curves can build many examples of finite Abelian groups with good parameters suitable for cryptographic purposes. In addition, elliptical curves are easy to implement on a computer, and the cryptographic strength can be achieved by choosing the characteristics of the finite field. Software cryptographic protocol for digital signature based on elliptic curves is designed and implemented. The protocol encrypts messages, forming a digital signature, message transmission and decoding at the receiver. Resistant cryptographic protocol is analyzed by several methods. A diagram of dependence of cryptographic security of the protocol on finite field characteristic, over which the elliptic curve is built, is given in the paper. The program in C++ programming environment Visual C++ 2010 with the support of large numbers GMP library is written. The program allows you to encrypt and decrypt the messages according to the generated protocol. It is also the instrument for transmission and receiving the messages with high degree of cryptographic strength and at reasonable rate.
Full text
cryptography, cryptographic protocols, elliptic curves, the cryptographic strength.
1. Cheremushkin A.V. Kriptograficheskie protokoly: osnovnye svoystva i uyazvimosti [Cryptographic Protocols: Basic Properties and Vulnerability]. Moscow, Akademiya, 2009.
2. Kobliz N. Kurs teorii chisel i kriptografii [The Course of Number Theory and Cryptography]. Moscow, TVP, 2001.
3. Kelsey J., Lucks S. Collisions and Near-Collisions for Reduced-Round Tiger, Proceedings of Fast Software Encryption. Graz, FSE, 2006.
4. Mendel F., Rijmen V. Cryptanalysis of the Tiger Hash Function. Heidelberg: ASIACRYPT, Springer Berlin, 2007.
5. Bolotov A.A., Gashkov S.B., Frolov A.B., Chasovskikh A.A. Algoritmicheskie osnovy ellipticheskoy kriptografii [Algorithmic Foundations of Elliptic Cryptography]. Moscow, MEI, 2000.
6. Romanets U.V., Nimofeev P.A., Shangin V.F. Zashchita informatsii v komp'yuternykh sistemakh i setyakh [The Protection of Information in Computer Systems and Networks]. Moscow, Radio i Svyaz', 2001.
7. Bondarenko M.F., Gorbenko I.D., Kachko E.G. Sushchnost' i rezul'taty issledovaniy svoystv perspektivnykh standartov tsifrovoy podpisi X9.62-1998 i raspredeleniya klyuchey X9.63-199X na ellipticheskikh krivykh [The Essence and Results of Research of the Properties of Perspective Digital Signature Standard X9.62-1998 and Key Distribution X9.63-199X on Elliptic Curves]. Radiotekhnika [Radiotechnique], 2000, no. 114, pp. 15-24.