Efficiency evaluation of different types of cryptography curves on low-power devices

OpenSSL represents the open source tool-kit of SSL and TLS protocols. This tool-kit includes the elliptic curve cryptography (ECC) among other things. The ECC part of OpenSSL provides curves of many standards and also curves of many sizes. The ECC is a current issue of information and communication technologies and it is implemented in many communication devices. We tested the elliptic curve cryptography on an embedded device MSP430, which is may be used i.e. in smart grid network with limited resources for securing communication. This article shows the results of these tests, it shows the efficiency of these curves and also discovers general problems and general questions of ECC. All the obtained results including practical outputs are concluded at the end of our paper.

[1]  Alfred Menezes,et al.  Elliptic Curve Cryptography , 2005, Encyclopedia of Cryptography and Security.

[2]  Daniel J. Bernstein,et al.  Curve25519: New Diffie-Hellman Speed Records , 2006, Public Key Cryptography.

[3]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[4]  Craig Costello,et al.  A brief discussion on selecting new elliptic curves , 2015 .

[5]  Jiri Misurec,et al.  Design of secure communication in network with limited resources , 2013, IEEE PES ISGT Europe 2013.

[6]  Horst G. Zimmer,et al.  Constructing elliptic curves with given group order over large finite fields , 1994, ANTS.

[7]  Hai Bin Zhang,et al.  Fast Elliptic Curve Point Multiplication Algorithm Optimization , 2013 .

[8]  Radek Fujdiak.  Measurement of Symmetric Cipher on Low Power Devices for Power Grids , 2015 .

[9]  Petr MLYNEK,et al.  Two-port Network Transfer Function for Power Line Topology Modeling , 2012 .

[10]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[11]  Zhe Liu,et al.  Low-Weight Primes for Lightweight Elliptic Curve Cryptography on 8-bit AVR Processors , 2013, Inscrypt.

[12]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[13]  Steven D. Galbraith,et al.  A Cryptographic Application of Weil Descent , 1999, IMACC.

[14]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1991, STOC '91.

[15]  Radek Fujdiak,et al.  Implementation of Elliptic Curve Diffie Hellman in ultra-low power microcontroller , 2015, 2015 38th International Conference on Telecommunications and Signal Processing (TSP).

[16]  R. Schoof.  Journal de Theorie des Nombres de Bordeaux 7 (1995), 219{254 , 2022 .