Demystifying elliptic curve cryptography: Curve selection, implementation and countermeasures to attacks

Abstract Elliptic curve cryptography (ECC) has been the main choice for the security experts from some time now. As the IoT has enveloped the world around us; ECC has became more popular as security solution for the resource-constrained devices which covers the physical layer of IoT. Different libraries are available for ECC. In this paper we have discussed various important aspects in the implementation of ECC, such as finite fields, selection of curve model and curves along with the attacks on ECC. Implementation of ECC has been carried out on NIST curve P-256 with ElGamal encryption.

[1]  A TawalbehLo'ai,et al.  Hardware Design and Implementation of ElGamal Public-Key Cryptography Algorithm , 2010 .

[2]  Zhe Liu,et al.  MoTE-ECC: Energy-Scalable Elliptic Curve Cryptography for Wireless Sensor Networks , 2014, ACNS.

[3]  Craig Costello,et al.  Selecting elliptic curves for cryptography: an efficiency and security analysis , 2016, Journal of Cryptographic Engineering.

[4]  Peng Ning,et al.  2008 International Conference on Information Processing in Sensor Networks TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks ∗ , 2022 .

[5]  P. L. Montgomery.  Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[6]  Cheng-Chi Lee,et al.  Cryptanalysis and improvement of a ECDLP based proxy blind signature scheme , 2018 .

[7]  Qun Li,et al.  Efficient Implementation of Public Key Cryptosystems on Mote Sensors (Short Paper) , 2006, ICICS.

[8]  Tanja Lange,et al.  Twisted Edwards Curves , 2008, AFRICACRYPT.

[9]  Hwajeong Seo,et al.  On Emerging Family of Elliptic Curves to Secure Internet of Things: ECC Comes of Age , 2017, IEEE Transactions on Dependable and Secure Computing.

[10]  Saadeh Sweidan,et al.  Hardware Design and Implementation of ElGamal Public-Key Cryptography Algorithm , 2010, Inf. Secur. J. A Glob. Perspect..

[11]  Jorge Sá Silva,et al.  Security for the Internet of Things: A Survey of Existing Protocols and Open Research Issues , 2015, IEEE Communications Surveys & Tutorials.

[12]  Tim Güneysu,et al.  MicroECC: A Lightweight Reconfigurable Elliptic Curve Crypto-processor , 2011, 2011 International Conference on Reconfigurable Computing and FPGAs.

[13]  Feng-Hsiag Hsiao,et al.  Applying elliptic curve cryptography to a chaotic synchronisation system: neural-network-based approach , 2017, Int. J. Syst. Sci..

[14]  Nissa Mehibel,et al.  A new enhancement of elliptic curve digital signature algorithm , 2020, Journal of Discrete Mathematical Sciences and Cryptography.