Elliptic curve digital signature system implementationon embedded ARM processor.

Abstract

Elliptic Curve Digital Signature Algorithm (ECDSA) is a widely-used cryptographic algorithm that verifie sth eauthenticit yo fdigita lmessages.Th emai nadvantag eo fECDS Aove rother signature algorithms is requiring smaller key sizes to achieve the same level of security. The smaller size of the key results in faster operations due to its employment in the most computationally heavy part of the ECDSA algorithm: the Elliptic Curve (EC) Point Multiplication (PM). Therefore, it is a target for optimization to achieve better speed, memory consumption, energy dissipation and security. Some approaches rely on hardware support such as the use of parallelism and more memory. Others, depend on a more efficie ntu se of ECarithmet ic as EC PM isbui lt onEC operations: Addition (ADD), and Doubling (DBL). The Radix- 2 w method for EC PM relies on the recoding of the scalar with fewer nonzero digits in a w-bit window serving to reduce the cost in terms of ADD operations used. This project focuses on the implementation of ECDSA using the Radix- 2 w method for EC point multiplication (PM) and Double Point Multiplication (DPM); DPM is the sum of two EC PMs. This implementation is realized in the context of national institute of standards and technology recommended binary ECs, and serves as proof of concept for the Radix- 2 w multiplication methods. The Zynq Evaluation and Development Board’s processing system (PS) is used for the implementation as it allows for later integration of PL blocks for the Radix- 2 w multiplication making up a hardware/software solution. The project was carried out in three parts. First, the Radix- 2 w multiplication methods were implemented on computer, and their functionality validated. Subsequently, they were tested to reveal a 58.63% improvement in the cost of the Radix- 2 w EC PM method over the binary EC PM method in terms of ADDs, and a 47.509% improvement in the cost (in terms of ADDs) for the Radix- 2 w EC DPM method over the binary EC DPM method. Second, the ECDSA protocol was implemented on computer, along with an encryption protocol to complement the security provided by the signature (authentication and non repudiation). The reason behind this is that signature algorithms do not provide confidentiality. Thus, for the purpose of encryption, El-Gamal algorithm was used for its compatibility with ECs. Third and finally, the complet eECDSA/El-Gama encryption protocol using Radix- 2w methods for multiplication was adapted to the zedboard PS. This project resulted in the successful signature generation/verificatio nan dmessag eencryption/decryptio nbetwee nth eboar dan d acomputer using Radix- 2 w methods for multiplication.