NOVEL ELLIPTIC CURVE SCALAR MULTIPLICATION ALGORITHMS FOR FASTER AND SAFER PUBLIC-KEY CRYPTOSYSTEMS


NOVEL ELLIPTIC CURVE SCALAR MULTIPLICATION ALGORITHMS FOR FASTER AND SAFER PUBLIC-KEY CRYPTOSYSTEMS

Vinay S. Iyengar

Oregon Episcopal School, Portland, Oregon, USA

ABSTRACT

Efficient and secure public-key cryptosystems are essential in today’s age of rapidly growing Internet communications. Elliptic curve scalar multiplication in particular, which refers to the operation of multiplying a large integer by a point on an elliptic curve, is crucial for both data encryption technology as well as testing the security of cryptographic systems. The purpose of this project was to design and implement an elliptic curve scalar multiplication algorithm 10% faster than one of the best algorithms currently used: the binary double-add algorithm. The algorithm designed was based off of an operation that allowed for the tripling of a point and was derived from point doubling and addition operations. The algorithm was further optimized using an integer representation in both ternary and balanced ternary form. Finally, a novel modification was made that allowed for the pre-computation and storage of multiples of a point. The algorithms were written and tested in a C++ program that selected random points over elliptic curves in both Weierstrass and Edwards form, and multiplied them by a large range of integers using each of the various algorithms. Timings for these operations were taken in terms of processor cycles and finally averaged out. The final averaged results showed that the most optimized algorithm was 66.63% more efficient that the binary double-add algorithm. In conclusion, the algorithm designed in this research showed a large improvement in efficiency compared to one of the best algorithms in commercial use today, and has significant implications for the field of cryptography.

KEYWORDS

Public-key cryptography, elliptic curves, scalar multiplication, point tripling, storage ladder.

SOURCE URL

https://wireilla.com/papers/ijcis/V2N3/2312ijcis05.pdf

VOLUME URL

https://wireilla.com/ijcis/vol2.html



Comments

Post a Comment

Popular posts from this blog

Implementation of a New Methodology to Reduce the Effects of Changes of Illumination in Face Recognition-based Authentication Andres

Image
Implementation of a New Methodology to Reduce the Effects of Changes of Illumination in Face Recognition-based Authentication Andres  Alarcon-Ramirez, and Mohamed F. Chouikha  Department of Electrical Engineering, Howard University, Washington DC ABSTRACT   In this paper, the study of the effects of illumination changes in the process of face recognition is discussed. Additionally, a new methodology that integrates Single-Scale Retinex (SSR) and Scale Invariant Feature Transform (SIFT) is presented. The proposed methodology addresses the problem of illumination changes in face recognition-based authentication systems. To do this, the SSR transform eliminates the component of luminance from the face image and recovers the reflectance component which is invariant to illumination changes; then, the SIFT transform detects interest points from the reflectance component of the face image. The interest points are features rich in information and may be used to ...
Read more

A DEFENSE MECHANISM FOR CREDIT CARD FRAUD DETECTION

Image
A DEFENSE MECHANISM FOR CREDIT CARD FRAUD DETECTION   M.Sasirekha , Sumaiya Thaseen   and Saira Banu School of Computing Science and Engineering, VIT University, Tamil Nadu, India. ABSTRACT Computer security is one of the key areas where lot of research is being done. Many intrusion detection techniques are proposed to ensure the network security, protect network resources and network infrastructures. Intrusion detection systems (IDS) attempt to detect attacks by gathering network data and analyze the information from various areas to identify the possible intrusions. This paper proposes a defense mechanism combining three approaches such as anomaly, misuse and decision making model to produce better detection accuracy and a decreased false positive rate. The defense mechanism can be built to detect the attacks in credit card system using Hidden Markov approach in the anomaly detection module. The credit card holder’s behaviours are taken as attributes and t...
Read more

DYNAMIC VALIDITY PERIOD CALCULATION OF DIGITAL CERTIFICATES BASED ON AGGREGATED SECURITY ASSESSMENT

Image
DYNAMIC VALIDITY PERIOD CALCULATION OF DIGITAL CERTIFICATES BASED ON AGGREGATED SECURITY ASSESSMENT  Alexander Beck, Jens Graupmann, Frank Ortmeier Computer Systems in Engineering, Otto-von-Guericke-University, Magdeburg, Germany  ABSTRACT  The paper proposes a method based on different security-related factors to dynamically calculate the validity period of digital certificates. Currently validity periods are most often defined statically without scientific justification. This approach is not sufficient to objectively consider the actual need for security. Therefore the approach proposed in this paper considers relevant security criteria in order to calculate a meaningful validity period for digital certificates. This kind of security assessment can be executed periodically in order to dynamically respond to changing conditions. Especially in the context of complex systems and infrastructures that have an increased need for security, privacy and availab...
Read more