Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)

Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)

Bibliographic Details
Main Author: Bommireddipalli, Nithesh Venkata Ramana Surya
Language:English
Published: University of Cincinnati / OhioLINK 2017
Subjects:
Computer Engineering
Elliptic Curve Cryptography
ECC Software
Public-Key Cryptography
RSA
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-ucin15118668329061482021-08-03T07:04:45Z Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC) Bommireddipalli, Nithesh Venkata Ramana Surya Computer Engineering Elliptic Curve Cryptography ECC Software Public-Key Cryptography RSA This thesis focuses on elliptic curve arithmetic over the prime field GF (p) and elliptic curve cryptography (ECC). ECC over GF(p) has its own arithmetic which is done over elliptic curves of the form y<sup>2</sup>; ≡ x<sup>3</sup>;+ax+b (mod p), where p is prime. ECC is gaining importance in security because it uses smaller keys to provide the same security level as the popular RSA. It is the superior cryptographic scheme based on time efficiency and resource utilization. It is more suitable than RSA for DNSSEC and IoT systems and devices.Unlike RSA, which is easily understood, ECC is complicated because of the arithmetic involved. It is not widely understood. We provide a tutorial on elliptic curve arithmetic and also explain the working of the ElGamal cryptosystem. We also describe general hardware-efficient methods to implement ECC such as Montgomery multiplication and projective coordinates. These methods are challenging to understand. Essentially, projective coordinates help reduce the number of inversions required in doing scalar multiplication. If Montgomery multiplication is used, a time-consuming operation like reduction modulo a prime p can be simplified. In this work, we also present a user-friendly Java GUI application to provide education in elliptic curve arithmetic and its applications in cryptosystems. Lastly, we provide a module of questions and solutions to do the same and also enable senior students and graduate students to use ECC in their project work.</p> 2017 English text University of Cincinnati / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148 http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Computer Engineering
Elliptic Curve Cryptography
ECC Software
Public-Key Cryptography
RSA
spellingShingle Computer Engineering
Elliptic Curve Cryptography
ECC Software
Public-Key Cryptography
RSA
Bommireddipalli, Nithesh Venkata Ramana Surya
Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
author Bommireddipalli, Nithesh Venkata Ramana Surya
author_facet Bommireddipalli, Nithesh Venkata Ramana Surya
author_sort Bommireddipalli, Nithesh Venkata Ramana Surya
title Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
title_short Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
title_full Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
title_fullStr Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
title_full_unstemmed Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
title_sort tutorial on elliptic curve arithmetic and introduction to elliptic curve cryptography (ecc)
publisher University of Cincinnati / OhioLINK
publishDate 2017
url http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148
work_keys_str_mv AT bommireddipallinitheshvenkataramanasurya tutorialonellipticcurvearithmeticandintroductiontoellipticcurvecryptographyecc
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