scholarly journals Comparative analysis of the scalar point multiplication algorithms in the NIST FIPS 186 elliptic curve cryptography

2021 ◽  
Author(s):  
M. Babenko ◽  
A. Tchernykh ◽  
A. Redvanov ◽  
A. Djurabaev
Keyword(s):  
Comparative Analysis ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Execution Time ◽  
Elliptic Curve Cryptosystem ◽  
Coordinate Systems ◽  
Point Multiplication ◽  
Window Method ◽  
Scalar Point Multiplication

In today's world, the problem of information security is becoming critical. One of the most common cryptographic approaches is the elliptic curve cryptosystem. However, in elliptic curve arithmetic, the scalar point multiplication is the most expensive compared to the others. In this paper, we analyze the efficiency of the scalar multiplication on elliptic curves comparing Affine, Projective, Jacobian, Jacobi-Chudnovsky, and Modified Jacobian representations of an elliptic curve. For each coordinate system, we compare Fast exponentiation, Nonadjacent form (NAF), and Window methods. We show that the Window method is the best providing lower execution time on considered coordinate systems.

scholarly journals Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1507 ◽  
Author(s):  
Utku Gulen ◽  
Selcuk Baktir
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Wireless Sensor ◽  
Network Nodes ◽  
Point Multiplication ◽  
Speed Up ◽  
Field Multiplication ◽  
First Time ◽  
Efficient Realization ◽  
Scalar Point Multiplication

We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve scalar point multiplication. We take advantage of the fast Fourier transform for the first time in the literature to speed up the number theoretic transform for an efficient realization of elliptic curve cryptography. Our implementation achieves elliptic curve scalar point multiplication in only 0.65 s and 1.31 s for multiplication of fixed and random points, respectively, and has similar or better timing performance compared to previous works in the literature.

Profiled Attacks Against the Elliptic Curve Scalar Point Multiplication Using Neural Networks

2021 ◽  
pp. 238-257
Author(s):  
Alessandro Barenghi ◽  
Diego Carrera ◽  
Silvia Mella ◽  
Andrea Pace ◽  
Gerardo Pelosi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Elliptic Curve ◽  
Point Multiplication ◽  
Scalar Point Multiplication

The Construction of ElGamal over Koblitz Curve

2014 ◽  
Vol 931-932 ◽  
pp. 1441-1446 ◽  
Author(s):  
Krissanee Kamthawee ◽  
Bhichate Chiewthanakul
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Scalar Multiplication ◽  
Computer Hardware ◽  
Point Multiplication ◽  
Koblitz Curves ◽  
Elliptic Curve Cryptosystems ◽  
Elgamal Cryptosystem ◽  
Primary Advantage

Recently elliptic curve cryptosystems are widely accepted for security applications key generation, signature and verification. Cryptographic mechanisms based on elliptic curves depend on arithmetic involving the points of the curve. it is possible to use smaller primes, or smaller finite fields, with elliptic curves and achieve a level of security comparable to that for much larger integers. Koblitz curves, also known as anomalous binary curves, are elliptic curves defined over F2. The primary advantage of these curves is that point multiplication algorithms can be devised that do not use any point doublings. The ElGamal cryptosystem, which is based on the Discrete Logarithm problem can be implemented in any group. In this paper, we propose the ElGamal over Koblitz Curve Scheme by applying the arithmetic on Koblitz curve to the ElGamal cryptosystem. The advantage of this scheme is that point multiplication algorithms can be speeded up the scalar multiplication in the affine coodinate of the curves using Frobenius map. It has characteristic two, therefore it’s arithmetic can be designed in any computer hardware. Moreover, it has more efficient to employ the TNAF method for scalar multiplication on Koblitz curves to decrease the number of nonzero digits. It’s security relies on the inability of a forger, who does not know a private key, to compute elliptic curve discrete logarithm.

scholarly journals Elliptic Curve Cryptosystem for Email Encryption

2010 ◽  
pp. 230-235
Author(s):  
Abhijit Mitra ◽  
Saikat Chakrabarty ◽  
Poojarini Mitra
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Galois Field ◽  
Elliptic Curve Cryptosystem ◽  
Public Network ◽  
Plain Text ◽  
The Core ◽  
Encryption And Decryption ◽  
Cryptographic Algorithms ◽  
Secure Transmission

The idea of information security lead to the evolution of cryptography. In other words, cryptography is the science of keeping information secure. It involves encryption and decryption of messages. The core of cryptography lies in the keys involved in encryption and decryption and maintaining the secrecy of the keys. Another important factor is the key strength, i.e. the difficulty in breaking the key and retrieving the plain text. There are various cryptographic algorithms. In this project we use Elliptic Curve Cryptography (ECC) over Galois field. This system has been proven to be stronger than known algorithms like RSA, DSA, etc. Our aim is to build an efficient elliptic curve cryptosystem for secure transmission or exchange of confidential emails over a public network.

scholarly journals Operations of Points on Elliptic Curve in Affine Coordinates

2019 ◽  
Vol 27 (3) ◽  
pp. 315-320
Author(s):  
Yuichi Futa ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Information Security ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Binary Operation ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem

Summary In this article, we formalize in Mizar [1], [2] a binary operation of points on an elliptic curve over GF(p) in affine coordinates. We show that the operation is unital, complementable and commutative. Elliptic curve cryptography [3], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

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