Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

Kumar, Manoj; Gupta, Pratik

doi:10.4236/am.2016.73027

Cited by 8 publications

(5 citation statements)

References 14 publications

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“…Mathematical concept on elliptic curve is existing on the various literatures [6][7][8][9][10]. A easier and simple mathematically concept on elliptic curves is given by the following [1]:…”

Section: Mathematical Background Of Eccmentioning

confidence: 99%

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A Verifiable Ring Signature Scheme of Anonymous Signcryption Using ECC

Gupta¹,

Kumar²

2021

IJMSC

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The ring signature does hide the member of actually signature in the all possible signer. This technique was introduced by Rivest, Tauman and Shamir in 2001. This paper presents elliptic curve cryptosystem using signcryption algorithm with the anonymity feature. In the present paper, combines ring signature scheme with signcryption method to produce the anonymity feature for the signcryption scheme and discuss the characteristic of the security. Because elliptic curve cryptosystem yields like as small bandwidth requirements, low computation load, and high security and methodology of ring signature gives without revealing the actual signer to all possible signers. Combining the benefits of these two methodology, the result is an efficient anonymous signcryption algorithm and highly secure.

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Section: Mathematical Background Of Eccmentioning

confidence: 99%

“…In the year 2001, Firstly Rivest et al [1] developed a new idea of ring signature and implemented in article "How to leak a secret". The main purpose of ring signature technique is parallel to the group signature scheme but with some changes.…”

Section: Introductionmentioning

confidence: 99%

A Verifiable Ring Signature Scheme of Anonymous Signcryption Using ECC

Gupta¹,

Kumar²

2021

IJMSC

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“…In this section first we discuss some essential arithmetic of elliptic curves (which are necessary to understand the proposed scheme). Although a lot of literature exist on arithmetic of elliptic curves [15], a simple and easier arithmetic of elliptic curves is given by the following [16]: An elliptic curve E(F p ) over a finite field F p is defined by the parameters a, b ∈ F p (a and b satisfy the relation 4a 3 + 27b 2 = 0 ), consists of the set of points (x, y) ∈ F p , satisfying the equation y 2 = x 3 + ax + b . The set of points on E(F p ) also include a point O, which is the point at infinity serve as the identity element under addition.…”

Section: Mathematical Background Of Eccmentioning

confidence: 99%

An Efficient and Authentication Signcryption Scheme Based on Elliptic Curves

Kumar

Gupta

2019

MATEMATIKA

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Signcryption schemes are compact and specially suited for efficiency-critical applications such as smart card dependent systems. Several researchers have performed a large number of significant applications of signcryption such as authenticated key recovery and key establishment in one mall data packet, secure ATM networks as well as light weight electronic transaction protocols and multi-casting over the internet. In this paper we have proposed an efficient and efficient scheme of signcryption symmetric key solutions, using elliptic curves by reducing senders computational cost. It needs two elliptic curve point multiplication for sender and comparative study of computational cost for sender and recipient as well as there is no any inverse computation for sender and recipient. This makes it more crucial than others.

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“…One of the earliest asymmetric cryptosystems is the famous RSA. Later on, many more asymmetric algorithms were introduced, such as ElGamal and ECC [2,3], which were based on the complexity of the integer factorization problem. It was further modified by different cryptologists in [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Cryptosystem on Matrix Algebra over a Chain Ring

2020

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The revolutionary idea of asymmetric cryptography brings a fundamental change to our modern communication system. However, advances in quantum computers endanger the security of many asymmetric cryptosystems based on the hardness of factoring and discrete logarithm, while the complexity of the quantum algorithm makes it hard to implement in many applications. In this respect, novel asymmetric cryptosystems based on matrices over residue rings are in practice. In this article, a novel approach is introduced. Despite the matrix algebra M(k,ℤn), the matrix algebra M(k,Rn′), Rn′ = ℤ2[w]⟨wn−1⟩ as the chain ring is considered. In this technique, instead of exponentiation, the inner product automorphisms the use for key generation. The chain ring provides computational complexity to its algorithm, which improves the strength of the cryptosystem. However, the residue ring endangers the security of the original cryptosystem, while it is hard to break using Rn′. The structure of the chain ring deals with the binary field ℤ2, which simplifies its calculation and makes it capable of efficient execution in various applications.

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Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

Cited by 8 publications

References 14 publications

A Verifiable Ring Signature Scheme of Anonymous Signcryption Using ECC

A Verifiable Ring Signature Scheme of Anonymous Signcryption Using ECC

An Efficient and Authentication Signcryption Scheme Based on Elliptic Curves

Asymmetric Cryptosystem on Matrix Algebra over a Chain Ring

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