Public-key cryptosystems based on cubic finite field extensions

1999 ◽  
Vol 45 (7) ◽  
pp. 2601-2605 ◽  
Author(s):  
Guang Gong ◽  
Lein Harn
Keyword(s):  
Finite Field ◽  
Public Key ◽  
Public Key Cryptosystems ◽  
Field Extensions

RSA-Public Key Cryptosystems Based on Quadratic Equations in Finite Field

2014 ◽  
pp. 238-258
Author(s):  
Sattar B. Sadkhan Al Maliky ◽  
Luay H. Al-Siwidi
Keyword(s):  
Finite Field ◽  
Chinese Remainder Theorem ◽  
Quadratic Equation ◽  
Public Key ◽  
Factorization Problem ◽  
Quadratic Equations ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Mathematical Problems ◽  
One Way Function

The importance of Public Key Cryptosystems (PKCs) in the cryptography field is well known. They represent a great revolution in this field. The PKCs depend mainly on mathematical problems, like factorization problem, and a trapdoor one-way function problem. Rivest, Shamir, and Adleman (RSA) PKC systems are based on factorization mathematical problems. There are many types of RSA cryptosystems. Rabin's Cryptosystem is considered one example of this type, which is based on using the square order (quadratic equation) in encryption function. Many cryptosystems (since 1978) were implemented under such a mathematical approach. This chapter provides an illustration of the variants of RSA-Public Key Cryptosystems based on quadratic equations in Finite Field, describing their key generation, encryption, and decryption processes. In addition, the chapter illustrates a proposed general formula for the equation describing these different types and a proposed generalization for the Chinese Remainder Theorem.

scholarly journals A Lightweight Buyer-Seller Watermarking Protocol

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Yongdong Wu ◽  
Hweehua Pang
Keyword(s):  
Field Theory ◽  
Finite Field ◽  
Public Key ◽  
Communication Overhead ◽  
Computational Power ◽  
Public Key Cryptosystems ◽  
Network Bandwidth ◽  
Watermarking Protocol ◽  
Substantial Network

The buyer-seller watermarking protocol enables a seller to successfully identify a traitor from a pirated copy, while preventing the seller from framing an innocent buyer. Based on finite field theory and the homomorphic property of public key cryptosystems such as RSA, several buyer-seller watermarking protocols (N. Memon and P. W. Wong (2001) and C.-L. Lei et al. (2004)) have been proposed previously. However, those protocols require not only large computational power but also substantial network bandwidth. In this paper, we introduce a new buyer-seller protocol that overcomes those weaknesses by managing the watermarks. Compared with the earlier protocols, ours isntimes faster in terms of computation, wherenis the number of watermark elements, while incurring onlyO(1/lN)times communication overhead given the finite field parameterlN. In addition, the quality of the watermarked image generated with our method is better, using the same watermark strength.

scholarly journals A Public Key Cryptosystem Using a Group of Permutation Polynomials

2020 ◽  
Vol 77 (1) ◽  
pp. 139-162
Author(s):  
Rajesh P. Singh ◽  
Bhaba K. Sarma ◽  
Anupam Saikia
Keyword(s):  
Finite Field ◽  
Public Key ◽  
Permutation Polynomials ◽  
Public Key Cryptosystem ◽  
Encryption Scheme ◽  
Public Key Cryptosystems ◽  
Polynomials Over Finite Fields ◽  
Cyclic Shifts ◽  
Trapdoor Function ◽  
Multivariate Public Key

AbstractIn this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field Fqm. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m2+3m – 4 left cyclic shifts, 5m2 +3m + 4 xor operations and 7 permutations on bits for decryption.

scholarly journals Implementation of Double Fold Text Encryption Based on Elliptic Curve Cryptography (ECC) with Digital Signature

2020 ◽  
Vol 8 (5) ◽  
pp. 3840-3846
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Digital Signature ◽  
Elliptic Curve Cryptography ◽  
Public Key ◽  
The Internet ◽  
Public Key Cryptosystems ◽  
The World ◽  
Recent Attention ◽  
Cryptographic Scheme

As the internet provides access to millions of communications in every second around the world, security implications are tremendously increasing. Transfer of important files like banking transactions, tenders, and e commerce require special security and authenticated mechanism in its journey from the sender to the receiver. Recent attention of cryptography is mainly focused on use of elliptic curves in public key cryptosystems. The present paper explains an innovative public key cryptographic scheme for protecting sensitive of critical information using elliptic curve over finite field. This mechanism besides providing the robustness of the cipher contributes the authentication of the message with digital signature.

Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials

2016 ◽  
Vol 26 (07) ◽  
pp. 1650112 ◽  
Author(s):  
Ali Shakiba ◽  
Mohammad Reza Hooshmandasl ◽  
Mohsen Alambardar Meybodi
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key ◽  
Floating Point ◽  
Real Numbers ◽  
Public Key Cryptosystems ◽  
Floating Point Arithmetic ◽  
Security Models ◽  
Point Arithmetic

In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.

Public-Key Encryption

2017 ◽  
Author(s):  
Keith M. Martin
Keyword(s):  
Elliptic Curve ◽  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Hybrid Encryption ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Encryption Schemes ◽  
Hard Problems ◽  
Set Up

In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key encryption schemes are based. We then discuss two of the best-known public-key cryptosystems, RSA and ElGamal. For each of these public-key cryptosystems, we discuss how to set up key pairs and perform basic encryption and decryption. We also identify the basis for security for each of these cryptosystems. We then compare RSA, ElGamal, and elliptic-curve variants of ElGamal from the perspectives of performance and security. Finally, we look at how public-key encryption is used in practice, focusing on the popular use of hybrid encryption.

On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

2010 ◽  
Vol 59 (10) ◽  
pp. 1392-1401 ◽  
Author(s):  
Xiaofeng Liao ◽  
Fei Chen ◽  
Kwok-wo Wong
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key
Sign in / Sign up

Export Citation Format

Share Document