scholarly journals Two Public-Key Cryptosystems Based on Expanded Gabidulin Codes

2021 ◽  
Author(s):  
Wenshuo Guo ◽  
Fang-Wei Fu
Keyword(s):  
Efficient Algorithm ◽  
Public Key ◽  
Cyclic Structure ◽  
Base Field ◽  
Gabidulin Codes ◽  
Obvious Advantage ◽  
Public Key Cryptosystems ◽  
The Third ◽  
Encryption Schemes ◽  
New Codes

Abstract This paper presents two public-key cryptosystems based on the so-called expanded Gabidulin codes, which are constructed by expanding Gabidulin codes over the base field. Exploiting the fast decoder of Gabidulin codes, we propose an efficient algorithm to decode these new codes when the noise vector satisfies a certain condition. Additionally, these new codes have an excellent error-correcting capability because of the optimality of their parent Gabidulin codes. Based on different masking techniques, we give two encryption schemes by using expanded Gabidulin codes in the McEliece setting. According to our analysis, these two cryptosystems can both resist the existing structural attacks. Furthermore, our proposals also have an obvious advantage in public-key representation without using the cyclic or quasi-cyclic structure compared to some other code-based cryptosystems. To achieve the security of 256 bits, for instance, a public-key size of 37005 bytes is enough for our first proposal, while around 1044992 bytes are needed for Classic McEliece selected as a candidate of the third round of the NIST PQC project.

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.

scholarly journals Some results of development of cryptographic transformations schemes using non-abelian groups

Radiotekhnika ◽  
2021 ◽  
pp. 66-72
Author(s):  
E.V. Kotukh ◽  
O.V. Severinov ◽  
A.V. Vlasov ◽  
A.O. Tenytska ◽  
E.O. Zarudna
Keyword(s):  
Abelian Group ◽  
Quantum Computer ◽  
Abelian Groups ◽  
Research Priorities ◽  
Braid Groups ◽  
Public Key ◽  
Direct Products ◽  
Key Establishment ◽  
Public Key Cryptosystems ◽  
Encryption Schemes

Implementation of a successful attack on classical public key cryptosystems becomes more and more real with the advent of practical results in the implementation of Shor's and Grover's algorithms on quantum computers. Modern results in tackling the problem of building a quantum computer of sufficiently power justify the need to revise the existing approaches and determine the most effective in terms of solving problems of post-quantum cryptography. One of these promising research priorities is the study of the cryptosystems based on non-abelian groups. The problems of conjugacy search, membership search, and others are difficult to solve in the theory of non-abelian groups and are the basis for building provably secure public key cryptosystems. This paper gives an overview of the most frequently discussed algorithms using non-abelian groups: matrix groups braid groups, semi direct products, and algebraic erasers (AE). The analysis of the construction of encryption and decryption schemes, key establishment mechanisms is given. Many non-abelian group-based key establishment protocols are associated with the Diffie – Hellman (DH) protocol. The paper analyzes the properties of non-abelian group public key encryption schemes. Various cryptographic primitives using non-commutative groups as a basis for post-quantum schemes are considered.

scholarly journals Recent Developments in Multivariate Public Key Cryptosystems

2020 ◽  
pp. 209-229
Author(s):  
Yasufumi Hashimoto
Keyword(s):  
Quantum Cryptography ◽  
The Other ◽  
Public Key ◽  
Signature Schemes ◽  
Public Key Cryptosystems ◽  
Suitable Parameter ◽  
Encryption Schemes ◽  
Recent Developments ◽  
Post Quantum Cryptography ◽  
Multivariate Public Key

Abstract The multivariate signature schemes UOV, Rainbow, and HFEv- have been considered to be secure and efficient enough under suitable parameter selections. In fact, several second round candidates of NIST’s standardization project of Post-Quantum Cryptography are based on these schemes. On the other hand, there are few multivariate encryption schemes expected to be practical and despite that, various new schemes have been proposed recently. In the present paper, we summarize multivariate schemes UOV, Rainbow, and (variants of) HFE generating the second round candidates and study the practicalities of several multivariate encryption schemes proposed recently.

scholarly journals Group ring based public key cryptosystems

2021 ◽  
pp. 1-22
Author(s):  
Gaurav Mittal ◽  
Sunil Kumar ◽  
Shiv Narain ◽  
Sandeep Kumar
Keyword(s):  
Group Ring ◽  
Public Key ◽  
Public Key Cryptosystems

ENCRYPTION-DECRYPTION TECHNIQUES FOR PICTURES

1989 ◽  
Vol 03 (03n04) ◽  
pp. 497-503
Author(s):  
RANI SIROMONEY ◽  
K. G. SUBRAMANIAN ◽  
P. J. ABISHA
Keyword(s):  
Public Key ◽  
Two Dimensional ◽  
Chain Code ◽  
Dimensional Array ◽  
Public Key Cryptosystems ◽  
Encryption Decryption ◽  
A Chain

Language theoretic public key cryptosystems for strings and pictures are discussed. Two methods of constructing public key cryptosystems for the safe transmission or storage of chain code pictures are presented; the first one encrypts a chain code picture as a string and the second one as a two-dimensional array.

Design of public key cryptosystems using idempotent elements

1985 ◽  
Vol 4 (4) ◽  
pp. 297-308 ◽  
Author(s):  
Józef P. Pieprzyk ◽  
Dominik A. Rutkowski
Keyword(s):  
Public Key ◽  
Public Key Cryptosystems
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