scholarly journals Strongly aperiodic logarithmic signatures

2013 ◽  
Vol 7 (2) ◽  
pp. 147-179
Author(s):  
Reiner Staszewski ◽  
Tran van Trung
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Public Key ◽  
Logarithmic Signatures ◽  
Public Key Cryptosystems ◽  
Private Key ◽  
Main Component

Abstract. Logarithmic signatures for finite groups are the essential constituent of public key cryptosystems and . Especially they form the main component of the private key of . Regarding the use of , it has become a vital issue to construct new classes of logarithmic signatures having features that do not share with the well-known class of transversal or fused transversal logarithmic signatures. For this purpose Baumeister and de Wiljes recently presented an interesting method of constructing aperiodic logarithmic signatures for abelian groups. In this paper we introduce the concept of strongly aperiodic logarithmic signatures and show their constructions for abelian p-groups on the basis of the Baumeister–de Wiljes method.

scholarly journals LOGARITHMIC SIGNATURES FOR ABELIAN GROUPS AND THEIR FACTORIZATION

2013 ◽  
Vol 57 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Pavol Svaba ◽  
Tran van Trung ◽  
Paul Wolf
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Efficient Algorithms ◽  
Finite Abelian Groups ◽  
Logarithmic Signatures ◽  
Vital Importance ◽  
Essential Component ◽  
Factorization Algorithms ◽  
Factoring Algorithm

ABSTRACT Factorizable logarithmic signatures for finite groups are the essential component of the cryptosystems MST1 and MST3. The problem of finding efficient algorithms for factoring group elements with respect to a given class of logarithmic signatures is therefore of vital importance in the investigation of these cryptosystems. In this paper we are concerned about the factorization algorithms with respect to transversal and fused transversal logarithmic signatures for finite abelian groups. More precisely we present algorithms and their complexity for factoring group elements with respect to these classes of logarithmic signatures. In particular, we show a factoring algorithm with respect to the class of fused transversal logarithmic signatures and also its complexity based on an idea of Blackburn, Cid and Mullan for finite abelian groups.

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.

On the Security of Two Public Key Cryptosystems Using Non-Abelian Groups

2004 ◽  
Vol 32 (1-3) ◽  
pp. 207-216
Author(s):  
M. I. González Vasco ◽  
D. Hofheinz ◽  
C. Martínez ◽  
R. Steinwandt
Keyword(s):  
Abelian Groups ◽  
Public Key ◽  
Public Key Cryptosystems

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 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

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

scholarly journals BESTIE: Broadcast Encryption Scheme for Tiny IoT Equipment

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1389
Author(s):  
Jiwon Lee ◽  
Jihye Kim ◽  
Hyunok Oh
Keyword(s):  
The Other ◽  
Public Key ◽  
Broadcast Encryption ◽  
Encryption Scheme ◽  
The Public ◽  
Private Key ◽  
Diffie Hellman ◽  
The Standard Model ◽  
Encryption Decryption ◽  
Subset Difference

In public key broadcast encryption, anyone can securely transmit a message to a group of receivers such that privileged users can decrypt it. The three important parameters of the broadcast encryption scheme are the length of the ciphertext, the size of private/public key, and the performance of encryption/decryption. It is suggested to decrease them as much as possible; however, it turns out that decreasing one increases the other in most schemes. This paper proposes a new broadcast encryption scheme for tiny Internet of Things (IoT) equipment (BESTIE), minimizing the private key size in each user. In the proposed scheme, the private key size is O(logn), the public key size is O(logn), the encryption time per subset is O(logn), the decryption time is O(logn), and the ciphertext text size is O(r), where n denotes the maximum number of users, and r indicates the number of revoked users. The proposed scheme is the first subset difference-based broadcast encryption scheme to reduce the private key size O(logn) without sacrificing the other parameters. We prove that our proposed scheme is secure under q-Simplified Multi-Exponent Bilinear Diffie-Hellman (q-SMEBDH) in the standard model.

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