scholarly journals Provably-Secure (Chinese Government) SM2 and Simplified SM2 Key Exchange Protocols

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ang Yang ◽  
Junghyun Nam ◽  
Moonseong Kim ◽  
Kim-Kwang Raymond Choo
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Chinese Government ◽  
Government Agencies ◽  
Security Models ◽  
Security Proof ◽  
Key Exchange Protocols ◽  
Security Properties ◽  
Commercial Applications ◽  
Provably Secure

We revisit the SM2 protocol, which is widely used in Chinese commercial applications and by Chinese government agencies. Although it is by now standard practice for protocol designers to provide security proofs in widely accepted security models in order to assure protocol implementers of their security properties, the SM2 protocol does not have a proof of security. In this paper, we prove the security of the SM2 protocol in the widely accepted indistinguishability-based Bellare-Rogaway model under the elliptic curve discrete logarithm problem (ECDLP) assumption. We also present a simplified and more efficient version of the SM2 protocol with an accompanying security proof.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

scholarly journals Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?

2020 ◽  
Vol 14 (1) ◽  
pp. 293-306
Author(s):  
Claire Delaplace ◽  
Alexander May
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Discrete Logarithm ◽  
Field Size ◽  
Square Root ◽  
Multivariate Polynomial ◽  
Bivariate Polynomial ◽  
Testing Problem ◽  
Polynomial Zero ◽  
Representation Technique

AbstractWe give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields a p1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to an o(p)-algorithm for ECDLP, since all involved lists are of size as small as $\begin{array}{} p^{\frac 3 4}, \end{array}$ only their computation is yet too costly.

(t,k,n) Multi-Blind Proxy Signature Scheme on Elliptic Curve

2011 ◽  
Vol 130-134 ◽  
pp. 291-294
Author(s):  
Guang Liang Liu ◽  
Sheng Xian Xie ◽  
Wei Fu
Keyword(s):  
Elliptic Curve ◽  
Secret Sharing ◽  
Proxy Signature ◽  
Elliptic Curve Cryptosystem ◽  
Secret Sharing Scheme ◽  
Signature Scheme ◽  
Forgery Attack ◽  
Threshold Secret Sharing ◽  
Sharing Scheme ◽  
Security Properties

On the elliptic curve cryptosystem proposed a new multi-proxy signature scheme - (t, k, n) threshold blind proxy signature scheme.In new program blind proxy signature and (t,k,n) threshold secret sharing scheme will be combined, and will not over-concentration of the rights of the blind proxy signer .Computation of the program is small, security is high, the achieve efficiency and the utility is better .can prevent a malicious user's forgery attack and have the security properties of proxy signature.

A Lightweight and Provably Secure Key Agreement System for a Smart Grid With Elliptic Curve Cryptography

2019 ◽  
Vol 13 (3) ◽  
pp. 2830-2838 ◽  
Author(s):  
Fan Wu ◽  
Lili Xu ◽  
Xiong Li ◽  
Saru Kumari ◽  
Marimuthu Karuppiah ◽  
...  
Keyword(s):  
Smart Grid ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Key Agreement ◽  
Provably Secure
Sign in / Sign up

Export Citation Format

Share Document