Proxy-Protected Proxy Multi-Signature Based on Elliptic Curve

2014 ◽  
Vol 3 (1) ◽  
pp. 67
Author(s):  
Manoj Kumar Chande ◽  
Balwant Singh Thakur
Keyword(s):  
Low Power ◽  
Elliptic Curve ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Proxy Signature ◽  
Entire Group ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Basic Properties ◽  
Digital Signature Algorithm

In this work, we propose a proxy-protected proxy multi-signature scheme based on EllipticCurve Digital Signature Algorithm (ECDSA), which aims at providing data authenticity,integrity, and non-repudiation to satisfy the basic properties of partial delegation proxy signaturedescribed by Mambo et al. as well as strong proxy signature properties defined byLee et. al. The proposed signing/verifying scheme combines the advantages of proxyprotectedsignature and multi-signature scheme. The security of the proposed schemes isbased on the difficulty of breaking the elliptic curve discrete logarithm problem (ECDLP).The scheme proposed is faster and secure than the multi-signature based on factoring ordiscrete logarithm problem (DLP). The final multi-signature of a message can be verifiedindividually for each signer or collectively for a subgroup or entire group as well. Finally,the proposed proxy-protected proxy multi-signature schemes can be used in E-commerceand E-government application, which can be implemented using low power and small processingdevices.

A Blind Proxy Re-Signatures Scheme Based on Random Oracle

2011 ◽  
Vol 204-210 ◽  
pp. 1062-1065 ◽  
Author(s):  
Yu Qiao Deng
Keyword(s):  
Digital Signature ◽  
Digital Signatures ◽  
Random Oracle ◽  
Proxy Signature ◽  
Public Key ◽  
Signature Scheme ◽  
Signature Schemes

Digital signature schemes allow a signer to transform any message into a signed message, such that anyone can verify the validity of the signed message using the signer’s public key, but only the signer can generate signed messages. A proxy re-signature, which is a type of digital signatures, has significant applications in many areas. Proxy signature scheme was first introduced by Blaze, Bleumer, and Strauss, but that scheme is inefficient and with limited features. After that, some Proxy re-signature schemes were proposed by researchers. This paper constructs a blind proxy re-signatures scheme. Comparing to the previous proxy re-signature schemes, the scheme adds a message blinded feature, and then the security of the scheme is proven.

Cryptographic Primitives

2020 ◽  
pp. 57-134
Author(s):  
Andreas Bolfing
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Encryption ◽  
Cryptographic Primitives ◽  
Digital Signature Algorithm ◽  
Digital Signature Scheme ◽  
Current Standards

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and trapdoor functions, considering the three major public-key encryption families like integer factorization, discrete logarithm and elliptic curve schemes. This is followed by an introduction to hash functions which are applied to construct Merkle trees and digital signature schemes. As modern cryptoschemes are commonly based on elliptic curves, the chapter then introduces elliptic curve cryptography which is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It considers the hardness of the ECDLP and the possible attacks against it, showing how to find suitable domain parameters to construct cryptographically strong elliptic curves. This is followed by the discussion of elliptic curve domain parameters which are recommended by current standards. Finally, it introduces the Elliptic Curve Digital Signature Algorithm (ECDSA), the elliptic curve digital signature scheme.

A Proxy Signature Based on the Difficulty of Solving Equations of Higher on Quaternion Ring

2014 ◽  
Vol 513-517 ◽  
pp. 1951-1954
Author(s):  
Hui Shao ◽  
Fan Zhang ◽  
Xiao Zhuan Yuan ◽  
Chuan Da Qi
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Proxy Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Multivariate Functions ◽  
Actual Application ◽  
Solving Equations ◽  
Computational Difficulty ◽  
High Degree

At present, all the applied schemes of the digital signature schemes based on the research of the factoring problem, discrete logarithm problem, and discrete logarithm problem on the elliptic curve cant meet the demand of actual application. This paper introduces the knowledge to the digital signature and studies the signature scheme based on the quaternion ring. The scheme introduces the multivariate functions of high degree to non-commutative quaternion ring, and its safety based on the computational difficulty to solve the the multivariate equations of high degree. The article applies this thought to proxy signature and designs a proxy signature scheme. Finally, it gives the safety analysis of the new scheme.

scholarly journals Post–Quantum Cryptography – A Primer

2020 ◽  
Author(s):  
P. V. Ananda Mohana
Keyword(s):  
Elliptic Curve ◽  
Quantum Cryptography ◽  
Digital Signature ◽  
Information Transfer ◽  
Discrete Logarithm ◽  
Digital Signatures ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Digital Signature Algorithm ◽  
Post Quantum Cryptography

Traditionally, information security needed encryption, authentication, key management, non-repudiation and authorization which were being met using several techniques. Standardization of algorithms by National Institute of Standards and Technology (NIST) has facilitated international communication for banking and information transfer using these standards. Encryption can be carried out using Advanced Encryption Standard (AES) using variable block lengths (128, 192 or 256 bits) and variable key lengths (128, 192 or 256 bits). Solutions for light weight applications such as those for Internet of Things (IoT) are also being standardized. Message integrity is possible using host of hash algorithms such as SHA-1, SHA-2 etc., and more recently using SHA-3 algorithm. Authentication is possible using well known Rivest-Shamir-Adleman (RSA) algorithm needing 2048/4096 bit operations. Elliptic Curve Cryptography (ECC) is also quite popular and used in several practical systems such as WhatsApp, Blackberry etc. Key exchange is possible using Diffie-Hellman algorithm and its variations. Digital Signatures can be carried out using RSA algorithm or Elliptic Curve Digital Signature Algorithm (ECDSA) or DSA (Digital Signature Algorithm). All these algorithms derive security from difficulty in solving some mathematical problems such as factorization problem or discrete logarithm problem. Though published literature gives evidence of solving factorization problem upto 768 bits only, it is believed that using Quantum computers, these problems could be solved by the end of this decade. This is due to availability of the pioneering work of Shor and Grover [1]. For factoring an integer of N bits, Shor’s algorithm takes quantum gates. As such, there is ever growing interest in being ready for the next decade with algorithms that may resist attacks in the quantum computer era. NIST has foreseen this need and has invited proposals from researchers all over the world. In the first round, about 66 submissions were received which have been scrutinized for completeness of submissions , novelty of the approach and security and 25 of these were promote to second round to improve based on the comments received on the first round submission. These will be analyzed for security and some will be selected for final recommendation for use by industry. These are for encryption/decryption, key agreement, hashing and Digital Signatures for both hardware and software implementations. In this paper, we present a brief survey of the state of the art in post-Quantum Cryptography (PQC) followed by study of one of technique referred to as Learning With Errors (LWE) in some detail.

MSEC Scheme for Providing Secure Data Transformation Using Coding Technique

2018 ◽  
Vol 7 (2.32) ◽  
pp. 264
Author(s):  
Ram Kumar.J ◽  
Veena Avutu ◽  
Anurag V
Keyword(s):  
Elliptic Curve ◽  
Operating Systems ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Data Encryption ◽  
Discrete Problem ◽  
The Public ◽  
General Terms ◽  
Systems Security ◽  
Digital Signature Algorithm

The MSEC which is the short from of Multiple Signature Elliptic curve Algorithm by using coding tchnique. It can be Digital Signature Algorithm (DSA) elliptic curve analogue. In 1999, the acknowledgement done such as standard of the ANSI. After that in 2000, it again acknowledged like benchmarks of the IEEE as well as NIST. Like this it again acknowledged in the year 1998 in the name of standard of ISO, as well as it was under thought to incorporate in some of other principles of ISO. unlike logarithm of standard discrete problem as well as number of issues of factorization, none of the  calculation of the sub exponential-time can called  to issue of the elliptic bend discrete logarithm. Similarly per-keybit quality can be generously much prominent  if consider the calculation which uses bends of  elliptic. This implemented system if or  executing the ANSI X9.62 ECDSA  on the bend of elliptic P-192, as well as talking regarding the relevant V of the security. Classes A as well as Subject D.4.6v Descriptors  which is Operating Systems: Security as well as Protection – getting  for  controlling, control of the confirmation cryptographic; E.3 [Data]:cryptosystem of the Data Encryption which is the Public key and standards. Algorithms, of the General Terms Security.  

A Provably Secure ID-Based Designated Verifier Proxy Signature Scheme Based on DLP

2013 ◽  
Vol 411-414 ◽  
pp. 721-724 ◽  
Author(s):  
Bao Dian Wei
Keyword(s):  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Proxy Signature ◽  
Signature Scheme ◽  
Signature Schemes ◽  
The Common ◽  
Designated Verifier ◽  
Provably Secure

Most of the existing ID-based designated verifier proxy signature schemes are implemented with pairings. The computation of parings is still much more expensive than the common modular multiplications and exponentiations. To obtain better efficiency, we construct an efficient ID-based DVPS scheme without pairings. The scheme is designed based on the hardness of the discrete logarithm problems. It is proven secure against adaptively chosen message attacks, in the random oracle model.

scholarly journals The Order of Edwards and Montgomery Curves

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Log P ◽  
Edwards Curves ◽  
Digital Signature Algorithm ◽  
Supersingular Curves ◽  
Edwards Curve

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA) [2]. It is well known that the problem of discrete logarithm is NP-hard on group on elliptic curve (EC) [5]. The orders of groups of an algebraic affine and projective curves of Edwards [3, 9] over the finite field Fpn is studied by us. We research Edwards algebraic curves over a finite field, which are one of the most promising supports of sets of points which are used for fast group operations [1]. We construct a new method for counting the order of an Edwards curve [F ] d p E over a finite field Fp . It should be noted that this method can be applied to the order of elliptic curves due to the birational equivalence between elliptic curves and Edwards curves. The method we have proposed has much less complexity 22 O p log p at not large values p in comparison with the best Schoof basic algorithm with complexity 8 2 O(log pn ) , as well as a variant of the Schoof algorithm that uses fast arithmetic, which has complexity 42O(log pn ) , but works only for Elkis or Atkin primes. We not only find a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, but we additionally find a general formula by which one can determine whether a curve [F ] d p E is supersingular over this field or not. The symmetric of the Edwards curve form and the parity of all degrees made it possible to represent the shape curves and apply the method of calculating the residual coincidences. A birational isomorphism between the Montgomery curve and the Edwards curve is also constructed. A oneto- one correspondence between the Edwards supersingular curves and Montgomery supersingular curves is established. The criterion of supersingularity for Edwards curves is found over F pn .

scholarly journals A New Method for Designing Post-Quantum Signature Schemes

2020 ◽  
pp. 747-754
Author(s):  
Minh Nguyen Hieu ◽  
◽  
Moldovyan Alexander Andreevich ◽  
Moldovyan Nikolay Andreevich ◽  
Canh Hoang Ngoc
Keyword(s):  
Digital Signature ◽  
Quantum Computer ◽  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Quantum Signature ◽  
Discrete Logarithm Problem ◽  
New Method ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Computational Difficulty

The current standards of the digital signature algorithms are based on computational difficulty of the discrete logarithm and factorization problems. Expected appearance in near future of the quantum computer that is able to solve in polynomial time each of the said computational puts forward the actual task of the development of the post-quantum signature algorithms that resist the attacks using the quantum computers. Recently, the signature schemes based on the hidden discrete logarithm problem set in finite non-commutative associative algebras had been proposed. The paper is devoted to a further development of this approach and introduces a new practical post-quantum signature scheme possessing small size of public key and signature. The main contribution of the paper is the developed new method for defining the hidden discrete logarithm problem that allows applying the finite commutative groups as algebraic support of the post-quantum digital signature schemes. The method uses idea of applying multipliers that mask the periodicity connected with the value of discrete logarithm of periodic functions set on the base of the public parameters of the signature scheme. The finite 4-dimensional commutative associative algebra the multiplicative group of which possesses 4-dimensional cyclicity is used as algebraic support of the developed signature scheme.

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