Variants of the Diffie-Hellman Problem

2018 ◽  
pp. 40-54
Author(s):  
Kannan Balasubramanian
Keyword(s):  
Elliptic Curve ◽  
Cyclic Group ◽  
Diffie Hellman

Many variations of the Diffie-Hellman problem exist that can be shown to be equivalent to one another. We consider following variations of Diffie-Hellman problem: square computational and Square decisional Diffie-Hellman problem, inverse computational and inverse computational decisional Diffie-Hellman problem and divisible computational and divisible decisional Diffie-Hellman problem. It can be shown that all variations of computational Diffie-Hellman problem are equivalent to the classic computational Diffie-Hellman problem if the order of a underlying cyclic group is a large prime. We also describe other variations of the Diffie-Hellman problems like the Group Diffie-Hellman problem, bilinear Diffie-Hellman problem and the Elliptic Curve Diffie-Hellman problem in this chapter.

scholarly journals Optimized CSIDH Implementation Using a 2-Torsion Point

Cryptography ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 20 ◽  
Author(s):  
Donghoe Heo ◽  
Suhri Kim ◽  
Kisoon Yoon ◽  
Young-Ho Park ◽  
Seokhie Hong
Keyword(s):  
Elliptic Curve ◽  
Group Action ◽  
Large Degree ◽  
Transitive Group ◽  
Optimization Method ◽  
Torsion Point ◽  
Torsion Points ◽  
Diffie Hellman ◽  
Odd Degree ◽  
Montgomery Curve

The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. Because the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) requires odd-degree isogenies up to at least 587, this inefficiency is the main bottleneck of using a Montgomery curve for CSIDH. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH, in which the three rational two-torsion points exist. By using the proposed parameters, the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a two-torsion point. We also proved that the CSIDH while using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.4% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved while only using Montgomery curves.

scholarly journals A novel Security Aware Sensitive Encrypted Storage approach to improve the encryption of big data

2020 ◽  
Author(s):  
Gitanjali Gupta ◽  
Kamlesh Lakhwani
Keyword(s):  
Elliptic Curve ◽  
Computing Time ◽  
Operating Time ◽  
Cloud Service ◽  
Security And Privacy ◽  
Financial Industry ◽  
Sensitive Data ◽  
Machine Learning Classification ◽  
Classification Technique ◽  
Diffie Hellman

Abstract The data security and privacy have become a critical issue that restricts many cloud applications. One of the major concerns about security and privacy is the fact that cloud operators have the opportunity to access sensitive data. This concern dramatically increases user anxieties and reduces the acceptability of cloud computing in many areas, such as the financial industry and government agencies. This paper focuses on this issue and proposes an intelligent approach to cryptography, which would make it impossible for cloud service operators to reach sensitive data directly. The suggested method divides the file with precision using an intelligent classification technique. An alternative approach is designed to determine whether data packets need splitting to shorten operating time and reduce storage space. Our experimental assessments of both safety and efficiency performance and experimental results show that our approach can effectively address major cloud hazards and that it requires an acceptable computing time using an intelligent machine learning classification technique. We have proposed a novel approach entitled as a model for Security Aware Sensitive Encrypted Storage (SA-SES). In this model, we used our proposed algorithms, including Convolution Neural Network with Logistic Regression (CNN-LR), Elliptic-curve Diffie–Hellman-Shifted Adaption Homomorphism Encryption (ECDH-SAHE) and Elliptic-curve Diffie–Hellman-Shifted Adaption Homomorphism Decryption (ECDH-SAHD) .

Problems in Cryptography and Cryptanalysis

2018 ◽  
pp. 23-39
Author(s):  
Kannan Balasubramanian ◽  
Rajakani M.
Keyword(s):  
Elliptic Curve ◽  
Optimization Problems ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Random Number Generators ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem ◽  
Diffie Hellman Key Exchange ◽  
Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

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