scholarly journals Preimage Selective Trapdoor Function: How to Repair an Easy Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Baocang Wang
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Constructive Method ◽  
Key Recovery ◽  
Public Key Cryptosystems ◽  
Cryptographic Primitive ◽  
The One ◽  
Trapdoor Function ◽  
One Way Function ◽  
Encryption Function

Public key cryptosystems are constructed by embedding a trapdoor into a one-way function. So, the one-wayness and the trapdoorness are vital to public key cryptography. In this paper, we propose a novel public key cryptographic primitive called preimage selective trapdoor function. This scenario allows to use exponentially many preimage to hide a plaintext even if the underlying function is not one-way. The compact knapsack problem is used to construct a probabilistic public key cryptosystem, the underlying encryption function of which is proven to be preimage selective trapdoor one-way functions under some linearization attack models. The constructive method can guarantee the noninjectivity of the underlying encryption function and the unique decipherability for ciphertexts simultaneously. It is heuristically argued that the security of the proposal cannot be compromised by a polynomial-time adversary even if the compact knapsack is easy to solve. We failed to provide any provable security results about the proposal; however, heuristic illustrations show that the proposal is secure against some known attacks including brute force attacks, linearization attacks, and key-recovery attacks. The proposal turns out to have acceptable key sizes and performs efficiently and hence is practical.

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.

One-Way Function Construction Based on the MQ Problem and Logic Function

2012 ◽  
Vol 220-223 ◽  
pp. 2360-2363
Author(s):  
Yan Jun Sun ◽  
Chang Ming Liu ◽  
Hai Yu Li ◽  
Zhe Yuan
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Logic Function ◽  
The Public ◽  
Relative Safety ◽  
Core Function ◽  
Long Time ◽  
New Type ◽  
One Way Function

Multivariate quadratic based public-key cryptography called MQ problem which based on calculation of a secure cryptography of multivariate equations and MQ cryptography security is based on the difficulty of the solution of multivariate equations. But computer and mathematician scientists put a lot of effort and a long time to research MQ cryptography and they have proved that MQ cryptography is NP complete problem. Therefore, before the P problem Equal to the NP problem we do not figure out selected multivariate equations by random in polynomial time. So we can use this feature to construct the relative safety method of the public key encryption. A new type of public-key cryptosystem has been brought up in this paper that one-way shell core function which has such advantages as more security and flexibility, and provides a more inclusive public-key cryptosystem.

scholarly journals Estimation of Various Scalar Multiplication Algorithms in ECC

2019 ◽  
Vol 8 (6S4) ◽  
pp. 183-186
Keyword(s):  
High Performance ◽  
Additive Group ◽  
Public Key Cryptography ◽  
Scalar Multiplication ◽  
Public Key ◽  
Integer Multiple ◽  
Public Key Cryptosystems ◽  
Fast Processing ◽  
Implementation Costs ◽  
Modern Era

this modern era of security, public key cryptography is quite popular and holds a great significance. Various public key cryptosystems are available in today’s environment such as RSA and ECC. Elliptic Curve cryptography is beneficial in a lot of aspects which includes shorter key as compared to other cryptosystems, high security, fast processing speed, low storage, low bandwidth, small software print, low hardware implementation costs, high performance. The main and the costliest step in ECC is the Scalar Multiplication. In scalar multiplication, integer multiple of an element in additive group of elliptic curves is calculated. In this paper, we compare various available algorithms for the scalar multiplication used in ECC.

Recent Developments in Cryptography

2018 ◽  
pp. 1-22 ◽  
Author(s):  
Kannan Balasubramanian
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Discrete Logarithms ◽  
Public Key Cryptosystems ◽  
Multivariate Cryptography ◽  
Public Keys ◽  
Recent Developments ◽  
Key Exchange Protocols ◽  
Lattice Based Cryptography ◽  
Public Key Signatures

The field of cryptography has seen enormous changes ever since the invention of Public Key Cryptography by Diffie and Hellman. The algorithms for complex problems like integer factorization, Discrete Logarithms and Elliptic Curve Discrete Logarithms have improved tremendously making way for attackers to crack cryptosystems previously thought were unsolvable. Newer Methods have also been invented like Lattice based cryptography, Code based cryptography, Hash based cryptography and Multivariate cryptography. With the invention of newer public Key cryptosystems, the signature systems making use of public key signatures have enabled authentication of individuals based on public keys. The Key Distribution mechanisms including the Key Exchange protocols and Public Key infrastructure have contributed to the development of algorithms in this area. This chapter also surveys the developments in the area of identity Based Cryptography, Group Based Cryptography and Chaos Based Cryptography.

Blind Signature Based on Discrete Logarithm Type Cryptosystem

2011 ◽  
Vol 204-210 ◽  
pp. 1318-1321
Author(s):  
Xuan Wu Zhou ◽  
Yan Fu
Keyword(s):  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Security Level ◽  
Signature Schemes ◽  
Public Key Cryptosystems ◽  
Trapdoor Function ◽  
Asymmetric Cryptosystem

Discrete logarithm problem is an important trapdoor function to design asymmetric cryptosystem, and some fast public key cryptosystems have been designed based on it. In the paper, we introduced fast asymmetric cryptosystem into the designing and analyzing of blind signature, and presented improved blind signature schemes based on ECC (Elliptic Curves Cryptosystem). The trapdoor function of the blind signatures is based on ECDLP (Elliptic Curves Discrete Logarithm Problem), and the algorithms of the scheme make full use of the superiority of ECC, such as high efficiency and short key length. The improved blind signature schemes can achieve the same security level with less storing space, smaller communication band-width and less overheads regarding software and hardware application. Furthermore, the algorithms in the schemes can be generalized into other public key cryptosystems based on discrete logarithm problem without any influence to efficiency or security.

Provable Security for Public Key Cryptosystems

2016 ◽  
pp. 317-341
Author(s):  
Syed Taqi Ali
Keyword(s):  
Provable Security ◽  
Ad Hoc ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Public Key Cryptosystems ◽  
Security Proofs ◽  
Security Proof ◽  
The One

In the early years after the invention of public key cryptography by Diffie and Hellman in 1976, the design and evaluation of public key cryptosystems has been done merely in ad-hoc manner based on trial and error. The public key cryptosystem said to be secure as long as there is no successful cryptanalytic attack on it. But due to various successful attacks on the cryptosystems after development, the cryptographic community understood that this ad-hoc approach might not be good enough. The paradigm of provable security is an attempt to get rid of ad hoc design. The goals of provable security are to define appropriate models of security on the one hand, and to develop cryptographic designs that can be proven to be secure within the defined models on the other. There are two general approaches for structuring the security proof. One is reductionist approach and other is game-based approach. In these approaches, the security proofs reduce a well known problem (such as discrete logarithm, RSA) to an attack against a proposed cryptosystem. With this approach, the security of public key cryptosystem can be proved formally under the various models viz. random oracle model, generic group model and standard model. In this chapter, we will briefly explain these approaches along with the security proofs of well known public key cryptosystems under the appropriate model.

RSA-Public Key Cryptosystems Based on Quadratic Equations in Finite Field

2014 ◽  
pp. 238-258
Author(s):  
Sattar B. Sadkhan Al Maliky ◽  
Luay H. Al-Siwidi
Keyword(s):  
Finite Field ◽  
Chinese Remainder Theorem ◽  
Quadratic Equation ◽  
Public Key ◽  
Factorization Problem ◽  
Quadratic Equations ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Mathematical Problems ◽  
One Way Function

The importance of Public Key Cryptosystems (PKCs) in the cryptography field is well known. They represent a great revolution in this field. The PKCs depend mainly on mathematical problems, like factorization problem, and a trapdoor one-way function problem. Rivest, Shamir, and Adleman (RSA) PKC systems are based on factorization mathematical problems. There are many types of RSA cryptosystems. Rabin's Cryptosystem is considered one example of this type, which is based on using the square order (quadratic equation) in encryption function. Many cryptosystems (since 1978) were implemented under such a mathematical approach. This chapter provides an illustration of the variants of RSA-Public Key Cryptosystems based on quadratic equations in Finite Field, describing their key generation, encryption, and decryption processes. In addition, the chapter illustrates a proposed general formula for the equation describing these different types and a proposed generalization for the Chinese Remainder Theorem.

Karatsuba-ZOT Multiplication Algorithm and its Application in Cryptography

2012 ◽  
Vol 241-244 ◽  
pp. 2417-2423 ◽  
Author(s):  
Shahram Jahani ◽  
Azman Samsudin
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Large Integer ◽  
Compact Representation ◽  
Number Representation ◽  
The Public ◽  
Public Key Cryptosystems ◽  
Multiplication Algorithm ◽  
Multiplication Operation ◽  
Integer Multiplication

The number theory based cryptography algorithms are the most commonly used public-key cryptosystems. One of the fundamental arithmetic operations for such systems is the large integer multiplication. The efficiency of these cryptosystems is directly related to the efficiency of this large integer multiplication operation. Classical multiplication algorithm and Karatsuba multiplication algorithm, and their hybrid, are among the most popular multiplication algorithms used for this purpose. In this paper, we propose a hybrid of Karatsuba and a classical-based multiplication algorithm, enhanced by a new number representation system. The new number representation, known as "Big-Digits”, is used to carry out the sub-multiplication operation in the new multiplication algorithm. Big-Digits has a compact representation with lower Hamming weight. As the result, the number of sub-multiplication operations for the multiplication algorithm that is based on the Big-Digits representation is significantly reduced. Our results show that the proposed multiplication algorithm is significantly faster than the classical, Karasuba and the hybrid of Karatsuba-Classical multiplication algorithms within the implementation domain of the public-key cryptography.

scholarly journals Design of a Modular Multiplier for Public-Key Cryptography Applications Using Residue Number System and Signed-Digit Representation

2020 ◽  
Author(s):  
Mohammad Hizzani
Keyword(s):  
Public Key Cryptography ◽  
Number System ◽  
Residue Number System ◽  
Public Key ◽  
Modular Multiplication ◽  
Secret Key ◽  
Public Key Cryptosystems ◽  
Number Systems ◽  
Wide Range ◽  
Residue Number

Public-Key Cryptosystems are prone to wide range of cryptanalyses due to its property of having key pairs one of them is public. Therefore, the recommended length of these keys is extremely large (e.g. in RSA and D-H the key is at least 2048 bits long) and this leads the computation of such cryptosystems to be slower than the secret-key cryptosystems (i.e. AES and AES-family). Since, the key operation in such systems is the modular multiplication; in this research a novel design for the modular multiplication based on the Montgomery Multiplication, the Residue Number Systems for moduli of any form, and the Signed-Digit Representation is proposed. The proposed design outperforms the current designs in the literature in terms of delay with at least 28% faster for the key of 2048 bits long. Up to our knowledge, this design is the first design that utilizes Signed-Digit Representation with the Residue Number System for moduli of any form.

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