scholarly journals Sieve Method for Polynomial Linear Equivalence

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Baocang Wang ◽  
Yupu Hu
Keyword(s):  
Finite Field ◽  
Linear Transformation ◽  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Sieve Method ◽  
Polynomial Maps ◽  
Algebraic Properties ◽  
Encryption Schemes ◽  
Multivariate Public Key

We consider the polynomial linear equivalence (PLE) problem arising from the multivariate public key cryptography, which is defined as to find an invertible linear transformationℒsatisfying𝒫=𝒮∘ℒfor given nonlinear polynomial maps𝒫and𝒮over a finite field𝔽q. Some cryptographic and algebraic properties of PLE are discussed, and from the properties we derive three sieves called multiplicative, differential, and additive sieves. By combining the three sieves, we propose a sieve method for the PLE problem. As an application of our sieve method, we show that it is infeasible to construct public key encryption schemes from the PLE problem.

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.

An applications of signed quadratic residues in public key cryptography

2018 ◽  
Vol 10 (06) ◽  
pp. 1850081
Author(s):  
Pinkimani Goswami ◽  
Madan Mohan Singh
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Quadratic Residues ◽  
Encryption Schemes

At Eurocrypt ’02, Cramer and Shoup introduced the idea of public key encryption schemes with double decryption mechanism (DD-PKE) and at Asiacrypt ’03, Bresson, Catalano and Pointcheval revisited the notion of DD-PKE. They proposed the first DD-PKE scheme (called BCP cryptosystem) over the group of quadratic residues. In this paper, we point out an attack against BCP cryptosystem and propose a secure variant constructed over the group of signed quadratic residues (SQR).

scholarly journals Building Secure Public Key Encryption Scheme from Hidden Field Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yuan Ping ◽  
Baocang Wang ◽  
Yuehua Yang ◽  
Shengli Tian
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Encryption Scheme ◽  
Public Key Encryption ◽  
Field Equations ◽  
Quadratic Equations ◽  
New Variant ◽  
Multivariate Public Key ◽  
Np Hardness

Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE) family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose a new variant of the HFE scheme by considering the special equation x2=x defined over the finite field F3 when x=0,1. We observe that the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. It is shown that the proposed public key encryption scheme is secure against known attacks including the MinRank attack, the algebraic attacks, and the linearization equations attacks. The proposal gains some advantages over the original HFE scheme with respect to the encryption speed and public key size.

The Design of Public Key Cryptography for Key Exchange Base on Multivariate Equations

2014 ◽  
Vol 513-517 ◽  
pp. 552-554 ◽  
Author(s):  
Chang Ming Liu ◽  
Lei Zhao ◽  
Yan Jun Sun
Keyword(s):  
Public Key Cryptography ◽  
Key Exchange ◽  
Public Key ◽  
Research Issue ◽  
Public Key Encryption ◽  
Important Research ◽  
Exchange Method ◽  
Open Standard ◽  
Multivariate Public Key ◽  
Encryption Method

. Public key encryption method contrasts with traditional encryption method has the advantage of very powerful, especially in applications and network security. With the development of these years public key encryption method is a mature, open, standard security mechanism for network encryption and digital signatures. The key exchange plays an important role in cryptography. It is an important research issue that how to ensure the security of key exchange. In this paper we present a key exchange method based on multivariate public key cryptography.

Public-Key Encryption In The Standard Model Against Strong Leakage Adversary

2020 ◽  
Vol 63 (12) ◽  
pp. 1904-1914
Author(s):  
Janaka Alawatugoda
Keyword(s):  
Standard Model ◽  
Building Blocks ◽  
Public Key ◽  
Log P ◽  
Encryption Scheme ◽  
Public Key Encryption ◽  
Security Parameter ◽  
The Standard Model ◽  
Encryption Schemes ◽  
Leakage Resilient

Abstract Over the years, security against adaptively chosen-ciphertext attacks (CCA2) is considered as the strongest security definition for public-key encryption schemes. With the uprise of side-channel attacks, new security definitions are proposed, addressing leakage of secret keys together with the standard CCA2 definition. Among the new security definitions, security against continuous and after-the-fact leakage-resilient CCA2 can be considered as the strongest security definition, which is called as security against (continuous) adaptively chosen-ciphertext leakage attacks (continuous CCLA2). In this paper, we present a construction of a public-key encryption scheme, namely LR-PKE, which satisfies the aforementioned security definition. The security of our public-key encryption scheme is proven in the standard model, under decision BDH assumption. Thus, we emphasize that our public-key encryption scheme LR-PKE is (continuous) CCLA2-secure in the standard model. For our construction of LR-PKE, we have used a strong one-time signature scheme and a leakage-resilient refreshing protocol as underlying building blocks. The leakage bound is $0.15n\log p -1$ bits per leakage query, for a security parameter $k$ and a statistical security parameter $n$, such that $\log p \geq k$ and $n$ is a function of $k$. It is possible to see that LR-PKE is efficient enough to be used for real-world usage.

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