The parallel improved Lanczos method for integer factorization over finite fields for public key cryptosystems

2002 ◽  
Author(s):  
L.T. Yang ◽  
R.P. Brent
Keyword(s):  
Finite Fields ◽  
Lanczos Method ◽  
Public Key ◽  
Integer Factorization ◽  
Public Key Cryptosystems

scholarly journals TOTAL EMBEDDED SURFACE ATTACK ON MPKCS FROM DIOPHANTINE EQUATIONS

2018 ◽  
Author(s):  
Adama Diene
Keyword(s):  
Finite Fields ◽  
Diophantine Equations ◽  
Computer Experiments ◽  
Lower Degree ◽  
Public Key ◽  
Public Key Cryptosystems ◽  
Embedded Surfaces ◽  
Characteristic 2 ◽  
Multivariate Public Key

In 2011, Gao and Heindl presented a new multivariate public key cryptosystems from Diophantine equations. However, by observing the decryption process, Ding et al. found recently that some special embedded surfaces could be used to decrypt the message efficiently. They showed that the three systems proposed by Gao and Heindl could be broken at the complexity of 252,261 and 252 respectively. But, the attack by Ding et al. can not implemented on a usual PC. It was mainly theoretical and worked only for finite fields of characteristic 2. In this paper, We present a practical attack on this family of multivariate public key cryptosystems. Our attack is implemented on a PC and it works for all finite fields. By doing computer experiments, we find many new lower-degree embedded surfaces which help us to break the cryptosystem.

scholarly journals Practical IBC using Hybrid-Mode Problems: Factoring and Discrete Logarithm

2015 ◽  
Vol 4 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Chandrashekhar Meshram
Keyword(s):  
Discrete Logarithm ◽  
Public Key ◽  
Integer Factorization ◽  
Hybrid Mode ◽  
Factorization Problem ◽  
The Public ◽  
Public Key Cryptosystems ◽  
Integer Factorization Problem ◽  
Security Challenges

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system.

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.

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