scholarly journals A Novel Niederreiter-like cryptosystem based on the (u|u + υ)-construction codes

2021 ◽  
Vol 55 ◽  
pp. 10
Author(s):  
Roumaissa Mahdjoubi ◽  
Pierre Louis Cayrel ◽  
Sedat Akleylek ◽  
Guenda Kenza
Keyword(s):  
Minimum Distance ◽  
Public Key ◽  
Low Rank ◽  
Public Key Encryption ◽  
Parity Check ◽  
Gabidulin Codes ◽  
Syndrome Decoding ◽  
New Variant ◽  
Different Types ◽  
Efficient Decoding

In this paper, we present a new variant of the Niederreiter Public Key Encryption (PKE) scheme which is resistant against recent attacks. The security is based on the hardness of the Rank Syndrome Decoding (RSD) problem and it presents a (u|u + υ)-construction code using two different types of codes: Ideal Low Rank Parity Check (ILRPC) codes and λ-Gabidulin codes. The proposed encryption scheme benefits are a larger minimum distance, a new efficient decoding algorithm and a smaller ciphertext and public key size compared to the Loidreau’s variants and to its IND-CCA secure version.

scholarly journals Low-rank parity-check codes over Galois rings

2020 ◽  
Author(s):  
Julian Renner ◽  
Alessandro Neri ◽  
Sven Puchinger
Keyword(s):  
Finite Fields ◽  
Failure Probability ◽  
Low Rank ◽  
Galois Rings ◽  
Parity Check ◽  
Gabidulin Codes ◽  
Rank Metric Codes ◽  
Small Failure Probability ◽  
Free Rank ◽  
Parity Check Codes

AbstractLow-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above.

Cryptanalysis of a combinatorial public key cryptosystem

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitaliĭ Roman’kov
Keyword(s):  
Public Key ◽  
Public Key Cryptosystem ◽  
Public Key Encryption ◽  
Elgamal Cryptosystem ◽  
Different Types ◽  
Encryption Schemes

AbstractWe discuss pitfalls in the security of the combinatorial public key cryptosystem based on Nielsen transformations inspired by the ElGamal cryptosystem proposed by Fine, Moldenhauer and Rosenberger. We introduce three different types of attacks to possible combinatorial public key encryption schemes and apply these attacks to the scheme corresponding to the cryptosystem under discussion. As a result of our observation, we show that under some natural assumptions the scheme is vulnerable to at least one of the proposed attacks.

scholarly journals A New Technique in Rank Metric Code-Based Encryption

Cryptography ◽  
2018 ◽  
Vol 2 (4) ◽  
pp. 32 ◽  
Author(s):  
Terry Lau ◽  
Chik Tan
Keyword(s):  
Public Key ◽  
Security Level ◽  
Goppa Codes ◽  
Gabidulin Codes ◽  
Rank Metric ◽  
Syndrome Decoding ◽  
Rank Metric Codes ◽  
Fixed Rank ◽  
A New Technique ◽  
The Hard Problem

We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over F q m of full column rank n. We show that IND-CPA security is achievable for our encryption under assumption of the Decisional Rank Syndrome Decoding problem. Furthermore, we also prove some bounds for the number of matrices of a fixed rank with entries over a finite field. Our proposal allows the choice of the error terms with rank up to r 2 , where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13 . 68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of 2 140 bits, our encryption scheme has a smaller public key size than the key size suggested by LOI17 Encryption.

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.

Cryptanalysis on an Improved Version of ElGamal-Like Public-Key Encryption Scheme for Encrypting Large Messages

Informatica ◽  
2012 ◽  
Vol 23 (4) ◽  
pp. 537-562 ◽  
Author(s):  
Ting-Yi Chang ◽  
Min-Shiang Hwang ◽  
Wei-Pang Yang
Keyword(s):  
Public Key ◽  
Encryption Scheme ◽  
Public Key Encryption
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