Reducing the Key Size of McEliece Cryptosystem from Automorphism-induced Goppa Codes via Permutations

2019 ◽  
pp. 599-617 ◽  
Author(s):  
Zhe Li ◽  
Chaoping Xing ◽  
Sze Ling Yeo
Keyword(s):  
Goppa Codes ◽  
Mceliece Cryptosystem

The Improved McEliece PKC and its Security Analysis

2014 ◽  
Vol 962-965 ◽  
pp. 2814-2817
Author(s):  
Si Min Liu ◽  
Jun Yao Ye
Keyword(s):  
Linear Codes ◽  
Security Analysis ◽  
Error Correcting Codes ◽  
Public Key ◽  
General Linear ◽  
Public Key Cryptosystem ◽  
Goppa Codes ◽  
Private Key ◽  
Mceliece Cryptosystem ◽  
Fast Decoding

Because the decoding problem of general linear codes is an NPC problem, at the same time Goppa codes have fast decoding algorithm, McEliece first proposed a public-key cryptosystem based on error-correcting codes. This paper constructs the largest distance codes based on metric, then improves the McEliece cryptosystem based on the largest distance codes. We've proved that the cryptosystem is able to resist the attack of getting the private key by a known public key. Finally, through the analysis of existing viable attack method, we proved the feasibility and security of the improved McEliece cryptosystem.

scholarly journals Overview of the Mceliece Cryptosystem and its Security

2014 ◽  
Vol 60 (1) ◽  
pp. 57-83 ◽  
Author(s):  
Marek Repka ◽  
Pavol Zajac
Keyword(s):  
Public Key ◽  
Goppa Codes ◽  
Implementation Challenges ◽  
Low Resource ◽  
Public Key Cryptosystems ◽  
Mceliece Cryptosystem ◽  
Side Channels ◽  
Current State ◽  
Selection Of

Abstract McEliece cryptosystem (MECS) is one of the oldest public key cryptosystems, and the oldest PKC that is conjectured to be post-quantum secure. In this paper we survey the current state of the implementation issues and security of MECS, and its variants. In the first part we focus on general decoding problem, structural attacks, and the selection of parameters in general. We summarize the details of MECS based on irreducible binary Goppa codes, and review some of the implementation challenges for this system. Furthermore, we survey various proposals that use alternative codes for MECS, and point out some attacks on modified systems. Finally, we review notable existing implementations on low-resource platforms, and conclude with the topic of side channels in the implementations of MECS

An Efficient Decoding of Goppa Codes for the McEliece Cryptosystem

2014 ◽  
Vol 133 (4) ◽  
pp. 387-397
Author(s):  
Seongan Lim ◽  
Hyang-Sook Lee ◽  
Mijin Choi
Keyword(s):  
Goppa Codes ◽  
Mceliece Cryptosystem ◽  
Efficient Decoding

Hiding Encrypted Message Using Image Algebra And McEliece Cryptosystem

2015 ◽  
pp. 255
Author(s):  
سعد عبدالعزيز عبدالرحمن ◽  
سناء احمد كاظم
Keyword(s):  
Image Algebra ◽  
Mceliece Cryptosystem

scholarly journals Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Juha Partala
Keyword(s):  
Error Correction ◽  
Network Coding ◽  
Linear Combination ◽  
Distributed Storage ◽  
Homomorphic Encryption ◽  
Error Correcting Codes ◽  
Symmetric Encryption ◽  
Goppa Codes ◽  
Linear Network ◽  
Linear Network Coding

A distributed storage system (DSS) is a fundamental building block in many distributed applications. It applies linear network coding to achieve an optimal tradeoff between storage and repair bandwidth when node failures occur. Additively homomorphic encryption is compatible with linear network coding. The homomorphic property ensures that a linear combination of ciphertext messages decrypts to the same linear combination of the corresponding plaintext messages. In this paper, we construct a linearly homomorphic symmetric encryption scheme that is designed for a DSS. Our proposal provides simultaneous encryption and error correction by applying linear error correcting codes. We show its IND-CPA security for a limited number of messages based on binary Goppa codes and the following assumption: when dividing a scrambled generator matrix G^ into two parts G1^ and G2^, it is infeasible to distinguish G2^ from random and to find a statistical connection between G1^ and G2^. Our infeasibility assumptions are closely related to those underlying the McEliece public key cryptosystem but are considerably weaker. We believe that the proposed problem has independent cryptographic interest.

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