scholarly journals A Cryptographic System Based on a New Class of Binary Error-Correcting Codes

2019 ◽  
Vol 73 (1) ◽  
pp. 83-96
Author(s):  
Pál Dömösi ◽  
Carolin Hannusch ◽  
Géza Horváth
Keyword(s):  
Coding Theory ◽  
Error Correcting Code ◽  
Discrete Math ◽  
Error Correcting Codes ◽  
Key Generation ◽  
New Class ◽  
Algebraic Coding Theory ◽  
Encryption And Decryption ◽  
Construction Of Self ◽  
Cryptographic System

Abstract In this paper we introduce a new cryptographic system which is based on the idea of encryption due to [McEliece, R. J. A public-key cryptosystem based on algebraic coding theory, DSN Progress Report. 44, 1978, 114–116]. We use the McEliece encryption system with a new linear error-correcting code, which was constructed in [Hannusch, C.—Lakatos, P.: Construction of self-dual binary 22k, 22k−1, 2k-codes, Algebra and Discrete Math. 21 (2016), no. 1, 59–68]. We show how encryption and decryption work within this cryptosystem and we give the parameters for key generation. Further, we explain why this cryptosystem is a promising post-quantum candidate.

Quantum McEliece public-key cryptosystem

2012 ◽  
Vol 12 (3&4) ◽  
pp. 181-203
Author(s):  
Hachiro Fujita
Keyword(s):  
Coding Theory ◽  
Explicit Construction ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Key Generation ◽  
Public Key Cryptosystems ◽  
Algebraic Coding Theory ◽  
Mceliece Cryptosystem ◽  
Alternative Systems ◽  
Encryption And Decryption

The McEliece cryptosystem is one of the best-known (classical) public-key cryptosystems, which is based on algebraic coding theory. In this paper, we present a quantum analogue of the classical McEliece cryptosystem. Our quantum McEliece public-key cryptosystem is based on the theory of stabilizer codes and has the key generation, encryption and decryption algorithms similar to those in the classical McEliece cryptosystem. We present an explicit construction of the quantum McEliece public-key cryptosystem using Calderbank-Shor-Steane codes based on generalized Reed-Solomon codes. We examine the security of our quantum McEliece cryptosystem and compare it with alternative systems.

scholarly journals An Application of p-Fibonacci Error-Correcting Codes to Cryptography

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 789
Author(s):  
Emanuele Bellini ◽  
Chiara Marcolla ◽  
Nadir Murru
Keyword(s):  
Error Correcting Code ◽  
Error Correcting Codes ◽  
Multiparty Computation ◽  
Zero Knowledge ◽  
Signature Schemes ◽  
Standardization Process ◽  
Technology Standardization

In addition to their usefulness in proving one’s identity electronically, identification protocols based on zero-knowledge proofs allow designing secure cryptographic signature schemes by means of the Fiat–Shamir transform or other similar constructs. This approach has been followed by many cryptographers during the NIST (National Institute of Standards and Technology) standardization process for quantum-resistant signature schemes. NIST candidates include solutions in different settings, such as lattices and multivariate and multiparty computation. While error-correcting codes may also be used, they do not provide very practical parameters, with a few exceptions. In this manuscript, we explored the possibility of using the error-correcting codes proposed by Stakhov in 2006 to design an identification protocol based on zero-knowledge proofs. We showed that this type of code offers a valid alternative in the error-correcting code setting to build such protocols and, consequently, quantum-resistant signature schemes.

scholarly journals Complexity of Error-Correcting Code Based on Nearest Neighbor Search Algorithm

2019 ◽  
pp. 7-20
Author(s):  
Levon Arsalanyan ◽  
Hayk Danoyan
Keyword(s):  
Time Complexity ◽  
Nearest Neighbor ◽  
Search Algorithm ◽  
Error Correcting Code ◽  
Error Correcting Codes ◽  
Code Word ◽  
Nearest Neighbor Search ◽  
Perfect Codes ◽  
Neighbor Search ◽  
Weight Structures

The Nearest Neighbor search algorithm considered in this paper is well known (Elias algorithm). It uses error-correcting codes and constructs appropriate hash-coding schemas. These schemas preprocess the data in the form of lists. Each list is contained in some sphere, centered at a code-word. The algorithm is considered for the cases of perfect codes, so the spheres and, consequently, the lists do not intersect. As such codes exist for the limited set of parameters, the algorithm is considered for some other generalizations of perfect codes, and then the same data point may be contained in different lists. A formula of time complexity of the algorithm is obtained for these cases, using coset weight structures of the mentioned codes

scholarly journals A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes

2019 ◽  
Vol 9 (2) ◽  
pp. 1232
Author(s):  
Issam Abderrahman Joundan ◽  
Said Nouh ◽  
Mohamed Azouazi ◽  
Abdelwahed Namir
Keyword(s):  
Coding Theory ◽  
Minimum Distance ◽  
Minimum Weight ◽  
Error Correcting Codes ◽  
Bch Codes ◽  
Search Problem ◽  
Public Key Cryptosystems ◽  
True Value ◽  
Efficient Scheme ◽  
Minimum Distances

<span>BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity.  ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper.</span>

scholarly journals Provide a New Encryption Algorithm for Medical Images and Evaluate the Proposed Algorithm

2019 ◽  
Vol 8 (1) ◽  
pp. 2
Author(s):  
Mehdi Lotfi ◽  
Hossein Kheiri ◽  
Azizeh Jabbari
Keyword(s):  
Differential Equations ◽  
Chaotic Systems ◽  
Medical Information ◽  
Medical Images ◽  
Encryption Algorithm ◽  
Key Generation ◽  
Time Period ◽  
Key Space ◽  
Encryption And Decryption ◽  
Very High

Introduction:  In this paper, an encryption algorithm for the security of medical images is presented, which has extraordinary security. Given that the confidentiality of patient data is one of the priorities of medical informatics, the algorithm can be used to store and send medical image.Material and Methods:  In this paper, the solutions of chaotic differential equations are used to generate encryption keys. This method is more than other methods used in encoding medical images, resistant to statistics attacks, low encryption and decryption time and very high key space. In the proposed algorithm, unlike other methods that use random key generation, this method uses the production of solutions of the chaotic differential equations in a given time period for generating a key. All simulations and coding are done in MATLAB software.Results:   Chaotic Differential Equations have two very important features that make it possible to encode medical images. One is the unpredictability of the system's behavior and the other is a severe sensitivity to the initial condition.Conclusion: These two features make the method resistant to possible attacks to decode the concept of synchronization chaotic systems. Using the results of the method, medical information can be made safer than existing ones.

scholarly journals Hamming Codes: Error Reducing Techniques

2021 ◽  
Vol 9 (11) ◽  
pp. 1972-1974
Author(s):  
Rohitkumar R Upadhyay
Keyword(s):  
Lower Bound ◽  
Error Correction ◽  
Coding Theory ◽  
Hamming Distance ◽  
Error Reduction ◽  
Error Correcting Codes ◽  
Significant Other ◽  
Hamming Codes ◽  
Decoding Algorithms ◽  
Reducing Properties

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

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