Goppa Codes | ScienceGate

Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound

Quantum Information Processing ◽

10.1007/s11128-006-0047-9 ◽

2006 ◽

Vol 6 (3) ◽

pp. 143-158 ◽

Cited By ~ 1

Author(s):

Annika Niehage

Keyword(s):

Goppa Codes

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Equivalent Irreducible Goppa Codes and the Precise Number of Quintic Goppa Codes of Length 32

AFRICON 2007 ◽

10.1109/afrcon.2007.4401625 ◽

2007 ◽

Cited By ~ 1

Author(s):

John A. Ryan ◽

Kondwani Magamba

Keyword(s):

Goppa Codes

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Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

Security and Communication Networks ◽

10.1155/2017/4321296 ◽

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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