Goppa codes

Goppa codes

Goppa codes are a type of error-correcting code that belong to the subclass of alternant codes and were defined by V. D. Goppa in 1970. They can be specified over any finite field and are commonly used in computers, telecommunication, and cryptographic applications due to their mathematical benefits.From: ICT for Competitive Strategies [2020], A Quantum Resistant Chameleon Hashing and Signature Scheme [2022], Mathematics in Cyber Research [2022]

Quantum-Safe Asymmetric Cryptosystems

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Published in Shashi Bhushan, Manoj Kumar, Pramod Kumar, Renjith V. Ravi, Anuj Kumar Singh, Holistic Approach to Quantum Cryptography in Cyber Security, 2023

Sagarika Ghosh, Marzia Zaman, Srinivas Sampalli

In 1978, a public-key encryption scheme that was based on hidden Goppa code [33] was proposed by Robert McEllice. Goppa codes are the relation between algebraic geometry and codes and are used as error-correcting codes. They rely on the NP-hard problem of decoding linear codes. The basic concept of the Goppa code depends on modular arithmetics. When a number series approaches a higher number, and once it reaches a specific number, the series starts from 0 again [1,8]. A classic McEllice cryptosystem includes the following phases (assuming Alice and Bob are the two legitimate participants) [28,33].

A Quantum Resistant Chameleon Hashing and Signature Scheme

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Published in IETE Journal of Research, 2022

P. Thanalakshmi, R. Anitha

Goppa codes are a subclass of alternant codes [17] and are widely used in cryptographic applications. Goppa codes of t error correcting capability are of length and dimension k = n−tm where m and . The probability of decoding each syndrome is . denotes the decoding algorithm corresponding to a Goppa code of parity check matrix H.

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Quantum-Safe Asymmetric Cryptosystems

A Quantum Resistant Chameleon Hashing and Signature Scheme