Binary goppa code

Binary goppa code

Public-Key Encryption

Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018

Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone

A special type of error-correcting code, called a Goppa code, may be used in step 3 of the key generation. For each irreducible polynomial g(x) of degree t over 𝔽2m, there exists a binary Goppa code of length n = 2m and dimension k ≥ n − mt capable of correcting any pattern of t or fewer errors. Furthermore, efficient decoding algorithms are known for such codes.

A Quantum Resistant Chameleon Hashing and Signature Scheme

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Journal Information

Published in IETE Journal of Research, 2022

P. Thanalakshmi, R. Anitha

It is described by the following algorithms: Setup: Select parameters m and t such that the t decoding in a Goppa code of length of dimension k = n−tm has complexity at least .Key Generation: Pick a random parity check matrix H of a - binary Goppa code C decoding t errors. This code remains secret. Choose a random permutation matrix P of order and a random non-singular matrix V of order and a hash function . The hash key is and the trapdoor key is . The hash function is modelled as random oracle.Hashing Computation: On input the hash key , the algorithm chooses an element such that , and a message and computes chameleon hash as follows: Output .Collision computation: On input the hash key , the collision algorithm F computes a collision on a valid hash value h using the trapdoor key as follows. It chooses a message and and computes Output Note that,

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Public-Key Encryption

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