Notice
2.1. Formal Definition
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Descriptif
Welcome to the second week of this MOOC entitledCode-Based Cryptography. This week, we will talk in detailabout the McEliece cryptosystem. First, in this session, wewill describe formally the McEliece and theNiederreiter systems, which are the principal public-key schemes,based on error-correcting code. Let K be a securityparameter. An encryption schemeis defined by thefollowing spaces: the space of all possible messages, thespace of all ciphertexts, thespace of the public-keys, andthe space of the secret-keys.Then, we need to definethe following algorithms.A key generationalgorithm, which is a randomized algorithm that outputs apublic-key and a secret-key;this algorithm should runin expected polynomial time.
An encryption algorithm,which is also a randomized algorithm that takes amessage and the public-key and outputs a ciphertext;this algorithm runs also inexpected polynomial time.And a decryption algorithm,which is an algorithm thattakes a ciphertext and asecret-key, and outputs theoriginal plaintext ordeclares a failure; this algorithmruns in polynomial time.It is required that thedecryption of the ciphertext isagain the plaintext, and wedemand that the fasten attack on the system requires atleast 2^k bit operations.In 1978, McElieceintroduced the first public-keycryptosystem, as we have alreadyseen, based on error-correcting codes.The security of this schemeis based on two intractableproblems: the hardness ofdecoding, and the problem ofdistinguishing a codewith a prescribed structure.This property makesthis scheme an interesting candidate forpost-quantum cryptography. Another advantage consists of its fastencryption and decryption algorithms. But the main drawback isthe large size of the keys. We will use as public-key,a large generator matrix.
Intervention
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