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On McEliece-Type Cryptosystems Using Self-Dual Codes With Large Minimum Weight
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DOI：10.1109/ACCESS.2023.3271767.png)
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Abstract
En 中文
One of the Round 3 Finalists in the NIST post-quantum cryptography call is the Classic McEliece cryptosystem. Although it is one of the most secure cryptosystems, the large size of its public key remains a practical limitation. In this work, we propose a McEliece-type cryptosystem using large minimum distance error-correcting codes derived from self-dual codes. To the best of our knowledge, such codes have not been implemented in a code-based cryptosystem until now. Moreover, we modify the decryption step of the system by introducing a decryption algorithm based on two private keys. We determine the parameters of binary codes with large minimum distance, which, if implemented into a McEliece-type cryptosystem, would provide a security level respectively of 80, 128, and 256 bits. For the 80-bit security case, we construct a large minimum distance self-dual code of length 1064, and use it to derive a random punctured code to be used in the corresponding McEliece-type cryptosystem. Compared to the original McEliece cryptosystem, the key size is reduced by about 38.5%, although an optimal decoding set is yet to be constructed to make the new system fully defined and usable.
Keywords:
Cryptograph
Security
Decoding
Encryption
Codecs
Linear codes
Generators
Codes
Post-quantum cryptography
McEliece cryptosystem
self-dual codes
Journal
IF:
3.6
Papers:
9.8W
Citations:
29.4W