Expanded low-rank parity-check codes and their application to cryptography

Abstract

In this paper, we define expanded LRPC codes from LRPC codes with a decoding algorithm using the one of the underlying LRPC codes. Next, we propose to use these codes for cryptography by deriving two cryptosystems in a McEliece setting. in order to reduce the key sizes, we use a generator matrix in systematic form for the first scheme, and an $m-$ order quasi-cyclic LRPC code that we define for the second scheme. The obtained code has a very poor structure and is more likely to be a random linear code. Next, we give some security parameters and compare the key sizes of our public key with the key sizes of some cryptosystems.

Keywords:

• Expanded codes
• LRPC codes
• public-key cryptosystems
• rank metric
• s-order quasi-cyclic codes

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Kamwa Djomou Franck Rivel

Kamwa Djomou Franck Rivel completed a Bsc in Mathematics and Computer Science at the University of Dschang in Cameroon. He then completed a Master degree in Mathematics at the University of Dschang. His research topics includes coding theory and applications. He is currently a PhD student at the University of Dschang.

Fouotsa Emmanuel

Fouotsa Emmanuel completed a Bsc in Mathematics and a Bsc in Computer Science at the University of Dschang in Cameroon. He then completed a Master degree in Mathematics at the University of Yaoundé 1 in Cameroon. He is an owner of a PhD in Mathematics with applications to cryptology obtained at the University of Rennes 1 in France. His research topics includes efficient and secured pairing computation and code based cryptography. He is currently an Associate Professor of Mathematics at the University of Bamenda in Cameroon.

Tadmon Calvin

Tadmon Calvin is a Full Professor of Applied Mathematics in the Department of Mathematics and Computer Science at the University of Dschang in Cameroon. He is the Leader of the Research Team ‘Committed Mathematics’ in the Research Unit on Mathematics and Applications in the Dschang School of Science and Technology where he is the coordinator of the Master and PhD programs in Mathematics and Computer Science. He is also holder of a Humboldt Research Fellowship for Experienced Researchers, from the Alexander von Humboldt Foundation in Germany. His research interests rely mainly on mathematical analysis of partial differential equations applied to various domains of Science such as Epidemiology, Biology, Physics, Finance, Economy, etc.