A new technique in rank metric code-based encryption

Abstract

We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over Fqm of full column rank n. We show that IND-CPA security is achievable for our encryption under assumption of the Decisional Rank Syndrome Decoding problem. Furthermore, we also prove some bounds for the number of matrices of a fixed rank with entries over a finite field. Our proposal allows the choice of the error terms with rank up to 2r, where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13.68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of 2140 bits, our encryption scheme has a smaller public key size than the key size suggested by LOI17 Encryption.