A New Encryption Scheme Based on Rank Metric Codes

Abstract

We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We distort the matrix used for our encryption by adding a random distortion matrix over \(\mathbb {F}_{q^m}\). We show that IND-CPA security is achievable for our encryption under assumption of Decisional Rank Syndrome Decoding problem. Our proposal allows the choice of the error terms with rank up to r/2, 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 \(2^{140}\) bits, our encryption scheme has smaller public key size than key size suggested by LOI17 Encryption [7].