A New Technique in Rank Metric Code-Based Encryption

• Main Authors: Terry Shue Chien Lau, Chik How Tan
• Format: Article
• Language: English
• Published: MDPI AG 2018-10-01
• Series: Cryptography
• Subjects: code-based cryptography; McEliece; public key encryption; provable security
• Online Access: http://www.mdpi.com/2410-387X/2/4/32

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 F q m 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 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 a smaller public key size than the key size suggested by LOI17 Encryption.