Security of the Cryptosystem GPT Based on Rank Codes and Term-rank Codes

This paper investigates public key cryptosystems (PKC) in the rank metric and term-rank metric. For security analysis of cryptosystems, we introduce a GPT system. Recently, respective structural attacks this system were proposed by Over-beck. For GPT system, Overbeck's attack succeeds in polynomial time. We will discuss the new construction of Shiki system. This paper describes Overbeck's attack to the new Shiki system. Also, investigation of the possibility of using term-rank codes in public key cryptosystems.