Cryptanalysis of Riccati equation encryption schemes TP-I and TP-II

TP-I (Tsafenat-Paaneah-I) and TP-II (Tsafenat-Paaneah-II) are two public-key encryption schemes based on simultaneous algebraic Riccati equations over finite fields, which were proposed by Peretz in 2016 [9]. In this research, we discovered the hidden linear structure of TP-I and TP-II, respectively. Hence, we are going to show how can one break the two schemes.