Efficient Nyberg-Rueppel type of NTRU digital signature algorithm

Message recovery is an important property in Nyberg-Rueppel type digital signature algorithms. However, the security of Nyberg-Rueppel type digital signature algorithms depends on the hard problems which might be vulnerable to quantum attacks. Therefore, quantum resistant Nyberg-Rueppel type digital signature algorithms with message recovery property are needed. Since NTRU-based cryptosystems are one of the best studied quantum-resistant schemes, using traditional NTRU encryption scheme has several advantages on the message recovery property. In this paper, we define Nyberg-Rueppel type of NTRU digital signature algorithm. It is carried out by combining NTRU-based encryption and signature algorithms. In the proposed scheme, efficient message recovery property is achieved with the help of NTRU. Then, we compare the computational cost of our Nyberg-Rueppel type signature scheme with the others in terms of the arithmetic complexity. According to the asymptotic complexity results, the proposed scheme has better arithmetic complexity than Nyberg-Rueppel type schemes. We also discuss the security properties of the proposed scheme by modifying attacks on Nyberg-Rueppel type algorithms and lattice-based algorithms.