Design Of Co-Z-Based Dual-field Scalar Multiplication And Lattice-Based Polynomial Multiplication

Compared with RSA, ECC has more security, less memory space, and lower bandwidth requirements. Moreover it has been widely used in industry for high security chip. ECC security depends on discrete logarithm problem. This problem has been proven not resist quantum attacks. Cryptographer is exploring a safe and efficient post-quantum cryptography. Therefore lattice-based encryption is attracted widespread attention. The design of practical hardware is still in the exploratory stage. The purpose of this paper is to provide a reliable and efficient hardware. On the other hand make an effort to reduce post-quantum encryption time and space overhead in the study of quantum cryptography. Making the lattice-based encryption system to replace the current encryption system becomes a possibility.This paper investigates the co-Z method and extends it to the binary field. According with co-Z protected NAF algorithm, the architecture is proposed to balance speed and area factors and to achieve optimal effectiveness. This architecture has normative false operation and been prevent safe-error attacks. The co-Z protected NAF architecture has 1.36 times faster than protected NAF in prime field. We expand it to binary field and it can offset 30.7% of false operation. Because of the architecture, the area of implementation has only less than 1% of the cost of the additional area to achieve the design.The LWE is an important method to construct lattice-based encryption in post-quantum cryptography. In order to fully reuse of limited resources, rational use of parallel structure and pipeline technology, we get a quick improvement modular FFT(Fast Fourier Transform) design. Application of the design can improve fast polynomial multiplication. We present a new efficient hardware implementation based on a Ring-LWE problem. The cycles of encryption and decryption faster than 21.5% and 56.5% compared with proposed in 2014. The encryption time will be reduced to 25.39 ?s and the decryption time will be reduced to 12.66 ?s.