Abstract
With the development of the Internet of Things (IoT) and cloud computing technology, various cryptographic systems have been proposed to protect increasing personal information. Recently, Post-Quantum Cryptography (PQC) algorithms have been proposed to counter quantum algorithms that threaten public key cryptography. To efficiently use PQC in a server environment dealing with large amounts of data, optimization studies are required. In this paper, we present optimization methods for FrodoKEM and NewHope, which are the NIST PQC standardization round 2 competition algorithms in the Graphics Processing Unit (GPU) platform. For each algorithm, we present a part that can perform parallel processing of major operations with a large computational load using the characteristics of the GPU. In the case of FrodoKEM, we introduce parallel optimization techniques for matrix generation operations and matrix arithmetic operations such as addition and multiplication. In the case of NewHope, we present a parallel processing technique for polynomial-based operations. In the encryption process of FrodoKEM, the performance improvements have been confirmed up to 5.2, 5.75, and 6.47 times faster than the CPU implementation in FrodoKEM-640, FrodoKEM-976, and FrodoKEM-1344, respectively. In the encryption process of NewHope, the performance improvements have been shown up to 3.33 and 4.04 times faster than the CPU implementation in NewHope-512 and NewHope-1024, respectively. The results of this study can be used in the IoT devices server or cloud computing service server. In addition, the results of this study can be utilized in image processing technologies such as facial recognition technology.
Highlights
The development of information communication technology such as the Internet of things (IoT) is rapidly increasing the amount of data exchanged in real time
With the advent of quantum computers, it has been suggested that modern cryptographic algorithms such as Rivest–Shamir–Adleman (RSA), elliptic curve cryptography (ECC), and the digital signature algorithm that rely on mathematical computational complexity like discrete mathematics are no Mathematics 2020, 8, 1781; doi:10.3390/math8101781
To reduce the burden on a server that encrypts the data of multiple IoT devices or user information in a cloud computing service, this paper proposes several methods for optimizing some lattice-based cryptography using a graphics processing unit (GPU)
Summary
The development of information communication technology such as the Internet of things (IoT) is rapidly increasing the amount of data exchanged in real time. Various modern cryptographic technologies such as symmetric-key and public-key encryption algorithms have been developed [1,2]. With the advent of quantum computers, it has been suggested that modern cryptographic algorithms such as Rivest–Shamir–Adleman (RSA), elliptic curve cryptography (ECC), and the digital signature algorithm that rely on mathematical computational complexity like discrete mathematics are no Mathematics 2020, 8, 1781; doi:10.3390/math8101781 www.mdpi.com/journal/mathematics. A new cryptographic method that is safe for quantum algorithms is needed, and various ideas based on computationally difficult problems have been proposed. Unlike the widely used and well-known public-key schemes such as RSA or ECC, which can theoretically be attacked by quantum computers, some lattice-based structures appear to be resistant to attack by classical and quantum computers. The mathematical principle of the lattice-based cryptography is as follows. The LWE problem, with n unknowns, m ≥ n samples, modulo q and with error distribution X is as follows: for a random secret s
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