Abstract
In order to solve the problem between low power of Internet of Things devices and the high cost of cryptography, lightweight cryptography is required. The improvement of the scalar multiplication can effectively reduce the complexity of elliptic curve cryptography (ECC). In this paper, we propose a fast formula for point septupling on elliptic curves over binary fields using division polynomial and multiplexing of intermediate values to accelerate the computation by more than 14%. We also propose a scalar multiplication algorithm based on the step multi-base representation using point halving and the septuple formula we proposed, which significantly reduces the computational cost. The experimental results show that our method is more efficient over binary fields and contributes to reducing the complexity of ECC.
Highlights
IntroductionWith the development of narrow band Internet of Things (NB-IoT) and the accelerating popularity of 5G, the cost of connecting devices to IoT has been reduced, which greatly promotes its development
The Internet of Things (IoT) is developing rapidly in theory and application
We propose an efficient formula for fast computation of the sevenfold of elliptic curve points over the binary fields, which can be used in Double-Base Number System (DBNS) and Multi-Base Number Representation (MBNR) to compute the scalar multiplication of elliptic curves
Summary
With the development of narrow band Internet of Things (NB-IoT) and the accelerating popularity of 5G, the cost of connecting devices to IoT has been reduced, which greatly promotes its development. More and more devices are connected to the Internet of Things in various fields, from smart terminals to industrial facilities. Devices connected to the Internet of Things continue to generate and transmit large amounts of information. It is not safe to transmit information in plaintext form on the Internet of Things. Cryptography is the most widely used method to ensure the security of data transmission and sharing in the network. Encrypted data transmission on the Internet of Things has become the key to secure communication between devices. In 1976, Hellman proposed a public key exchange algorithm based on the Discrete Logarithm Problem (DLP) [1]. In 1986, Miller [2], Koblitz [3] independently proposed the Elliptic
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