Efficient ECC scalar multiplication algorithm based on symmetric ternary in wireless sensor networks

摘要

With the rapid development of communication technology, wireless sensor networks have been widely used in several fields ranging from environmental monitoring and medical care to military uses. Sensor networks are typically deployed in hostile environments, which makes data security problems particularly severe. Therefore, it is necessary to encrypt the data and add authentication function. Elliptic curve cryptosystem (ECC) is a nice way to solve the problem. ECC has the advantages of high security, fast processing speed, low storage space and low bandwidth requirement. Thus, it is getting a lot of attention. The most critical operation in ECC is the multiplication of the user's private key with the base point, which is called scalar multiplication. It is the most basic mathematical operation in ECC. The speed of the operation decides the efficiency of elliptic curve cryptography system on the whole. To improve efficiency, it is necessary to optimize the scalar multiplication in elliptic curve cryptosystem. Based on the scalar representation of symmetric ternary, this paper optimizes the bottom operation using the Jacobi coordinate. In this way, we can eliminate the field inversion in scalar multiplication. Furthermore, this paper optimizes the symmetric ternary representation method, which can be used to improve the efficiency of scalar multiplication. The principle of this optimizing is that the point doubling is faster than point addition in Jacobi coordinate. By changing the scalar representation, the non-zero Hamming weight is reduced and point doubling is used to replace the point addition on the processing dot. The calculating amount is analyzed, so we can see that the optimized symmetric ternary scalar multiplication has a efficiency improvement at 4.3% compared with the earlier algorithm.