Abstract: To address the challenge of computational performance optimization in the domestic cryptographic algorithm SM9,a suite of performance enhancement techniques has been developed and applied.These methods include fixed-point scalar multiplication precomputation on elliptic curves,an improved Miller algorithm with precomputation,an optimized construction for the hard part of final exponentiation,modular exponentiation within the cyclotomic subgroup,and modular exponentiation employing a Comb-based fixed-base strategy.Through these tailored approaches,significant enhancements have been achieved in the computation of the SM9 algorithm,especially in the time-consuming steps,such as scalar multiplication on elliptic curves,bilinear pairing,and modular exponentiationin the 12th extension field.The seven fundamental SM9 algorithms,encompassing digital signature generation and verification,key exchange,key encapsulation and decapsulation,as well as encryption and decryption,have been effectively implemented in Python.Comprehensive testing reveals that the integration of these optimization techniques yields performance improvements ranging from 32% to 352% for the SM9 algorithms,marking a substantial advance in their computational efficiency.

Key words: Domestic cryptographic algorithm, SM9, Performance optimization, Elliptic curve, Bilinear pairing, Python