Efficient modular multiplication circuit suitable for SM2 encryption operation and operation method thereof

Abstract

According to the efficient modular multiplication operation circuit suitable for the SM2 encryption operation, the idea of dividing and conquering of the karatsuba algorithm is utilized, secondary iteration expansion is carried out on the karatsuba algorithm, large number multiplication operation is carried out in a local parallel mode, and large number modular multiplication operation is carried out through a prime number field P256 recommended in the national cryptographic algorithm. According to the algorithm, multiplication results are firstly obtained in three periods, and then reduction operation is carried out by utilizing the characteristics of P256. In the operation process, a divide-and-conquer method is utilized for one-time expansion, then three 64-bit karatsuba multipliers are utilized for parallel execution, three partial products can be obtained respectively (for operation of the partial products, an improved karatsuba algorithm is adopted for operation of the partial products), modular reduction operation is carried out after the three partial products are accumulated, and time and resources are saved. A contrast experiment shows that only 13.45 k LUTs needs to be consumed for completing one modular multiplication operation on an Artix-7 development board of 100 MHZ, and the modular multiplication operation can be completed within 0.04 us. And optimization of resource consumption and execution time is realized.

Description

technical field [0001] The invention belongs to the technical field of circuit operation, and more particularly, the invention relates to a high-efficiency modular multiplication circuit suitable for SM2 encryption operation and an operation method thereof. Background technique [0002] Elliptic Curve Cryptography (ECC) and RSA encryption algorithms are two very popular and powerful public key encryption algorithms. However, at the same level of security, ECC has fewer key bits than RSA. The 256-bit ECC algorithm on the prime field has the same level of security as the 3072-bit RSA algorithm. Additionally, elliptic curve cryptosystems consume fewer hardware resources. Modular multiplication is the most time-consuming operation in the process of elliptic curve encryption, so the speed of modular multiplication becomes the bottleneck in the process of elliptic encryption. How to speed up the operation of modular multiplication is the key to improving the speed of elliptic en...

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Problems solved by technology

How to get C fast 15 ~C 0 (dividing C into 16 32-bit C 15 ~C 0 ) is another key issue in the design of modular multiplication. Since the resource and time consumption of multiplication is much greater than that of addition and subtraction, how to perform multiplication of large numbers also needs to be designed reasonably. The existing karatsuba-Ofman based on one-time expansion Algorithm (hereinafter referred to as Karatsuba algorithm), this algorithm needs to use a 129-bit multiplier. With the increase of the number of multiplication digits, the resource consumption of the multiplier increases exponentially, so the resource consumption of this solution is too serious.

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