Large integer modular arithmetic device for realizing signature algorithm in ECC cryptosystem and modular method therefor

Abstract

The invention discloses a large integer modular arithmetic device for realizing signature algorithm in an ECC cryptosystem; the device comprises an integer register, a module value register, an integer searching module, a module value searching module, a digit number subtraction module, a shift register, a data subtraction module and an output module, wherein the integer register stores the value of integer a to be modularized; the module value register stores the value of module n; the module value searching module searches the digit number of the most significant digit of the module n; the integer searching module searches the bit number of most significant digit of the data a in the integer register; the digit number subtraction module calculates the digit difference between the most significant digit of the integer a and the most significant digit of the module n; when the digit difference is more than 0, the shift register shifts data n to the left twice, and then the data subtraction module subtract the integer a from shifted result to obtain value a', and then the data subtraction module updates the data a in the integer register module into the value a'; when the digit difference is less than or equal to 0, the output module finally outputs the final modular result. Compared with the prior art, the invention has lower cost, strong generality, and high efficiency.

Description

technical field [0001] The invention belongs to the technical field of communication, and relates to a large integer modulo operation device in an elliptic curve cryptosystem ECC, which is used for authentication of communication between mobile terminals and digital signature for non-repudiation services. Background technique [0002] The current cryptosystems can generally be divided into two types, namely symmetric cryptosystems and public key cryptosystems. [0003] The symmetric cryptographic system requires the communication parties A and B to share the same key K, and to ensure that when A and B negotiate the key, the channel is confidential and fidelity. This leads to its key distribution problems and key management problems. In addition, because two or more entities share keys, the symmetric key system cannot implement digital signatures for authentication and non-repudiation services. . [0004] Different from the symmetric cryptosystem, the public key cryptosyste...

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Problems solved by technology

[0032] There are mainly three kinds of existing modulo-seeking techniques: the first one is based on the definition of modulus-seeking, and calculates a mod n by repeatedly subtracting modulus n from the modulus a to be sought. Although this method is simple and general in theory, However, it is not applicable to the modulus between large integers in practice, because as the data bit width increases, its calculation time will be an astronomical figure, which is actually not feasible; the second method is developed by the American Institute of Standards and Technology NIST Some fast modulo algorithms on special prime fields given in the digital signature standard, but these fast modulo algorithms can only be used for special cases and are not general; the third is the Barrett reduction method, which has general also works for large integers, but requires a costly modulo-dependent computation to support

If a general, effective and low-cost FPGA implementation method cannot be found to improve the efficiency of the modulo operation of large integers, it will not be able to reflect the hardware implementation advantages of ECC under the normal base representation of the binary domain

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