Montgomery modular multiplication method and circuit thereof

Abstract

The invention relates to a Montgomery modular multiplication method and a circuit thereof. In the method, a modular length k=sw, wherein w is a word size processed each time by an algorithm, and s is the frequency required by the circulation of the algorithm for; input parameters include a, b and a modulus n; r is a memory, a high k place is used for accommodating the input parameter a and an r2 of an output result, and a lower k place is used for accommodating an r1 of the input parameter b; t is a temporary calculation result of a polynomial, and the rest is intermediate variables. Calculation steps are as follows: calculating according to a formula that r2=MonPro(a,b,n)=a*b*2<-k> mod n, assigning zero for t and i, ensuring that r32=r[i], supposing the i to be 0 and starting external circulation, calculating according to formulae as follows: (c,z1)=t[i]+r[i]*r32, (c, z1)=z1*n0', x2=z1 and x1=r[i], supposing j to be 0 and starting the internal circulation, calculating according formulae as follows: (c, t[i+j])=t[i+j]+x1*r[i]+x2*n[i]+c and t[i+s]=c, adding 1 to the variable j, repeating the internal circulation when the j is smaller than the s, and quitting the internal circulation otherwise, adding 1 to the variable i, repeating the external circulation when the i is smaller than the s, and quitting the external circulation otherwise, judging whether the high k place of the t is larger than n, if yes, enabling that r2=r2-n and assigning the low k place of the t to the r2 otherwise, and outputting a modular multiplication result according to the r2. According to the method and the circuit thereof, the calculating speed of the algorithm can be increased, and the power consumption is reduced.

Description

technical field [0001] The present invention relates to the field of public key encryption, more specifically, to a Montgomery modular multiplication method and a circuit thereof. Background technique [0002] Public-key cryptography utilizes asymmetric cryptography, using two independent keys that are mathematically related: a public key and a private key. The parties to the communication keep their own private keys secret and disclose their public keys. The sender encrypts with the receiver's shake, and the receiver decrypts with his own private key. Public key cryptography can also be used to solve the problem of digital signatures. [0003] RSA is a public key encryption algorithm, which can be used for data encryption and decryption as well as digital signature and verification, which makes the algorithm widely used, such as network information security, smart cards, security chips, and mobile communications. The security of the RSA algorithm depends on the difficulty...

AI Technical Summary

Problems solved by technology

However, due to the high power consumption of the multiplier-adder, the existing method is generally implemented with multiple clocks, which is very slow

Images