Digital Signature Algorithm¶
Digital Signature Algorithm (DSA) is a public-key cryptosystem. It’s is used to generate and verify digital signature. Details of DSA could be found in FIPS.186-4, section 4.
DSA have two pair of functions: updateSigningParam and sign, updateVerifyingParam and verify. Also we have two implementation for updateSigningParam and updateVerifyingParam, a trivial one and another one with one extra arguments. The extra argument is actually 2^(2*N) mod P. If you have this arguments pre-calculated, you could call the one with this argument. Otherwise you could call the one without this arguments and we will calculate it on chip with extra resource.
Optimized Implementation on FPGA¶
Like RSA, DSA also relies on modular exponential calculation. We adopt the same method and do the expensive modular exponential calculaiton on the Montgomery field and then convert it back to normal representation. In this way, we could eliminate most integer division and multiplication to save resource and have higher frequency.
Peter Montgomery. “Modular Multiplication Without Trial Division”, Mathematics of Computation, vol. 44 no. 170, pp. 519–521, April 1985.
“Efficient architectures for implementing montgomery modular multiplication and RSA modular exponentiation” by Alan Daly, William Marnane
FIPS.186-4, section 4