Design And Implementation Of Polynomial And Large-number Operation For SDLCA

SDLCA(Special Description Language for the Cryptographic Algorithm) is aprofessional description language for cryptographic algorithms.Polynomial andlarge-number operation is often used in cryptographic algorithms.So, a polynomialfunction and large-number operation was designed and implementated on the basis ofthe grammar system of SDLCA in this paper.Based on SDLCA grammar system, open stream cipher was analysed, thecharacteristics of stream cipher algorithm was summarized and concluded anddescription module of a polynomial function was abstracted.Boolean function, linearfeedback shift register and nonlinear feedback shift register was implemented with theuse of polynomial functions.The public key cryptographic algorithm of RSA which isbased on a large integer factorization were studied and large integer arithmetic ofSDLCA was implemented using bit-string variable as storage structure for largeinteger.On the basis of large integer arithmetic,fast modular exponentiationmultiplication, large prime number generation, multiplicative inverse and otherpublic-key cryptographic algorithm module were implemented.Test program waswritten to test the correctness of polynomial function description module and largeinteger arithmetic module.On the basis of the new cryptographic module,23cryptographic algorithms weredescripted including block ciphers,stream ciphers and public key cryptpgraphicalgorithm,for example AES,Grain,RSA and so on. These algorithms were executed bySDLCA interpreter, the result were compared with the test vectors, verified theimplementation of the correctness of the SDLCA.Cryptographic algorithms descriptionof the C language and SDLCA were compared,and verify the simplicity andpracticality of the SDLCA.