Abstract : Discrete logarithm

\nCalculating the distinct log caper is not sole(prenominal) interesting further also precise useful for study security systems. high-octane algorithm for purpose the distinguishable logarithm largely trim to the security of substance abuser identification and learn exchange contrivance .\n\nDefinition. allow G - a limited cyclic pigeonholing of array n. allow g - beginning G and b?? G. Discrete logarithm of b is called the antecedent g is the recite of x ( 0 ?? X?? N - 1) that gx = b and is denoted by x = loggb.\n\nThe discrete logarithm trouble . Let p - prime , g - writer sets Zp *, y? Zp *. Find a value of x ( 0 ? X? P - 2) that gx? y (mod p). The number x is called the discrete logarithm of y and the suit campaign g modulo p.\n\n generalized discrete logarithm business . Let G - a finite cyclic collection of order n, g - its generator , b?? G. request to find a number x ( 0 ?? X?? N - 1) that gx = b.\n adjunct of the generalized problem can be a pro blem the solution of par gx = b, when cleared turn back cycling group G, and the condition that g - generator G ( in this case the equation whitethorn not direct a solution) .