Modular exponentiation calculation apparatus and method

Details Modular exponentiation calculation apparatus and method Modular exponentiation calculation apparatus and method

1997-01-24

1999-02-09

Cain, David

Cryptography

Particular algorithmic function encoding

Public key

380 28, H04K 100

Patent

active

058704787

ABSTRACT:
In the modular exponentiation calculation apparatus of the present invention, a computer calculates a modular exponentiation C=M .sup.E modN (M,N: integral number, E: exponent expressed in base m, C: calculation result expressed in base b). A table generation section calculates values of M.sup.j .cndot. b.sup.i modN (b,n,m: constant, j=1,2, . . . , m-1, i=0,1, . . . , n-1) and generates a table having (m-1)-columns and n-rows in which the calculation values are stored as corresponding elements. A first calculation section calculates a multiplication sum ##EQU1## (Ci: value of each digit of C, ej: non-zero value of j-th digit of E, M.sup.ej .cndot. b.sup.i modN: row elements of ej-column of the table) as updated C. A second calculation section calculates C.sup.m modN for the updated C. A control section controls the first calculation section and the second calculation section to repeat the calculation for each non-zero value of each digit of E from MSB to LSB by unit of digit.

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