Patent ID: 7404089

Claim:
A method for cryptographically securing a message using a secret key d to iteratively perform a binary group operation of addition or multiplication [op] on a digital quantity G, said method comprising: expressing d in base 2 W as d k−1 d k−2 . . . d 0 , where W is a window width and k is a number of windows required to express d; determining values G i , for 0≦i≦k−1, where G i =[op] 2 iW G; for values j where 1≦j≦2 W −1, establishing a table of register positions [j] where, for each of said values of j, register position [j] stores each of said values of i where d i =j; setting values A=I, and B=I, where I is the identity element in a set including said quantity G for the binary group operation [op]; setting a value j=2 W −1; and then for all of said values i stored in register positions [j], updating said value B=B[op]G i ; updating A=A[op]B; setting said value j=j−1; and if said value j>0 returning to update said value B=B[op]G i ; and otherwise returning said value A, where said value A=[op] d G, for use as a cryptographic key; and using said cryptographic key to cryptographically secure said message.