Patent Document ID: 20130202104
Application ID: 12958273
Patent Flag: 0

Claim One:
1. A computerized method of performing XZ-elliptic curve cryptography, comprising the steps of: (a) a sending correspondent and a receiving correspondent selecting and agreeing upon an elliptic curve set EC 3 ; (b) the sending correspondent and the receiving correspondent further agreeing upon a random scalar k and a random shared secret key for communication E s , and agreeing upon a base point (X B ,Y B ,Z B )εEC 3 ; the sending correspondent then performs the following steps: (c) embedding a first secret message bit string into an elliptic curve message point (X m ,Y m ,Z m ); (d) computing a scalar multiplication between the base point (X B ,Y B ,Z B ) and the scalar k as (X Bk , Y Bk ,Z Bk )=k(X B ,Y B ,Z B ); (e) computing a cipher point (X c ,Y c ,Z c ) as (X c , Y c ,Z c )=(X m ,Y m ,Z m )+k(X B ,Y B ,Z B ); (f) embedding a second secret message bit string into a data transformation index E m ; (g) transforming the cipher point coordinates X c and Z c as {circumflex over (X)} C =X C E s and {circumflex over (Z)} C =Z C E m , respectively; (h) calculating a cipher transformation index E c as E c = E s E m ; (i) sending a set of appropriate bits of {circumflex over (X)} c , {circumflex over (Z)} c and E c to the receiving correspondent; the receiving correspondent then performs the following steps: (j) calculating the data transformation index E m as E m = E s E c ; (k) calculating the cipher point coordinates X c and Z c as X C ={circumflex over (X)} C E s −1 and Z C ={circumflex over (Z)} C E m −1 , respectively; (l) computing a scalar multiplication between the base point (X B ,Y B ,Z B ) and the scalar k as (X Bk , Y Bk ,Z Bk )=k(X b , Y B ,Z B ); (m) computing the elliptic curve message point (X m ,Y m ,Z m ) as (X m ,Y m ,Z m )=(X c ,Y c ,Z c )−k(X B ,Y B ,Z B ); and (n) retrieving the first secret message bit string from the elliptic curve message point (X m ,Y m ,Z m ).