Cryptography – Particular algorithmic function encoding – Public key
Reexamination Certificate
2007-02-07
2010-12-21
Chen, Shin-Hon (Department: 2431)
Cryptography
Particular algorithmic function encoding
Public key
C380S028000
Reexamination Certificate
active
07856101
ABSTRACT:
The method for elliptic curve scalar multiplication is a method for fast, efficient multiplication of a point on an elliptic curve by a scalar. Two different parameters are used to assign separate projective coordinates to the x-coordinate and the y-coordinate. The x- and y-coordinates are projected by ZLxand ZLy, where Lxand Lyare exponential functions having a common base, i.e., Lx=gnxand Ly=gny, respectively. The use of projective coordinates reduces the number of inversions in scalar multiplication, thereby speeding processing time. Furthermore, since the parameters Lxand Lyare exponential functions, and since the base g is invariant, g−1can be precomputed and stored. This practically eliminates any further inversions, since Lx−1=(g−1)nxand Ly−1=(g−1)nyso that inversions are simplified to exponentiation by substitution, further speeding processing time and reducing storage requirements.
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Al-Gahtani Theeb A.
Ibrahim Mohammad K.
Chen Shin-Hon
King Fahd University of Petroleum and Minerals
Litman Richard C.
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