Wavefront and caustic surfaces of refractive laser beam shaper
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
In cryptographic protocols it is often necessary to verify/certify the "tools" in use. This work demonstrates certain subtleties in treating a family of trapdoor permutations in this context, noting the necessity to "check" certain properties of these functions. The particular case we illustrate is that of noninteractive zero-knowledge. We point out that the elegant recent protocol of Feige, Lapidot, and Shamir for proving NP statements in noninteractive zero-knowledge requires an additional certification of the underlying trapdoor permutation, and suggest a method for certifying permutations which fills this gap. © 1996 International Association for Cryptologic Research.
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
Imran Nasim, Michael E. Henderson
Mathematics
Charles Micchelli
Journal of Approximation Theory
Alfred K. Wong, Antoinette F. Molless, et al.
SPIE Advanced Lithography 2000