| Summary: | 博士 === 國立成功大學 === 電機工程研究所 === 82 === Two research topics are covered in this dissertation. The one
is the developments of fast computer arithmetic for efficient
public key cryptosystem implementations. The other focuses on
the construction and analysis of some public key cryptosystems.
The basic form of exponentiation, x^e, is extended to the multi-
exponentiation as Π{i=1 to p} xi^ei and an efficient algorithm
is proposed. This computational algorithm is extremely useful
for many important cryptographic schemes, e.g., the Digital
Signature Algorithm (DSA) proposed by NIST. Fast computational
algorithm and mathematical modeling for the recently reported
LUC scheme which uses second order linear recursion instead of
exponentiation are also studied. Many research results of
digital signature are shown in this dissertation. The DSA
proposed by NIST is modified such that either the signature
signer or the signature verifier can eliminate the computation
of one modular inverse. A new concept and scheme for batch
verification of signatures are proposed which can perform much
better than its original, the Schnorr''s signature, when batch
processing is considered. A new group of signatures named the
verifier specified signature schemes are considered. The SASC
cryptographic computational model is thoroughly studied. In
this group of computations, the client-server computational
strategy is employed. A two-phase strategy for the SASC is
given to make it secure against cryptographic attacks. A newly
reported scheme, called the access control with user
authentication, is improved on both the space and time
complexities and some novel features are proposed to make the
scheme more flexible. Finally, an extended version of key
distribution called the conference key distribution is
considered and an efficient protocol is developed based on the
applications of threshold scheme.
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