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In this thesis, three public key systems are discussed. At
first, we analyze another possible weakness of LUC cry-
ptosystem that does not figure out before. We derive a gen-
eral formula for the number of messages which cannot be con-
cealed in LUC system. From the formula, we can know that the
number of messages which cannot be concealed in LUC is grea-
ter than in RSA in many cases. It implies that the choice of
public keys in LUC system need more limitations than that
used in RSA system. Hence, the formula is useful to design a
LUC type system. Second, we present a cryptoanalysis of Lin et
al's kna- psack cryptosystem and define a new easy knapsack
sequence. Due to the fact that Lin et al's scheme generates a
new easy knapsack sequence. We show that there exists an easy
method to obtain the message from ciphertext that does not need
se- cret key. Hence, Lin et al's public key scheme is
insecure under ciphertext only attack. Finally, we propose an
indistinguished box satisfied ho- morphism under addition
operation and use the proposed black box to implement Simmon's
ZKIP(Zero-Knowledge Identification Proof) scheme whose
security is based on knapsack problem. The indistinguished box
has not been proposed since Simmon's scheme was proposed.As to
our best knowledge,it is the first concrete implementation of
Simmon's ZKIP scheme.We also impl ement the well-known low-
density attack on knapsack public key cryptosystem which was
first proposed by Lagarias and Odlyzko. In our experiments,
even if low-density attack can be used to break Merkle-Hellman
knapsack public key crypt- osystem it still can not be
used to attack the proposed Simmon's ZKIP scheme.
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