Welcome to the resource topic for 2003/232
Title:
The Statistical Zero-knowledge Proof for Blum Integer Based on Discrete Logarithm
Authors: Chunming Tang, Zhuojun Liu, Jinwang Liu
Abstract:Blum integers (BL), which has extensively been used in the domain
of cryptography, are integers with form p^{k_1}q^{k_2}, where
p and q are different primes both \equiv
3\hspace{4pt}mod\hspace{4pt}4 and k_1 and k_2 are odd
integers. These integers can be divided two types: 1) M=pq, 2)
M=p^{k_1}q^{k_2}, where at least one of k_1 and k_2 is
greater than 1.\par
In \cite{dbk3}, Bruce Schneier has already proposed an open
problem: {\it it is unknown whether there exists a truly practical
zero-knowledge proof for M(=pq)\in BL}. In this paper, we
construct two statistical zero-knowledge proofs based on discrete
logarithm, which satisfies the two following properties: 1) the
prover can convince the verifier M\in BL ; 2) the prover can
convince the verifier M=pq or M=p^{k_1}q^{k_2}, where at least
one of k_1 and k_2 is more than 1.\par
In addition, we propose a statistical zero-knowledge proof in
which the prover proves that a committed integer a is not equal
to 0.\par
ePrint: https://eprint.iacr.org/2003/232
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