Paper 2003/232
The Statistical Zeroknowledge Proof for Blum Integer Based on Discrete Logarithm
Chunming Tang, Zhuojun Liu, and 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 zeroknowledge proof for $M(=pq)\in BL$}. In this paper, we construct two statistical zeroknowledge 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 zeroknowledge proof in which the prover proves that a committed integer $a$ is not equal to 0.\par
Metadata
 Available format(s)
 PDF PS
 Category
 Cryptographic protocols
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 cryptographyBlum integerstatistical zeroknowledge
 Contact author(s)
 ctang @ mmrc iss ac cn
 History
 20031108: revised
 20031108: received
 See all versions
 Short URL
 https://ia.cr/2003/232
 License

CC BY
BibTeX
@misc{cryptoeprint:2003/232, author = {Chunming Tang and Zhuojun Liu and Jinwang Liu}, title = {The Statistical Zeroknowledge Proof for Blum Integer Based on Discrete Logarithm}, howpublished = {Cryptology ePrint Archive, Paper 2003/232}, year = {2003}, note = {\url{https://eprint.iacr.org/2003/232}}, url = {https://eprint.iacr.org/2003/232} }