## CryptoDB

### Zhuojun Liu

#### Publications

**Year**

**Venue**

**Title**

2008

EPRINT

Perfectly Hiding Commitment Scheme with Two-Round from Any One-Way Permutation
Abstract

Commitment schemes are arguably among the most important and
useful primitives in cryptography. According to the computational
power of receivers, commitments can be classified into three
possible types: {\it computational hiding commitments,
statistically hiding commitments} and {\it perfect computational
commitments}. The fist commitment with constant rounds had been
constructed from any one-way functions in last centuries, and the
second with non-constant rounds were constructed from any one-way
functions in FOCS2006, STOC2006 and STOC2007 respectively,
furthermore, the lower bound of round complexity of statistically
hiding commitments has been proven to be $\frac{n}{logn}$ rounds
under the existence of one-way function.
Perfectly hiding commitments implies statistically hiding, hence,
it is also infeasible to construct a practically perfectly hiding
commitments with constant rounds under the existence of one-way
function. In order to construct a perfectly hiding commitments
with constant rounds, we have to relax the assumption that one-way
functions exist. In this paper, we will construct a practically
perfectly hiding commitment with two-round from any one-way
permutation. To the best of our knowledge, these are the best
results so far.

2004

EPRINT

Provably Secure Delegation-by-Certification Proxy Signature Schemes
Abstract

In this paper, we first show that previous proxy
signature schemes by delegation with certificate are not provably
secure under adaptive-chosen message attacks and adaptive-chosen
warrant attacks. The schemes do not provide the strong
undeniability. Then we construct a proxy signature scheme by
delegation with certificate based on Co-GDH group from bilinear
map. Our proxy signature scheme is existentially unforgeable
against adaptive-chosen message attacks and adaptive-chosen
warrant attacks in random oracle model. We adopt a straight method
of security reduction in which our scheme's security is reduced to
hardness of the computational co-Diffie-Hellem problem. The
proposed signature scheme is the first secure
delegation-by-certificate proxy signature based on co-GDH groups
from bilinear maps under the formal security model in random
oracle model.

2004

EPRINT

Non-Interactive and Information-Theoretic Secure Publicly Verifiable Secret Sharing
Abstract

A publicly verifiable secret sharing scheme is more applicable
than a verifiable secret sharing because of the property that the
validity of the shares distributed by the dealer can be verified
by any party. In this paper, we construct a non-interactive and
information-theoretic publicly verifiable secret sharing by a
computationally binding and unconditionally hiding commitment
scheme and zero-knowledge proof of knowledge.

2004

EPRINT

Delegateable Signature Using Witness Indistinguishable and Witness Hiding Proofs
Abstract

A delegateable signature scheme is a signature scheme where the
owner of the signing key(Alice) can securely delegate to another
party(Bob) the ability to sign on Alice's behalf on a restricted
subset $S$ of the message space. Barak first defined and
constructed this signature scheme using non-interactive
zero-knowledge proof of knowledge(NIZKPK)\cite{Barak}. In his
delegateable signature scheme, the function of NIZKPK is to
prevent the signing verifier from tell which witness(i.e.
restricted subset) is being used.
Witness indistinguishable(WI) and witness hiding(WH) proof systems
are weaker proof model than zero-knowledge proof and were proposed
by Feige and Shamir in \cite{FS}, however, the verifier cannot
also distinguish the witness which is being used in these two
protocols. In this paper, we construct delegateable signature
scheme using WI and WH proof protocols.

2003

EPRINT

A Verifiable Secret Sharing Scheme with Statistical zero-knowledge
Abstract

In this paper, we first propose a protocol in which the prover can
show that a=b holds for two committed integers a and b;
also, we present a protocol in which the prover can prove that
a\neq 0 holds for committed integer a; then, we construct a
protocol to prove that the degree of a polynomial f(x) equals to
t-1 exactly, which has been as an open problem(see[21]);
finally, we provide a protocol in which the prover proves that a
pair (x,y) is generated by a polynomial f(x), i.e., y=f(x)(mod m), where m is a prime.
Based on above four protocols, we put forward a verifiable
(t,n)-secret sharing scheme, which can avoid all known the
dealer's cheats.
In particular, all above protocols are statistical zero-knowledge.

2003

EPRINT

The Statistical Zero-knowledge Proof for Blum Integer Based on Discrete Logarithm
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

#### Coauthors

- Yong He (1)
- Jinwang Liu (1)
- Dingyi Pei (3)
- Zuowen Tan (1)
- Chunming Tang (5)
- Mingsheng Wang (2)
- Zheng-an Yao (1)