5 citations · 14 across the 20 of their papers we have counts for
20 papers
New Algorithms for Subset Sum Problem
Zhengjun Cao, Lihua Liu
Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solvi…
Analysis of Nederlof's algorithm for subset sum
Zhengjun Cao, Zhen Chen, Lihua Liu
We show that Nederlof's algorithm [Information Processing Letters, 118 (2017), 15-16] for constructing a proof that the number of subsets summing to a particular integer equals a c…
A Note on "New techniques for noninteractive zero-knowledge"
Zhengjun Cao, Lihua Liu
In 2012, Groth, et al. [J. ACM, 59 (3), 1-35, 2012] developed some new techniques for noninteractive zero-knowledge (NIZK) and presented: the first perfect NIZK argument system for…
An Elementary Proof for Ljunggren Equation
Zhengjun Cao, Lihua Liu
We present an elementary proof for Ljunggren equation
A Note On One Realization of a Scalable Shor Algorithm
Zhengjun Cao, Lihua Liu
Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we r…
A Note on the Alon-Kleitman Argument for Sum-free Subset Theorem
Zhengjun Cao, Lihua Liu
In 1990, Alon and Kleitman proposed an argument for the sum-free subset problem: every set of n nonzero elements of a finite Abelian group contains a sum-free subset A of size |A|>…
A note on "achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud"
Zhengjun Cao, Lihua Liu
We show that the Lei et al.'s scheme [Information Sciences, 280 (2014), 205-217] fails, because the verifying equation does not hold over the infinite field R. For the field R, the…
A Note on "Confidentiality-Preserving Image Search: A Comparative Study Between Homomorphic Encryption and Distance-Preserving Randomization"
Zhengjun Cao, Lihua Liu
Recently, Lu et al. have proposed two image search schemes based on additive homomorphic encryption [IEEE Access, 2 (2014), 125-141]. We remark that both two schemes are flawed bec…
A Note on "Efficient Algorithms for Secure Outsourcing of Bilinear Pairings"
Lihua Liu, Zhengjun Cao
We show that the verifying equations in the scheme [Theoretical Computer Science, 562 (2015), 112-121] cannot filter out some malformed values returned by the malicious servers. We…
Comment on Two schemes for Secure Outsourcing of Linear Programming
Zhengjun Cao, Lihua Liu
Recently, Wang et al. [IEEE INFOCOM 2011, 820-828], and Nie et al. [IEEE AINA 2014, 591-596] have proposed two schemes for secure outsourcing of large-scale linear programming (LP)…
The Paillier's Cryptosystem and Some Variants Revisited
Zhengjun Cao, Lihua Liu
At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In t…
On the Weakness of Fully Homomorphic Encryption
Zhengjun Cao, Lihua Liu
Fully homomorphic encryption (FHE) allows anyone to perform computations on encrypted data, despite not having the secret decryption key. Since the Gentry's work in 2009, the primi…
A Note On Boneh-Gentry-Waters Broadcast Encryption Scheme and Its Like
Zhengjun Cao, Lihua Liu
Key establishment is any process whereby a shared secret key becomes available to two or more parties, for subsequent cryptographic use such as symmetric-key encryption. Though it…
The Barth-Boneh-Waters Private Broadcast Encryption Scheme Revisited
Zhengjun Cao, Lihua Liu
The primitive of private broadcast encryption introduced by Barth, Boneh and Waters, is used to encrypt a message to several recipients while hiding the identities of the recipient…
Remarks on the Cryptographic Primitive of Attribute-based Encryption
Zhengjun Cao, Lihua Liu
Attribute-based encryption (ABE) which allows users to encrypt and decrypt messages based on user attributes is a type of one-to-many encryption. Unlike the conventional one-to-one…
A Note on the Bellare-Rivest Protocol for Translucent Cryptography
Zhengjun Cao, Lihua Liu
We remark that the Bellare-Rivest protocol for translucent cryptography [J. Cryptology (1999) 12: 117-139] can not truly enable the government to decrypt partial encrypted communic…
Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm
Zhengjun Cao, Zhenfu Cao, Lihua Liu
An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov…
Remarks on AKS Primality Testing Algorithm and A Flaw in the Definition of P
Zhengjun Cao, Lihua Liu
We remark that the AKS primality testing algorithm [Annals of Mathematics 160 (2), 2004] needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. The require…
A Fast String Matching Algorithm Based on Lowlight Characters in the Pattern
Zhengjun Cao, Lihua Liu
We put forth a new string matching algorithm which matches the pattern from neither the left nor the right end, instead a special position. Comparing with the Knuth-Morris-Pratt al…
Ordered Probability Mass Function
Zhengjun Cao, Lihua Liu
Suppose that in the four tests Alice's scores are 90, 95, 85, 90, and Bob's scores are 85, 95, 90, 90. How to evaluate their scores? In this paper, we introduce the concept of orde…