Searcharxiv⌕ Search

arXiv subjects

Zhengjun Cao

Publications and source records attributed to Zhengjun Cao.

At least 19 recordsLinked to original sources
arXiv2018

New Algorithms for Subset Sum Problem

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 solving this problem, including exhaustive search, divide-and-conquer method, and Bellman's dynamic programming method. However, none of them could generate universal and light code. In this paper, we present a new deterministic algorithm based on a novel data arrangement, which could generate such code and return all solutions. If n is small enough, it is efficient for usual purpose. We also present a probabilistic version with one-sided error and a greedy algorithm which could generate a solution with minimized variance.

cs.DS↗
arXiv2018

Analysis of Nederlof's algorithm for subset sum

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 claimed quantity is flawed because: 1) its consistence is not kept; 2) the proposed recurrence formula is incorrect.

cs.DS↗
arXiv2018

A Note on "New techniques for noninteractive zero-knowledge"

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 all NP; the first universally composable NIZK argument for all NP in the presence of an adaptive adversary; the first noninteractive zap for all NP, which is based on a standard cryptographic security assumption. These solved several long-standing open questions. In this note, we remark that their basic system is flawed because the prover can cheat the verifier to accept a false claim. Thus, these problems remain open now.

cs.CR↗
arXiv2017

A Note on the Alon-Kleitman Argument for Sum-free Subset Theorem

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|>\frac{2}{7}n. In this note, we show that the argument confused two different randomness. It applies only to the finite Abelian group G = (Z/pZ)^s where p is a prime. For the general case, the problem remains open.

math.CO↗
arXiv2016

A note on "achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud"

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 computational errors should be considered seriously. We also remark that the incurred communication cost in the scheme could be overtake the computational gain, which makes it somewhat artificial.

cs.CR↗
arXiv2016

A Note on "Confidentiality-Preserving Image Search: A Comparative Study Between Homomorphic Encryption and Distance-Preserving Randomization"

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 because: (1) the first scheme does not make use of the additive homomorphic property at all; (2) the additive homomorphic encryption in the second scheme is unnecessary and can be replaced by a more efficient symmetric key encryption.

cs.CR↗
arXiv2015

A Note on "Efficient Algorithms for Secure Outsourcing of Bilinear Pairings"

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 also remark that the two untrusted programs model adopted in the scheme is somewhat artificial, and discuss some reasonable scenarios for outsourcing computations.

cs.CR↗
arXiv2015

Comment on Two schemes for Secure Outsourcing of Linear Programming

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). They did not consider the standard form: minimize c^{T}x, subject to Ax=b, x>0. Instead, they studied a peculiar form: minimize c^{T}x, subject to Ax = b, Bx>0, where B is a non-singular matrix. In this note, we stress that the proposed peculiar form is unsolvable and meaningless. The two schemes have confused the functional inequality constraints Bx>0 with the nonnegativity constraints x>0 in the linear programming model. But the condition x>0 is indispensable to the simplex method. Therefore, both two schemes failed.

cs.CR↗
arXiv2015

The Paillier's Cryptosystem and Some Variants Revisited

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 this paper, we show that there is a big difference between the original Paillier's encryption and some variants. The Paillier's encryption can be naturally transformed into a signature scheme but these variants miss the feature. In particular, we simplify the alternative decryption procedure of Bresson-Catalano-Pointcheval encryption scheme proposed at Asiacrypt'03. The new version is more applicable to cloud computing because of its double trapdoor decryption mechanism and its flexibility to be integrated into other cryptographic schemes. It captures a new feature that its two groups of secret keys can be distributed to different users so as to enhance the robustness of key management.

cs.CR↗
arXiv2015

On the Weakness of Fully Homomorphic Encryption

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 primitive has interested many researchers. In this paper, we stress that any computations performed on encrypted data are constrained to the encrypted domain (finite fields or rings). This restriction makes the primitive useless for most computations involving common arithmetic expressions and relational expressions. It is only applicable to the computations related to modular arithmetic. We want to reaffirm that cryptography uses modular arithmetic a lot in order to obscure and dissipate the redundancies in a plaintext message, not to perform any numerical calculations. We think it might be an overstated claim that FHE is of great importance to client-server computing or cloud computing.

cs.CR↗
arXiv2015

A Note On One Realization of a Scalable Shor Algorithm

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 remark that the report is somewhat misleading because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles behind the demonstration have not been explained properly, including its correctness and complexity.

quant-ph↗
arXiv2015

A Note On Boneh-Gentry-Waters Broadcast Encryption Scheme and Its Like

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 is widely known that the primitive of encryption is different from key establishment, we find some researchers have confused the two primitives. In this note, we shall clarify the fundamental difference between the two primitives, and point out that the Boneh-Gentry-Waters broadcast encryption scheme and its like are key establishment schemes, not encryption schemes.

cs.CR↗
arXiv2014

Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm

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 and Saeedi, et al., are flawed. We also remark that some experimental demonstrations of Shor's algorithm are misleading, because they violate the necessary condition that the selected number $q=2^s$, where $s$ is the number of qubits used in the first register, must satisfy $n^2 \leq q < 2n^2$, where $n$ is the large number to be factored.

cs.DS↗
arXiv2014

On Shor's Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers

Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity argument is sound. This contradicts the argument that the second register has $r$ possible measured values. There is an anonymous comment which argues that the states in these registers are entangled. If so, the entanglement involving many quantum registers can not be interpreted by the mechanism of EPR pairs and the like. In view of this peculiar entanglement has not yet been mentioned and investigated, we think the claim that the Shor's algorithm runs in polynomial time needs more physical verifications. We also discuss the problem to certify quantum computers.

cs.DS↗
arXiv2014

The Barth-Boneh-Waters Private Broadcast Encryption Scheme Revisited

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 recipients. In their construction, a recipient has to first decrypt the received ciphertext to extract the verification key for one-time signature. He then uses the verification key to check whether the ciphertext is malformed. The authors did not consider that information delivered over a channel, especially over a broadcast channel, should be authenticated as to its origin. We remark that the conventional public key signature suffices to authenticate data origin and filter out all malformed ciphertexts. We also discuss the disadvantages of the primitive of one-time signature used in their construction.

cs.CR↗
arXiv2014

Remarks on the Cryptographic Primitive of Attribute-based Encryption

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 encryption which has no intention to exclude any partners of the intended receiver from obtaining the plaintext, an ABE system tries to exclude some unintended recipients from obtaining the plaintext whether they are partners of some intended recipients. We remark that this requirement for ABE is very hard to meet. An ABE system cannot truly exclude some unintended recipients from decryption because some users can exchange their decryption keys in order to maximize their own interests. The flaw discounts the importance of the cryptographic primitive.

cs.CR↗