高维矩阵在密码学中的应用

本文利用高维矩阵给出一类新型的公钥分配方案,并将它推广到会议情形;接着在此公钥分配方案的基础上给出了另一类自确认密码体系.

Measuring-Basis Encrypted Quantum Key Distribution with Four-State Systems

A measuring-basis encrypted quantum key distribution scheme is proposed by using twelve nonorthogohal states in a four-state system and the measuring-basis encryption technique. In this scheme, two bits of classical information can be encoded on one four-state particle and the transmitted particles can be fully used.

Cryptanalysis of Cryptosystems Based on General Linear Group

Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. In this background, Majid Khan et al.proposed two novel public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring. In this paper we show that the two schemes are not secure. We present that they are vulnerable to a structural attack and that, it only requires polynomial time complexity to retrieve the message from associated public keys respectively. Then we conduct a detailed analysis on attack methods and show corresponding algorithmic description and efficiency analysis respectively. After that, we propose an improvement assisted to enhance Majid Khan's scheme. In addition, we discuss possible lines of future work.

Asymmetrical Quantum Encryption Protocol Based on Quantum Search Algorithm

Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.

Quantum Key Distribution Scheme Based on Dense Encoding in Entangled States

A quantum key distribution protocol, based on the quantum dense encoding in entangled states, is presented. In this protocol, we introduce an encoding process to encode two classical bits information into one of the four one-qubit unitary operations implemented by Alice and the Bell states measurement implemented by Bob in stead of direct measuring the previously shared Einstein-Podolsky-Rosen pairs by both of the distant parties, Alice and Bob.Considering the practical application we can get the conclusion that our protocol has some advantages. It not only simplifies the measurement which may induce potential errors, but also improves the effectively transmitted rate of the generated qubits by the raw key. Here we also discuss eavesdropping attacks against the scheme and the channel loss.

A Composed Protocol of Quantum Identity Authentication Plus Quantum Key Distribution Based on Squeezed States

It is established that a single quantum cryptography protocol usually cooperates with other cryptographicsystems,such as an authentication system,in the real world.However,few protocols have been proposed on how tocombine two or more quantum protocols.To fill this gap,we propose a composed quantum protocol,containing bothquantum identity authentication and quantum key distribution,using squeezed states.Hence,not only the identity canbe verified,but also a new private key can be generated by our new protocol.We also analyze the security under anoptimal attack,and the efficiency,which is defined by the threshold of the tolerant error rate,using Gaussian errorfunction.

A Comprehensive Study of Algebraic Fault Analysis on PRINCE

PRINCE is a 64-bit lightweight block cipher with a 128-bit key published at ASIACRYPT 2012. Assuming one nibble fault is injected, previous different fault analysis(DFA) on PRINCE adopted the technique from DFA on AES and current results are different. This paper aims to make a comprehensive study of algebraic fault analysis(AFA) on PRINCE. How to build the equations for PRINCE and faults are explained. Extensive experiments are conducted. Under nibble-based fault model, AFA with three or four fault injections can succeed within 300 seconds with a very high probability. Under other fault models such as byte-based, half word-based, word-based fault models, the faults become overlapped in the last round and previous DFAs are difficult to work. Our results show that AFA can still succeed to recover the full master key. To evaluate security of PRINCE against fault attacks, we utilize AFA to calculate the reduced entropy of the secret key for given amount of fault injections. The results can interpret and compare the efficiency of previous work. Under nibble-based fault model, the master key of PRINCE can be reduced to 29.69 and 236.10 with 3 and 2 fault injections on average, respectively.

The NP-Complete Face of Information-Theoretic Security

The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution （QKD）, which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors＇ results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure （in case that P, NP） or infrastructures facilitating perfectly confidential communication can be constructed efficiently （in case that P = NP）.

Key Exchange Protocol Based on Tensor Decomposition Problem

The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.

Fluctuation Analysis of Decoy State QKD with Finite Data-Set Size

Decoy state method quantum key distribution (QKD) is one of the promising practical solutions for BB84QKD with coherent light pulses.The number of data-set size in practical QKD protocol is always finite,which will causestatistical fluctuations.In this paper,we apply absolutely statistical fluctuation to amend the yield and error rate of thequantum state.The relationship between exchanged number of quantum signals and key generation rate is analyzed inour simulation,which offers a useful reference for experiment.

Distributed Certificateless Key Encapsulation Mechanism Secure Against the Adaptive Adversary

This paper proposes an adaptively secure solution to certificateless distributed key encapsulation mechanism from pairings by using Canetti＇s adaptive secure key generation scheme based on discrete logarithm. The proposed scheme can withstand adaptive attackers that can choose players for corruption at any time during the run of the protocol, and this kind of attack is powerful and realistic. In contrast, all previously presented threshold certificateless public key cryptosystems are proven secure against the more idealized static adversaries only. They choose and fix the subset of target players before running the protocol. We also prove security of this scheme in the random oracle model.

On enumeration of polynomial equivalence classes

The isomorphism of polynomials （IP）, one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials. Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate publi9 key cryptosystem. In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX^2qi when char（Fq） = 2, which implies that these polynomials are all weak IP instances. Moreover, we study the cardinality of an equivalence class containing the binomial aX2qi ＋ bX2qj （i ≠ j） over Fqn without the restriction that char（Fq） = 2, which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.

Counterfactual Quantum Deterministic Key Distribution

We propose a new counterfactual quantum cryptography protocol concerning about distributing a deterministic key.By adding a controlled blocking operation module to the original protocol [T.G.Noh,Phys.Rev.Lett.103(2009) 230501],the correlation between the polarizations of the two parties,Alice and Bob,is extended,therefore,one can distribute both deterministic keys and random ones using our protocol.We have also given a simple proof of the security of our protocol using the technique we ever applied to the original protocol.Most importantly,our analysis produces a bound tighter than the existing ones.

Performance analysis of quantum key distribution based on air-water channel

Considering the air-water interface and ocean water’s optical attenuation,the performance of quantum key distribution(QKD)based on air-water channel is studied.The effects of photons’various incident angles to air-water interface on quantum bit error rate(QBER)and the maximum secure transmission distance are analyzed.Taking the optical attenuation of ocean water into account,the performance bounds of QKD in different types of ocean water are discussed.The simulation results show that the maximum secure transmission distance of QKD gradually reduces as the incident angle from air to ocean water increases.In the clearest ocean water with the lowest attenuation,the maximum secure transmission distance of photons far exceeds the the working depth of underwater vehicles.In intermediate and murky ocean waters with higher attenuation,the secure transmission distance shortens,but the underwater vehicle can deploy other accessorial methods for QKD with perfect security.So the implementation of OKD between the satellite and the underwater vehicle is feasible.

FPGA based digital phase-coding quantum key distribution system

Quantum key distribution （QKD） is a technology with the potential capability to achieve information-theoretic security. Phase- coding is an important approach to develop practical QKD systems in fiber channel. In order to improve the phase-coding modulation rate, we proposed a new digital-modulation method in this paper and constructed a compact and robust prototype of QKD system using currently available components in our lab to demonstrate the effectiveness of the method. The system was deployed in laboratory environment over a 50 km fiber and continuously operated during 87 h without manual interaction. The quantum bit error rate （QBER） of the system was stable with an average value of 3.22% and the secure key generation rate is 8.91 kbps. Although the modulation rate of the photon in the derno system was only 200 MHz, which was limited by the Faraday- Michelson interferometer （FMI） structure, the proposed method and the field programmable gate array （FPGA） based electronics scheme have a great potential for high speed QKD systems with Giga-bits/second modulation rate.