Block encryption of quantum messages

In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots of researches have shown that quantum cryptography can outperform the limitation of traditional cryptography. This article proposes a new constructive mode for private quantum encryption, named $\mathcal{EHE}$, which is a very simple method to construct quantum encryption from classical primitive. Based on $\mathcal{EHE}$ mode, we construct a quantum block encryption (QBE) scheme from pseudorandom functions. If the pseudorandom functions are standard secure, our scheme is indistinguishable encryption under chosen plaintext attack. If the pseudorandom functions are permutation on the key space, our scheme can achieve perfect security. In our scheme, the key can be reused and the randomness cannot, so a $2n$-bit key can be used in an exponential number of encryptions, where the randomness will be refreshed in each time of encryption. Thus $2n$-bit key can perfectly encrypt $O(n2^n)$ qubits, and the perfect secrecy would not be broken if the $2n$-bit key is reused for only exponential times. Comparing with quantum one-time pad (QOTP), our scheme can be the same secure as QOTP, and the secret key can be reused (no matter whether the eavesdropping exists or not). Thus, the limitation of perfectly secure encryption (Shannon's theory) is broken in the quantum setting. Moreover, our scheme can be viewed as a positive answer to the open problem in quantum cryptography "how to unconditionally reuse or recycle the whole key of private-key quantum encryption". In order to physically implement the QBE scheme, we only need to implement two kinds of single-qubit gates (Pauli $X$ gate and Hadamard gate), so it is within reach of current quantum technology.Comment: 13 pages, 1 figure. Prior version appears in eprint.iacr.org(iacr/2017/1247). This version adds some analysis about multiple-message encryption, and modifies lots of contents. There are no changes about the fundamental result

Top-squark mixing effects in the supersymmetric electroweak corrections to top quark production at the Tevatron

Taking into account the mixing effects between left- and right-handed top-squarks, we calculate the genuine supersymmetric eletroweak correction to top quark production at the Tevatron in the minimal supersymmetric model. The analytic expressions of the corrections to both the parton level cross section and the total hadronic cross section are presented. Some numerical examples are also given to show the size of the corrections.Comment: 11 pages, 3 figures, available at reques

On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.Comment: 41 page

Selection of Statistical Software for Solving Big Data Problems for Teaching

The need for analysts with expertise in big data software is becoming more apparent in 4 today’s society. Unfortunately, the demand for these analysts far exceeds the number 5 available. A potential way to combat this shortage is to identify the software sought by 6 employers and to align this with the software taught by universities. This paper will 7 examine multiple data analysis software – Excel add-ins, SPSS, SAS, Minitab, and R – and 8 it will outline the cost, training, statistical methods/tests/uses, and specific uses within 9 industry for each of these software. It will further explain implications for universities and 10 students (PDF