The min-entropy is a widely used metric to quantify the randomness of generated random numbers, which measures the difficulty of guessing the most likely output. It is difficult to accurately estimate the min-entropy of a non-independent and identically distributed (non-IID) source. Hence, NIST Special Publication (SP) 800-90B adopts ten different min-entropy estimators and then conservatively selects the minimum value among ten min-entropy estimates. Among these estimators, the longest repeated substring (LRS) estimator estimates the collision entropy instead of the min-entropy by counting the number of repeated substrings. Since the collision entropy is an upper bound on the min-entropy, the LRS estimator inherently providesoverestimatedoutputs. In this paper, we propose two techniques to estimate the min-entropy of a non-IID source accurately. The first technique resolves the overestimation problem by translating the collision entropy into the min-entropy. Next, we generalize the LRS estimator by adopting the general Rényi entropy instead of the collision entropy (i.e., Rényi entropy of order two). We show that adopting a higher order can reduce the variance of min-entropy estimates. By integrating these techniques, we propose a generalized LRS estimator that effectively resolves the overestimation problem and provides stable min-entropy estimates. Theoretical analysis and empirical results support that the proposed generalized LRS estimator improves the estimation accuracy significantly, which makes it an appealing alternative to the LRS estimator.

Recently, the standard ResNet-20 network was successfully implemented on the fully homomorphic encryption scheme, residue number system variant Cheon-Kim-Kim-Song (RNS-CKKS) scheme using bootstrapping, but the implementation lacks practicality due to high latency and low security level. To improve the performance, we first minimize total bootstrapping runtime using multiplexed parallel convolution that collects sparse output data for multiple channels compactly. We also propose the imaginary-removing bootstrapping to prevent the deep neural networks from catastrophic divergence during approximate ReLU operations. In addition, we optimize level consumptions and use lighter and tighter parameters. Simulation results show that we have 4.67x lower inference latency and 134x less amortized runtime (runtime per image) for ResNet-20 compared to the state-of-the-art previous work, and we achieve standard 128-bit security. Furthermore, we successfully implement ResNet-110 with high accuracy on the RNS-CKKS scheme for the first time.

The min-entropy is a widely used metric to quantify the randomness of generated random numbers, which measures the difficulty of guessing the most likely output. It is difficult to accurately estimate the min-entropy of a non-independent and identically distributed (non-IID) source. Hence, NIST Special Publication (SP) 800-90B adopts ten different min-entropy estimators and then conservatively selects the minimum value among ten min-entropy estimates. Among these estimators, the longest repeated substring (LRS) estimator estimates the collision entropy instead of the min-entropy by counting the number of repeated substrings. Since the collision entropy is an upper bound on the min-entropy, the LRS estimator inherently provides overestimated outputs. In this paper, we propose two techniques to estimate the min-entropy of a non-IID source accurately. The first technique resolves the overestimation problem by translating the collision entropy into the min-entropy. Next, we generalize the LRS estimator by adopting the general Rényi entropy instead of the collision entropy (i.e., Rényi entropy of order two). We show that adopting a higher order can reduce the variance of min-entropy estimates. By integrating these techniques, we propose a generalized LRS estimator that effectively resolves the overestimation problem and provides stable min-entropy estimates. Theoretical analysis and empirical results support that the proposed generalized LRS estimator improves the estimation accuracy significantly, which makes it an appealing alternative to the current-standard LRS estimator.

The comparison operation for two numbers is one of the most frequently used operations in several applications, including deep learning. As such, lots of research has been conducted with the goal of efficiently evaluating the comparison operation in homomorphic encryption schemes. Recently, Cheonet al.(Asiacrypt 2020) proposed new comparison methods that approximated the sign function on homomorphically encrypted data using composite polynomials and proved that these methods had optimal asymptotic complexity. In this article, we propose a practically optimal method that approximates the sign function using compositions of minimax approximation polynomials. We prove that this approximation method is optimal with respect to depth consumption and the number of non-scalar multiplications. In addition, we propose a polynomial-time algorithm that determines the optimal composition of minimax approximation polynomials for the proposed homomorphic comparison operation using dynamic programming. The numerical analysis demonstrates that when minimizing runtime, the proposed comparison operation reduces the runtime by approximately 45 percent on average when compared to the previous algorithm. Likewise, when minimizing depth consumption, the proposed algorithm reduces the runtime by approximately 41 percent on average. In addition, when high precision in the comparison operation is required, the previous algorithm does not achieve 128-bit security, while the proposed algorithm does due to its small depth consumption.

The min-entropy is a widely used metric to quantify the randomness of generated random numbers in cryptographic applications; it measures the difficulty of guessing the most likely output. An important min-entropy estimator is thecompression estimatorof NIST Special Publication (SP) 800-90B, which relies on Maurer’s universal test. In this paper, we propose two kinds of min-entropy estimators to improve computational complexity and estimation accuracy by leveraging two variations of Maurer’s test: Coron’s test (for Shannon entropy) and Kim’s test (for Rényi entropy). First, we propose a min-entropy estimator based on Coron’s test. It is computationally more efficient than the compression estimator while maintaining the estimation accuracy. The secondly proposed estimator relies on Kim’s test that computes the Rényi entropy. This estimator improves estimation accuracy as well as computational complexity. We analytically characterize the bias-variance tradeoff, which depends on the order of Rényi entropy. By taking into account this tradeoff, we observe that the order of two is a proper assignment and focus on the min-entropy estimation based on the collision entropy (i.e., Rényi entropy of order two). The min-entropy estimation from the collision entropy can be described by a closed-form solution, whereas both the compression estimator and the proposed estimator based on Coron’s test do not have closed-form solutions. By leveraging the closed-form solution, we also propose a lightweight estimator that processes data samples in an online manner. Numerical evaluations demonstrate that the first proposed estimator achieves the same accuracy as the compression estimator with much less computation. The proposed estimator based on the collision entropy can even improve the accuracy and reduce the computational complexity.

Recently underground subways are often constructed to accommodate more pleasant public transportation conditions in metropolitan areas. For mobile operators, it is required to provide proper cellular coverage in the underground subway tunnels with certain coverage requirement. In this paper, we propose a novel LTE cell design approach for underground tunnels based on minimum data throughput requirement over the certain percentage of coverage. The feasibility of the design approach is verified by actual measurement. We also provide a simple two-slope propagation model for tunnel environment.

Conventional cell radius of LTE system is limited up to 100 km. However, there has been needs for the longer coverage, especially in LTE maritime system for public safety. In this paper, we demonstrate the feasibility of an LTE maritime system with coverage ranging more than 100 km through experiments. The experiments were performed with multi-cell configuration, where one cell covers up to 100 km and another covers 80 km to 180 km. We also propose a simplified three-slope radio propagation model in ocean area with various base station antenna heights based on the measurement performed in the experiments.

The authors propose new McEliece cryptosystems based on punctured Reed–Muller (RM) codes. They successfully show that the commonly known attacks, such as the Minder–Shokrollahi attack, the Chizhov–Borodin attack, and the square code attack, are ineffective against the proposed RM code‐based McEliece cryptosystem. We developed an optimal puncturing scheme to prevent the above‐mentioned attacks for the proposed RM code‐based cryptosystems in a sense that the exact locations of puncturing positions with the minimum number of punctured columns of the generator matrix should be found for attacking. It is important to carry out the minimum number of punctures, however, as code modification resulting from puncturing can reduce security. Additionally, the square code attack can be prevented in the proposed RM code‐based McEliece cryptosystems by using both the proposed puncturing method and random insertion methods.

Abstract Zhang introduced a novel reversible data‐hiding scheme for encrypted images. At the receiver, the hidden data is extracted by exploiting the spatial correlation in the image. But Zhang's scheme does not perform well for smaller block sizes and incurs bit extraction errors during recovery. We eliminate this problem by omitting those blocks from the data‐hiding operation that causes extraction errors. To identify those blocks at the receiver, we embed their index information into a small portion of the image using a difference expansion method. The experimental results from the proposed scheme indicate that all the hidden data can be successfully retrieved without errors. Copyright © 2017 John Wiley & Sons, Ltd.

Recently, an efficient homomorphic MAC scheme for authentication in network coding is proposed and it is claimed that it achieves a security parameter$1/q^l$where$l$is selected according to different security requirements. However, in this paper, we show that there is an attack to make the security parameter$1/q$instead of$1/q^l$. And we propose a way to avoid the presented attack.

In this paper, a new class of (N, K) near-optimal partial Hadamard codebooks is proposed. The construction of the proposed codebooks from Hadamard matrices is based on binary row selection sequences, which are generated by quadratic have parameters N = pnand K = (p - 1/2 p)(N + √N) + 1 for an odd prime p and an even positive integer n. We prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large p and derive their inner product distribution.

Large prime numbers are one of inevitable ingredients in the public key crypto-systems. However, the decision of the primality requires significant computational resources. In this paper, we proposed two efficient methods to generate large prime numbers. Firstly, an accelerating method by utilizing pre-installed modular multiplier which is used to calculate public key algorithm is proposed. Secondly, new improved algorithm which reduces computational resources is presented. In the latter algorithm, the requirement for the related parameters are reinforced in order to prevent generating random numbers with small prime factors. In addition, by slightly releasing the requirement for the parameters, it is possible to remove the unit generation procedure in Joye and Paillier's scheme. Through these modifications, it is possible to obtain new efficient prime number generation algorithm.

In this paper, we provides a coding theoretic construction of DNA codes. Previously, some works have been carried out on DNA codes with biologically motivated constraints such as minimum Hamming distance and constant GC-content. Therefore, for given code-length N, the number of GC-content w, and minimum hamming distance d, it is interesting to construct DNA codes with maximum size A4GC(N, w, d). In the previous works, the DNA codes from the quaternary constant weight codes have been proposed [5]. In this paper, we propose another approach based on the binary constant weight codes, not quaternary ones. It is found that the size of the new DNA codes from binary constant weight codes is greater than or equal to that from the quaternary ones. First a general approach to constructing DNA codes from a binary constant weight code is proposed. Second, a specific DNA code with parameters (2n- 1, 2n-1, 2n-1) from binary sequences with ideal autocorrelation property is constructed.

In this paper, a new generation method of quaternary sequences of period 2(2n-1) with ideal autocorrelation and balance property is proposed using the binary sequences of period 2n- 1 with ideal autocorrelation and reverse Gray mapping. The autocorrelation distribution of the proposed quaternary sequences is also derived.

In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the Legendre sequences of period p. The distribution of autocorrelation function of the proposed quaternary sequences is also derived.

We propose a new construction of quaternary sequences using the reverse Gray mapping of a pair of binary Sidel'nikov sequences. The proposed construction provides sequences of even period N with the maximum nontrivial auto-correlation magnitude, Rmax= 2. For N ≡ 0 mod 4, the new quaternary sequences have the optimal Rmax= 2 and are almost-balanced in contrast to the only earlier optimal construction Sj[1].

In this paper, a new extending method of q-ary low correlation zone(LCZ) sequence sets is proposed, which is a generalization of binary LCZ sequence set by Kim, Jang, No, and Chung. Using this method, q-ary LCZ sequence set with parameters (N,M,L, isin) is extended as a q-ary LCZ sequence set with parameters (pN, pM, plfloor(L + 1)/plfloor - 1, pisin), where p is prime and p|q.

In this paper, for a positive integer M and a prime p such that M|pn- 1, a family of M-ary sequences using the M-ary Sidel'nikov sequences with period pn-1 is constructed. This family has its maximum magnitude of correlation values upper bounded by 3radic(pn) + 6 and the family size is (M-I)2(2n-1-1) + M - 1 for p = 2 or (M-1)2(pn-3)/2+ M (M-1)/2 for an odd prime p.

In this correspondence, for a positive integerMand a prime p such that M|pn- 1, three families of M-ary sequences using theM-ary Sidel'nikov sequences with period pn- 1 are constructed. Two small families contain [(pn- 1)/2]+M-2 or pn+M-3M-ary sequences, and both of their maximum magnitudes of correlation values are upper bounded by 2 radic{pn} + 6. The largest family has its maximum magnitude of correlation values upper bounded by 3 radic{pn}+5 and the family size is (M-1)2(2n-1-1) +M-1 for p = 2 or (M-1)2(pn- 3)/2 +M(M-1)/2 for an odd prime p.

For an odd prime p, n=4k, and d=((p2k+1)/2)2, there are (p2k+1)/2 distinct decimated sequences s(dt+l), 0lesl2k+)/2,of a p-ary m-sequence s(t) of period pn-1 because gcd(d,pn-1)=(p2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l),0lesl2k+1)/2, takes the values in {-1, -1 -radic(pn),-1+radic(pn),-1+2radic(pn)} and their cross-correlation distribution is also derived.

For an odd prime p, an even integer n, and d = pk+ 1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 les In- 1 since gcd(d, pn-1) = p + 1. In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p+1 distinct decimated sequences s(dt+l) is derived. The maximum magnitude of their cross-correlation values is l+p radic pnif I = 0 mod p + 1 for n = 0 mod 4 or I = (p + l)/2 mod p + 1 for n = 2 mod 4 and otherwise, 1 + radicpn. Also by using s(t) and s(dt + I), a new family of p-ary sequences of period pn-1 is constructed, whose family size is pnmiddot and Cmaxis 1+ pradicpn.

For an odd prime p, n=4k, and d=((p2k+1)/2)2, there are (p2k+1)/2distinct decimated sequences s(dt+l), 0lesl2k+1)/2, of a p-ary m-sequence s(t) of period pn-1 because gcd(d,pn-1)=(p2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+I), 0lesl2k+1)/2, takes the values in {-1, -1 - radicpn, -1+radicpn-1+2radicpn} and their cross-correlation distribution is also derived.

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn- 1,pe- 1, (pn- 1)/(p - 1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. But the method used in the proof is quite different from that used in the quaternary LCZ sequence. The proof used in this paper can be used for the proof of quaternary LCZ sequence

In this paper, we present several construction methods for low-correlation zone (LCZ) sequence sets. First, we propose a design scheme for binary LCZ sequence sets with parameters (2n+1-2,M,L,2). In this scheme, we can freely set the LCZ length L and the resulting LCZ sequence sets have the size M, which is almost optimal with respect to Tang, Fan, and Matsufuji bound. Second, given a q-ary LCZ sequence set with parameters (N,M,L,epsi) and even q, we construct another q-ary LCZ sequence set with parameters (2N,2M,L,2epsi) or (2N,2M,L-1,2epsi). Especially, the new set with parameters (2N,2M,L,2) can be optimal in terms of the set size if a q-ary optimal LCZ sequence set with parameters (N,M,L,1) is used

In this paper, we derive the cyclotomic numbers of order 5 over an extension field Fpnusing the well-known results of quintic Jacobi sums over Fp(B. C. Berndt, et al., 1998). For p ne 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over Fpn. For p equiv 1 mod 5, we express the cyclotomic number of order 5 over Fpnin terms of the solution of the diophantine system which is required to evaluate the cyclotomic number of order 5 over Fpn. Using the cyclotomic numbers of order 5 over Fpn, autocorrelation distributions of 5-ary Sidel'nikov sequences of period pn- 1 are also derived

In this paper, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not only on M but also on the period of the sequence, but always less than or equal to (2M) + 1

In this paper, we derive linear complexity over Fpof the M-ary Sidel'nikov sequences using discrete Fourier transform. As an example, we represent the linear complexity of the ternary Sidel'nikov sequences. It turned out that the ternary Sidel'nikov sequences have the linear complexity nearly close to their periods

For a prime p and positive integers M and n such that M|p/sup n/-1, Sidel'nikov introduced M-ary sequences (called Sidel'nikov sequences) of period p/sup n/-1, the out-of-phase autocorrelation magnitude of which is upper bounded by 4. In this correspondence, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not only on M but also on the period of the sequence, but always less than or equal to (M/2)+1.

In this paper, using p-ary bent functions defined on vector space over the intermediate finite field, we generalized the construction method of the families of p-ary bent sequences with balanced and optimal correlation properties introduced by Kumar and Moreno for an odd prime p, called generalized p-ary bent sequences.

For an odd prime p and integers n, m, and k such that n=(2m+1)k, a new family of p-ary sequences of period p/sup n/-1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p/sup n/. That is, the maximum nontrivial correlation value R/sub max/ of all pairs of distinct sequences in the family does not exceed p/sup n/2/+1, which means the family has optimal correlation in terms of Welch's lower bound. The symbol distribution of the sequences in the family is enumerated. It is also shown that the linear span of the sequences in the family is (m+2)n except for the m-sequence in the family.

An approach for designing a hybrid parallel system that can perform different levels of parallelism adaptively is presented. An adaptive parallel computer vision system (APVIS) is proposed to attain this goal. The APVIS is constructed by integrating two different types of parallel architectures, i.e. a multiprocessor based system (MBS) and a memory based processor array (MPA), tightly into a single machine. One important feature in the APVIS is that the programming interface to execute data parallel code onto the MPA is the same as the usual subroutine calling mechanism. Thus the existence of the MPA is transparent to the programmers. This research is to design an underlying base architecture that can be optimally executed for a broad range of vision tasks. A performance model is provided to show the effectiveness of the APVIS. It turns out that the proposed APVIS can provide significant performance improvement and cost effectiveness for highly parallel applications having a mixed set of parallelisms. Also an example application composed of a series of vision algorithms, from low-level and medium-level processing steps, is mapped onto the MPA. Consequently, the APVIS with a few or tens of MPA modules can perform the chosen example application in real time when multiple images are incoming successively with a few seconds inter-arrival time.

In this paper an effective memory-processor integrated architecture, called memory based processor array (MPA), for computer vision is proposed. The MPA can be easily attached into any host system via memory interface. In order to measure the impact of the memory interface structure an analytical model is derived. The performance improvement on the proposed model for the memory interface architecture of the MPA system can be 6%/spl sim/40% for vision tasks consisting of sequential and data parallel tasks. The asymptotic time complexities of the mapping algorithms are evaluated to verify the cost-effectiveness and the efficiency of the MPA system.