Journal•ISSN: 0916-8508

# IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Institute of Electronics, Information and Communication Engineers

About: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences is an academic journal published by Institute of Electronics, Information and Communication Engineers. The journal publishes majorly in the area(s): Computer science & Adaptive filter. It has an ISSN identifier of 0916-8508. Over the lifetime, 9985 publications have been published receiving 66412 citations. The journal is also known as: IEICE transactions & Institute of Electronics, Information and Communication Engineers transactions on fundamentals of electronics, communications and computer sciences.

Topics: Computer science, Adaptive filter, Decoding methods, CMOS, Orthogonal frequency-division multiplexing

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830 citations

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TL;DR: The aim is to characterizing elliptic curve traces by FR-reduction and investigate explicit conditions of traces vulnerable or secure against FR- reduction, and to show new explicit Conditions of elliptic Curve traces for FRreduction.

Abstract: Elliptic curve cryptosystems([19],[25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FRreduction([11],[17]) and anomalous elliptic curve over Fq ([3], [33], [35]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller definition field. ECDLP has an interesting property that the security deeply depends on elliptic curve traces rather than definition fields, which does not occur in the case of the discrete logarithm problem(DLP). Therefore it is important to characterize elliptic curve traces explicitly from the security point of view. As for FR-reduction, supersingular elliptic curves or elliptic curve E/Fq with trace 2 have been reported to be vulnerable. However unfortunately these have been only results that characterize elliptic curve traces explicitly for FRand MOV-reductions. More importantly, the secure trace against FR-reduction has not been reported at all. Elliptic curves with the secure trace means that the reduced extension degree is always higher than a certain level. In this paper, we aim at characterizing elliptic curve traces by FR-reduction and investigate explicit conditions of traces vulnerable or secure against FR-reduction. We show new explicit conditions of elliptic curve traces for FRreduction. We also present algorithms to construct such elliptic curves, which have relation to famous number theory problems. key words: elliptic curve cryptosystems, trace, FRreduction

623 citations

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TL;DR: A class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms, which work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-d determined (over-complete) case if data are sufficiently sparse.

Abstract: Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multi-sensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the alpha and beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-determined (over-complete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for N-th order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multi-layer hierarchical NMF approach [3].

527 citations

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450 citations

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TL;DR: In this paper, a bit commitment scheme, BC(.), and efficient statistical zero knowledge (SZK) protocols are proposed, in which, for any given multi-variable polynomial f(X 1,...,X t ) and any given modulus n, prover P gives (I 1,..,I t ) to verifier V and can convince V that P knows (x 1,...,x t ) satisfying f(x 1,...x t ), 0 (mod n) and I i = BC(x i ), (i = 1

Abstract: This paper proposes a bit commitment scheme, BC(.), and efficient statistical zero knowledge (in short, SZK) protocols in which, for any given multi-variable polynomial f(X 1 ,...,X t ) and any given modulus n, prover P gives (I 1 ,...,I t ) to verifier V and can convince V that P knows (x 1 ,...,x t ) satisfying f(x 1 ,...x t )? 0 (mod n) and I i = BC(x i ), (i = 1,.., t). The proposed protocols are O(|n|) times more efficient than the corresponding previous ones [Dam93, Dam95, Oka95]. The (knowledge) soundness of our protocols holds under a computational assumption, the intractability of a modified RSA problem (see Def.3), while the (statistical) zero-knowledgeness of the protocols needs no computational assumption. The protocols can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.

431 citations