Authorship：Last author   Language：English   Publishing type：Research paper (other academic)  

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.4064/bc126-7

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s13160-023-00580-z

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Other Link： https://link.springer.com/article/10.1007/s13160-023-00580-z/fulltext.html

Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)  

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.dam.2022.04.018

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us 10 develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. CMAP-LAP facilitates the implementation of large-scale parallel strategies for lattice problems since all the functions are designed to he customizable and abstract. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.

DOI： 10.1109/hipc53243.2021.00018

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.dam.2021.07.035

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Authorship：Last author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-85987-9_1

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-92641-0_10

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Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (bulletin of university, research institution)  

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

Lattice-based cryptography has received attention as a next-generation encryption technique, because it is believed to be secure against attacks by classical and quantum computers. Its essential security depends on the hardness of solving the shortest vector problem (SVP). In the cryptography, to determine security levels, it is becoming significantly more important to estimate the hardness of the SVP by high-performance computing. In this study, we develop the world's first distributed and asynchronous parallel SVP solver, the MAssively Parallel solver for SVP (MAP-SVP). It can parallelize algorithms for solving the SVP by applying the Ubiquity Generator framework, which is a generic framework for branch-and-bound algorithms. The MAP-SVP is suitable for massive-scale parallelization, owing to its small memory footprint, low communication overhead, and rapid checkpoint and restart mechanisms. We demonstrate its performance and scalability of the MAP-SVP by using up to 100,032 cores to solve instances of the Darmstadt SVP Challenge.

DOI： 10.1109/sc41405.2020.00064

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Authorship：Last author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：Informa UK Limited  

DOI： 10.1080/19393555.2020.1836288

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-981-15-8061-1_3

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Other Link： https://dblp.uni-trier.de/db/conf/icmc2/icmc2020.html#NakamuraTKIYF20

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s10623-020-00765-4

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Publishing type：Research paper (scientific journal)  

DOI： 10.1049/iet-ifs.2019.0220

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：ACM  

DOI： 10.1145/3384940.3388956

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Other Link： https://dblp.uni-trier.de/db/conf/ccs/asiapkc2020.html#IkematsuFKYTY20

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1515/jmc-2020-0072

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Publishing type：Research paper (scientific journal)  

DOI： 10.1515/jmc-2019-0029

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Authorship：Lead author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter GmbH  

<title>Abstract</title>In recent years, the block Korkine-Zolotarev (BKZ) and its variants such as BKZ 2.0 have been used as de facto algorithms to estimate the security of a lattice-based cryptosystem. In 2017, DeepBKZ was proposed as a mathematical improvement of BKZ, which calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. DeepBKZ can find a short lattice vector by smaller blocksizes than BKZ. In this paper, we develop a self-dual variant of DeepBKZ, as in the work of Micciancio and Walter for self-dual BKZ. Like DeepBKZ, our self-dual DeepBKZ calls both DeepLLL and its dual variant as main subroutines in order to accelerate to find a very short lattice vector. We also report experimental results of DeepBKZ and our self-dual DeepBKZ for random bases on the Darmstadt SVP challenge.

DOI： 10.1515/jmc-2015-0053

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Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s10623-019-00634-9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Tokyo  

In this paper, we analyze the security of cryptosystems using short generators over ideal lattices. Our approach is based on a recent work by Cramer et al. on analysis of the recovering short generators problem on q-th cyclotomic fields with prime powers q. In their analysis, implicit lower bounds of the special values of Dirichlet L-functions at 1 are essentially used for estimating some sizes of the dual bases of the log-unit lattices of the q-th cyclotomic fields. Our contribution is to improve Cramer et al.’s analysis by giving explicit lower and upper bounds of the special values of Dirichlet L-functions at 1. Our improvement allows one to analyze the RSG attack not only asymptotically but also explicitly for fixed practical parameters. Moreover, we give experimental evidence that recovering short generators over 2 k-th cyclotomic fields for k≥ 10 is succeeded with high probability.

DOI： 10.1007/s13160-018-0306-z

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

Lattice basis reduction algorithms have been used as a strong tool for cryptanalysis. The most famous one is LLL, and its typical improvements are BKZ and LLL with deep insertions (DeepLLL). In LLL and DeepLLL, at every time to replace a lattice basis, we need to recompute the Gram-Schmidt orthogonalization (GSO) for the new basis. Compared with LLL, the form of the new GSO vectors is complicated in DeepLLL, and no formula has been known. In this paper, we give an explicit formula for GSO in DeepLLL, and also propose an efficient method to update GSO in DeepLLL. As another work, we embed DeepLLL into BKZ as a subroutine instead of LLL, which we call “DeepBKZ”, in order to find a more reduced basis. By using our DeepBKZ with blocksizes up to β = 50, we have found a number of new solutions for the Darmstadt SVP challenge in dimensions from 102 to 123.

DOI： 10.1007/978-3-319-76620-1_9

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Publishing type：Research paper (international conference proceedings)   Publisher：ACM  

DOI： 10.1145/3267323.3268952

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Other Link： https://dblp.uni-trier.de/db/conf/wpes/wpes2018.html#RatheeMY18

Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-030-00434-7_19

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Other Link： https://dblp.uni-trier.de/db/conf/cans/cans2018.html#KudoYTY18

Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-030-00434-7_18

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Other Link： https://dblp.uni-trier.de/db/conf/cans/cans2018.html#LeMDY18

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.

DOI： 10.1007/978-3-319-89339-6_10

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Other Link： https://dblp.uni-trier.de/db/conf/africacrypt/africacrypt2018.html#YasudaYON18

Language：English   Publishing type：Research paper (international conference proceedings)  

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Publishing type：Research paper (scientific journal)  

DOI： 10.14495/jsiaml.9.65

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

Albrecht et al. [1] at Crypto 2016 and Cheon et al. [4] at ANTS 2016 independently presented a subfield attack on overstretched NTRU problem. Their idea is to map the public key down to the subfield (by norm and trace map respectively) and hence obtain a lattice of smaller dimension for which a lattice reduction algorithm is efficiently applicable. At Eurocrypt 2017, Kirchner and Fouque proposed another variant attack which exploits the presence of orthogonal bases within the cyclotomic number rings and instead of using the matrix of the public key in the subfield, they use the multiplication matrix by the public key in the full field and apply a lattice reduction algorithm to a suitable projected lattice of smaller dimension. They also showed a tight estimation of the parameters broken by lattice reduction and implementation results that their attack is better than the subfield attack. In this paper, we exploit technical results from Kirchner and Fouque [12] for the relative norm of field elements in the subfield and we use Hermite factor for estimating the output of a lattice basis reduction algorithm in order to analyze general choice of parameters for the subfield attack by Albrecht et al. [1]. As a result, we obtain the estimation for better choices of the subfields for which the attack works with smaller modulus. Our experiment results show that we can attack overstretched NTRU with modulus smaller than that of Albrecht et al. and of Kirchner and Fouque.

DOI： 10.1007/978-3-319-69659-1_5

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Other Link： https://dblp.uni-trier.de/db/conf/isw/isc2017.html#DuongYT17

Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-319-72359-4_24

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Other Link： https://dblp.uni-trier.de/db/conf/ispec/ispec2017.html#YasudaSTAYY17

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

Homomorphic encryption allows to perform various calculations on encrypted data without decryption. In this paper, we propose an efficient method for secure multiple matrix multiplications over the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan. Our method is a generalization of Duong et al.’s method, which computes only one multiplication between two matrices. In order to minimize both the ciphertext size and the computation cost, our method packs every matrix into a single ciphertext so that it enables efficient matrix multiplications over the packed ciphertexts. We also propose several modifications to obtain practical performance of secure multiplications among matrices with larger size and entries. We show implementation results of our packing method with modifications for secure multiplications among two and three matrices with 32 × 32 and 64 × 64 sizes and entries from 16-bit to 64-bit.

DOI： 10.1007/978-3-319-72359-4_18

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Other Link： https://dblp.uni-trier.de/db/conf/ispec/ispec2017.html#MishraDY17

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

At CRYPTO 2016, Kim and Barbulescu proposed an efficient number field sieve (NFS) algorithm for the discrete logarithm problem (DLP) in a finite field. The security of pairing-based cryptography (PBC) is based on the difficulty in solving the DLP. Hence, it has become necessary to revise the bitlength that the DLP is computationally infeasible against the efficient NFS algorithms. The timing of the main operations of PBC (i.e. pairing, scalar multiplication on the elliptic curves, and exponentiation on the finite field) generally becomes slower as the bitlength becomes longer, so it has become increasingly important to compute the main operations of PBC more efficiently. To choose a suitable pairing-friendly curve from among various pairing-friendly curves is one of the factors that affect the efficiency of computing the main operations of PBC. We should implement the main operations of PBC and compare the timing among some pairing-friendly curves in order to choose the suitable pairing-friendly curve precisely. In this paper, we focus on the five candidate pairing-friendly curves from the Barreto- Lynn-Scott (BLS) and Kachisa-Schaefer-Scott (KSS) families as the 256- bit secure pairing-friendly curves and show the following two results
(1) the revised bitlength that the DLP is computationally infeasible against the efficient NFS algorithms for each candidate pairing-friendly curve, (2) the suitable pairing-friendly curve by comparing the timing of the main operations of PBC among the candidate pairing-friendly curves using the revised bitlength.

DOI： 10.1007/978-3-319-61204-1_4

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Other Link： https://dblp.uni-trier.de/db/conf/acns/acns2017.html#KiyomuraIKYTK17

Publishing type：Research paper (scientific journal)  

DOI： 10.1515/jmc-2016-0008

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Taylor and Francis Inc.  

With widespread development of biometrics, concerns about security and privacy are rapidly increasing. Homomorphic encryption enables us to operate on encrypted data without decryption, and it can be applied to construct a privacy-preserving biometric system. In this article, we apply two homomorphic encryption schemes based on ideal-lattice and ring-LWE (Learning with Errors), which both have homomorphic correctness over the ring of integers of a cyclotomic field. We compare the two schemes in applying them to privacy-preserving biometrics. In biometrics, the Hamming distance is used as a metric to compare two biometric feature vectors for authentication. We propose an efficient method for secure Hamming distance. Our method can pack a biometric feature vector into a single ciphertext, and it enables efficient computation of secure Hamming distance over our packed ciphertexts.

DOI： 10.1080/19393555.2017.1293199

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.

DOI： 10.1007/s00200-016-0291-x

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：De Gruyter Open Ltd  

Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix multiplication over the packed ciphertexts. Our packing method generalizes Yasuda et al.'s methods (Security Comm. Networks 2015 and ACISP 2015), which are for secure inner product. We also implement our methods and give a comparison with previous packing methods.

DOI： 10.1515/tmmp-2016-0031

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER INTERNATIONAL PUBLISHING AG  

With the widespread development of biometrics, concerns about security and privacy are increasing. In biometrics, template protection technology aims to protect the confidentiality of biometric templates (i.e., enrolled biometric data) by certain conversion. The fuzzy commitment scheme gives a practical way to protect biometric templates using a conventional error-correcting code. The scheme has both concealing and binding of templates, but it has some privacy problems. Specifically, in case of successful matching, stored biometric templates can be revealed. To address such problems, we improve the scheme. Our improvement is to coat with two error-correcting codes. In particular, our scheme can conceal stored biometric templates even in successful matching. Our improved scheme requires just conventional error-correcting codes as in the original scheme, and hence it gives a practical solution for both template security and privacy of biometric templates.

DOI： 10.1007/978-3-319-30303-1_8

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER INT PUBLISHING AG  

With the widespread development of biometric systems, concerns about security and privacy are increasing. An active area of research is template protection technology, which aims to protect registered biometric data. We focus on a homomorphic encryption approach, which enables building a "cryptographically-secure" system. In DPM 2013, Yasuda et al. proposed an efficient template protection system, using the homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan. In this work, we improve and fortify their system to withstand impersonation attacks such as replay and spoofing attacks. We introduce a challenge-response authentication mechanism in their system and design a practical distributed architecture where computation and authentication are segregated. Our comprehensive system would be useful to build a large-scale and secure biometric system such as secure remote authentication over public networks.

DOI： 10.1007/978-3-319-29883-2_12

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN  

DOI： 10.4064/aa8425-6-2016

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER INTERNATIONAL PUBLISHING AG  

The security of a number of modern cryptographic schemes relies on the computational hardness of the learning with errors (LWE) problem. In 2015, Laine and Lauter analyzed a key recovery (or decoding) attack against the search variant of LWE. Their analysis is based on a generalization of the Boneh-Venkatesan method for the hidden number problem to LWE. They adopted the LLL algorithm and Babai's nearest plane method in the attack against LWE, and they also demonstrated a successful range of the attack by experiments for hundreds of LWE instances. In this paper, we give an alternative analysis of the key recovery attack. While Laine and Lauter's analysis gives explicit information about the effective approximation factor in the LLL algorithm and Babai's nearest plane method, our analysis is useful to estimate which LWE instances can be solved by the key recovery attack. Furthermore, our analysis enables one to determine a successful range of the attack with practical lattice reduction such as the BKZ algorithm.

DOI： 10.1007/978-3-319-44524-3_10

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY-BLACKWELL  

In biometrics, template protection technology aims to protect the confidentiality of a biometric template (i.e., enrolled biometric information) by certain conversion. Here, we focus on the key-binding approach for template protection. This approach generates a secure template from joint data of a user's specific key with a user's template, and the key can be correctly extracted from the secure template only when a queried biometric feature is close to the plain template. While almost all conventional schemes use the error correcting code technique, we present a new technique based on lattices to give a new key-binding scheme. Our proposed scheme can provide several requirements (e.g., diversity and revocability) for template protection, which cannot be provided by error correcting code based typical schemes such as the fuzzy commitment and the fuzzy vault. Copyright (C) 2015 John Wiley & Sons, Ltd.

DOI： 10.1002/sec.1267

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

For a prime p, let zeta(p) denote a fixed primitive pth root of unity. Let E be an elliptic curve over a number field k with a p-torsion point. Then the p-torsion subgroup of E gives a Kummer extension over k(zeta(p)). In this paper, for p = 5 and 7, we study the ramification of such Kummer extensions using explicit Kummer generators directly computed by Verdure in 2006.

DOI： 10.1142/S1793042115500736

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Publishing type：Research paper (international conference proceedings)   Publisher：ACM  

DOI： 10.1145/2732516.2732521

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Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-319-19962-7_27

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Publishing type：Research paper (scientific journal)  

DOI： 10.1002/sec.1164

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

Somewhat homomorphic encryption is public key encryption supporting a limited number of both additions and multiplications on encrypted data, which is useful for performing fundamental computations with protecting the data confidentiality. In this paper, we focus on the scheme proposed by Lauter, Naehrig and Vaikuntanathan (ACM CCSW 2011), and present two types of packed ciphertexts based on their packing technique. Combinations of two types of our packing method give practical size and performance for wider computations such as statistical analysis and distances. To demonstrate its efficiency, we implemented the scheme with our packing method for secure Hamming distance, which is often used in privacy-preserving biometrics. For secure Hamming distance between two binary vekoshiba@mail.saitama-u.ac.jpctors of 2048-bit, it takes 5.31ms on an Intel Xeon X3480 at 3.07 GHz. This gives the best performance in the state-of-the-art work using homomorphic encryption.

DOI： 10.1007/978-3-642-54568-9_3

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Publishing type：Research paper (scientific journal)  

DOI： 10.1515/jmc-2013-0024

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

The basic pattern matching problem is to find the locations where a pattern occurs in a text. We give several computations enabling a client to obtain matching results from a database so that the database can not learn any information about client's queried pattern. For such computations, we apply the symmetric-key variant scheme of somewhat homomorphic encryption proposed by Brakerski and Vaikuntanathan (CRYPTO 2011), which can support a limited number of both polynomial additions and multiplications on encrypted data. We also utilize the packing method introduced by Yasuda et al. (CCSW 2013) for efficiency. While they deal with only basic problems for binary vectors, we address more complex problems such as the approximate and wildcards pattern matching for non-binary vectors. To demonstrate the efficiency of our method, we implemented the encryption scheme for secure wildcards pattern matching of DNA sequences. Our implementation shows that a client can privately search real-world genomes of length 16,500 in under one second on a general-purpose PC.

DOI： 10.1007/978-3-319-08344-5_22

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

Template protection technology can protect the confidentiality of a biometric template by certain conversion. We focus on the key-binding approach for template protection. This approach generates a secure template (or a conversion template) from joint data of a user's specific key with a user's template, and the key can be correctly extracted from the secure template only when a queried biometric feature is sufficiently close to the original template. While almost all conventional schemes use the error correcting code (ECC) technique, we present a new technique based on lattices to give a new key-binding scheme. Our proposed scheme can provide several requirements (e.g., diversity and revocability) for template protection, which cannot be provided by ECC-based schemes such as the fuzzy commitment and the fuzzy vault.

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Other Link： http://dblp.uni-trier.de/db/conf/biosig/biosig2014.html#conf/biosig/SugimuraYYAS14

Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

For a prime p, let zeta(p) denote a fixed primitive pth root of unity. Let E be an elliptic curve over a number field K with a p-torsion point. Then the p-torsion subgroup of E gives a Kummer extension over K(zeta(p)), and in this paper, we study the ramification of such Kummer extensions using the Kummer generators directly computed by Verdure in 2006. For quadratic fields K, we also give unramified Kummer extensions over K(zeta(p)) generated from elliptic curves over K having a p-torsion point with bad reduction at certain primes. Many of these unramified Kummer extensions have not appeared in the previous work using fundamental units of quadratic fields.

DOI： 10.1142/S1793042113500541

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Publishing type：Research paper (international conference proceedings)   Publisher：ACM  

DOI： 10.1145/2517488.2517497

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Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-642-40588-4_5

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Language：English   Publishing type：Research paper (scientific journal)  

Let K be a number field and fix a prime number p. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set BK,p of primes of K satisfying that any elliptic curve over K with BK,p-reduction has no p-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with BK,p reduction and a p-torsion point. The action of the absolute Galois group on the p-torsion subgroup of E gives its associated Galois representation PE,p modulo p. We also study the irreducibility and surjectivity of ρE,p for semistable elliptic curves with BK,p-reduction. © 2013 The Korean Mathematical Society.

DOI： 10.4134/BKMS.2013.50.1.083

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Language：English   Publishing type：Research paper (scientific journal)  

In pairing-based cryptography, it is necessary to choose an elliptic curve with a small embedding degree and a large prime-order subgroup, which is called a pairing-friendly curve. In this paper, we study the number of the pairing-friendly curves with a given large prime-order subgroup. © 2012 Academic Publications, Ltd.

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Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we study elliptic curves E over ( such thatthe 3-torsion subgroup E[3] is split as μ3 ⊕ ℤ/3ℤ. For a non-zero integer m, let Cm denote the curve x3 + y3 = m. We consider the relation between the set of integral points of Cm and the elliptic curves E with E[3] ≃ μ3 ⊕ ℤ/3ℤ. © 2012 The Korean Mathematical Society.

DOI： 10.4134/CKMS.2012.27.3.497

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a positive integer α from elements G, αG, α d G in an additive cyclic group generated by G of prime order r and a positive integer d dividing r -1. In 2011, Sakemi et al. implemented Cheon's algorithm for solving DLPwAI, and solved a DLPwAI in a group with 128-bit order r in about 131 hours with a single core on an elliptic curve defined over a prime finite field which is used in the TinyTate library for embedded cryptographic devices. However, since their implementation was based on Shanks' Baby-step Giant-step (BSGS) algorithm as a sub-algorithm, it required a large amount of memory (246 GByte) so that it was concluded that applying other DLPwAIs with larger parameter is infeasible. In this paper, we implemented Cheon's algorithm based on Pollard's ρ-algorithm in order to reduce the required memory. As a result, we have succeeded solving the same DLPwAI in about 136 hours by a single core with less memory (0.5 MByte). © 2012 Springer-Verlag Berlin Heidelberg.

DOI： 10.1007/978-3-642-27890-7_8

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Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-642-32928-9_17

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Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-642-40012-4_1

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a from G, alpha G, alpha(d)G in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r - 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon's algorithm). This paper reports our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

Let X be a non-singular projective (n + 1)-fold defined over an algebraically closed field k of characteristic p &gt;= 0, and B be a non-singular complete curve defined over k. A surjective morphism f : X -&gt; B is said to be an n-abelian fiber space if almost all fibers are n-dimensional abelian varieties. We examine the canonical bundle formula for n-abelian fiber spaces.

DOI： 10.2996/kmj/1301576761

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Language：English   Publisher：Information and Media Technologies Editorial Board  

Let G be an additive group generated by an element <i>G</i> of prime order <i>r</i>. The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find &alpha; on inputs <i>G</i>, &alpha;<i>G</i>, &alpha;<i>^dG</i> &isin; G for a positive integer <i>d</i> dividing <i>r</i>-1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3¹²⁷). Moreover, based on our experimental results, we estimate the required cost of Cheon's algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter <i>d</i> is chosen.

DOI： 10.11185/imt.6.1175

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE Computer Society  

Cheon introduced a novel algorithm for solving the discrete logarithm problems with auxiliary input (DLPwAI). Since the infeasibility of DLPwAI assures the security of some cryptographic schemes, some implementational results have been reported. This paper estimates the required time for solving DLPwAI on elliptic curves over finite fields with characteristics 3 by extrapolating previous results. © 2011 IEEE.

DOI： 10.1109/IMIS.2011.113

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Information Processing Society of Japan  

Let G be an additive group generated by an element G of prime order r. The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α on inputs G, αG, α&lt
sup&gt
d&lt
/sup&gt
G ∈ G for a positive integer d dividing r − 1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon’s algorithm on a pairing-friendly elliptic curve defined over GF(3&lt
sup&gt
127&lt
/sup&gt
). Moreover, based on our experimental results, we estimate the required cost of Cheon’s algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter d is chosen.

DOI： 10.2197/ipsjjip.19.441

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE COMPUTER SOC  

The discrete logarithm problem (DLP) is one of the familiar problem on which some cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms.
In this paper, we show our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF (3(127)). It is shown that the algorithm combined with the kangaroo method has an advantage over that combined with the baby-step giant-step method in the sense that the required time and space are smaller.
Then, for the algorithm combined with the kangaroo-method, speeding-up techniques are introduced. Based on our experimental results and the speeding-up techniques, we evaluate the required time and space for some pairing-friendly elliptic curves curves. As results, a portion of pairing-friendly elliptic curves can be analyzed by Cheon's algorithm at reasonable cost.

DOI： 10.1109/AINA.2011.37

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find alpha from G, alpha G, alpha(d)G in an additive cyclic group generated by G of prime order r and a positive integer d dividing r - 1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI. This paper shows our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we succeeded to solve DLPwAI in a group with 128-bit order in 45 hours with a single PC on an elliptic curve defined over a prime finite field with 256-bit elements which is used in the TinyTate library.

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE COMPUTER SOC  

The discrete logarithm problem (DLP) is one of the familiar problem on which cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms. This paper firstly reports experimental results on Cheon's algorithm for DLP on a supersingular elliptic curve defined over GF(3(127)), which is used for efficient pairing computation in practice. About 8 hours and 34 MByte database are required for the 1st step of Cheon's algorithm, and about 6 hours and 23 MByte data-base for the 2nd step. In total, about 14 hours are required for solving the problem. Our results imply that the security evaluation from a viewpoint of Cheon's algorithm is crucial.

DOI： 10.1109/ARES.2010.55

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

The hardness of the elliptic curve discrete logarithm problem (ECDLP) on a finite field is essential for the security of all elliptic curve cryptographic schemes. The ECDLP on a field K is as follows: given an elliptic curve E over K, a point S is an element of E(K), and a point T is an element of E(K) with T is an element of &lt; S &gt;, find the integer d such that T = dS. A number of ways of approaching the solution to the ECDLP on a finite field is known, for example, the MOV attack [5], and the anomalous attack [7,10]. In this paper, we propose an algorithm to solve the ECDLP on the p-adic field Q(p). Our method is to use the theory of formal groups associated to elliptic curves, which is used for the anomalous attack proposed by Smart [10], and Satoh and Araki [7].

DOI： 10.1007/978-3-642-12827-1_9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

We consider the torsion points of elliptc curves over certain number fields with good reduction everywhere.

DOI： 10.2996/kmj/1225980443

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DOI： 10.1145/1394042.1394074

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Authorship：Corresponding author   Language：English   Publishing type：Meeting report  

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Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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Authorship：Lead author  

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Language：Japanese   Publisher：日本数式処理学会  

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Language：English   Publisher：京都大学数理解析研究所  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication schemes in which authentication process is exectuted on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption proposed by Hattori et al. when a binary coding is used. In addition, we have also proposed a countermeasure to our attack. Furthermore, a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption by Yasuda et al. have been proposed. In this paper, we consider about applicability of the proposed countermeasure which verifies whether a feature vector is a binary code or not to our attack against Hattori et al. scheme to Yasuda et al. scheme. As a result, it is difficult to apply the countermeasure to Yasuda et al. scheme. Then, we consider about new countermeasure that uses Xor masking, multiplicative masking and additive masking, respectively.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication in which authentication is executed on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user against a cancelable biometric authentication scheme by using homomorphic encryption proposed by Hattori et al. when binary coding is used. In addition, a recovery attack for encrypted template have been proposed by using our spoofing attack. These attack use a problem in process that calculates a squared euclidean distance between template and biometric information to compare. Therefore, our attack is not applicable to scheme that does not use a squared euclidean distance. This paper shows that an adversary can spoof to an arbitrary users with high probability against a privacy-preserving biometric authentication scheme by Yasuda et al. that uses hamming distance. Furthermore, by extending our proposed spoofing attack, we show that an adversary is able to recover the original biometric information by using the decryption server as a authentication oracle. These proposed attack are applicable if the feature vector is represented by a binary coding.

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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication schemes in which authentication process is exectuted on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption proposed by Hattori et al. when a binary coding is used. In addition, we have also proposed a countermeasure to our attack. Furthermore, a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption by Yasuda et al. have been proposed. In this paper, we consider about applicability of the proposed countermeasure which verifies whether a feature vector is a binary code or not to our attack against Hattori et al. scheme to Yasuda et al. scheme. As a result, it is difficult to apply the countermeasure to Yasuda et al. scheme. Then, we consider about new countermeasure that uses Xor masking, multiplicative masking and additive masking, respectively.

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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

Vulnerability in a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

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Language：English   Publisher：Institute of Mathematics for Industry, Kyushu University ; c2014-  

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Language：Japanese   Publisher：Forum on Information Technology  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

Recently, the biometric template protection technology has been actively researched in biometrics.In this technology, the enrollment biometric data called a template are protected by some conversion.Among many approaches for the template protection technology, we here focus on the key binding approach. In the key binding approach, helper data is generated from joint data of a user's specific key with user's biometric data, and the user's specific key can be extracted only when the enrolled biometric data and a query data are sufficiently similar.By handling digital signature or document information as a user's specific key, the key binding approach can be applied to the digital signature, and document encryption/decryption.Hence the key binding approach is expected to be applied not only to authentication but also to various application scenarios. While conventional schemes like fuzzy commitment and fuzzy vault schemes use the error correcting code technique to achieve the key binding approach, we present a new scheme using so called the lattice masking.The notion of the lattice masking is derived from a combination of the random masking technique and the lattice theory. In this paper, we describe the feature of our scheme and also introduce a concrete application example.

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Language：Japanese   Publisher：京都大学  

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Language：English   Publisher：Rikkyo University  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

After Gentry proposed a concrete method for constructing a fully homomorphic encryption scheme, it becomes popular to research on applications with homomorphic encryption schemes. Gentry's construction starts from a somewhat homomorphic encryption (SHE) scheme, which supports limited evaluation over encrypted data. To analyze the relation between its evaluations and security, we attacked the lattice problem ensuring the security of Gentry's SHE scheme. In this paper, we mainly report our experimental results of attacking the lattice problem of 512 dimension using the LLL algorithm.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

After Gentry proposed a concrete method for constructing a fully homomorphic encryption scheme, it becomes popular to research on applications with homomorphic encryption schemes. Gentry's construction starts from a somewhat homomorphic encryption (SHE) scheme, which supports limited evaluation over encrypted data. To analyze the relation between its evaluations and security, we attacked the lattice problem ensuring the security of Gentry's SHE scheme. In this paper, we mainly report our experimental results of attacking the lattice problem of 512 dimension using the LLL algorithm.

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Other Link： http://id.nii.ac.jp/1001/00077497/

Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

A fully-homomorphic encryption is a public-key encryption that allows one to fully interact with encypted data without being able to decrypt, and it is expected to be applied for the area of cloud computing. In this paper, we consider the security of the fully-homomorphic encryption scheme based on ideal lattices. The security of this scheme relies on the infeasibility of the SSSP and the BDDP, which are computational mathematical problems. We here study on the relation between the parameters of this scheme and the infeasibility of the BDDP.

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a positive integer α from elements G, αG, α^dG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r-1. In 2010, Sakemi et al. implemented Cheon's algorithm for solving DLPwAI, and solved a DLPwAI in a group with 128-bit order r in about 131 hours with a single core on an elliptic curve defined over a prime finite field which is used in the TinyTate library for embedded cryptographic devices. However, since their implementation was based on Shanks' Baby-step Giant-step (BSGS) algorithm as a sub-algorithm, it required a large amount of memory (246 GByte) so that it was concluded that applying other DLPwAIs with larger parameter is infeasible. In this article, we implemented Cheon's algorithm based on Pollard's ρ-algorithm in order to reduce the required memory. As a result, we have succeeded solving the same DLPwAI in about 136 hours by a single core with less memory (0.5 MByte).

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Language：English   Publisher：Faculty of Mathematics, Kyushu University  

Pollard's rho method is the asymptotically fastest known attack for the elliptic curve discrete logarithm problem (ECDLP) except special cases. It works by giving a pseudo-random sequence defined by an iteration function and then detecting a collision in the sequence. We note that the number of iterations before obtaining a collision is significant for the running time of the rho method and depends on the choice of an iteration function. For many iteration functions suitable for the ECDLP on elliptic curves except Koblitz curves, the number of iterations before obtaining a collision had been investigated. In this paper, we propose a new iteration function on Koblitz curves which is an extension of the iteration function proposed by Gallant et al. and analyze the performance on our iteration function experimentally.

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Other Link： http://hdl.handle.net/2324/20144

Language：Japanese  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The security of publick-key cryptographic protocols are reduced to the infeasibility of underlying mathematical problems. More cryptographic protocols have been designed, more new mathematical problems have been introduced. Especially in paring-based protocols, a various problems related to the Diffie-Hellman problem (Diffie-Hellman related problems) have been used. Compared to the fundamental mathematical problems such as the integer factoring problem or the discrete logarithm problem, the infeasibility of these newly introduced problems are not fully evaluated yet. In 2006, Cheon proposed an algorithm to solve the discrete logarithm problem with auxiliary input (DLPwAI), however, since the problem is tightly related to the Diffie-Hellman related problems, Cheon's algorithm also solves Diffie-Hellman related problems. This manuscript discusses the relation between the security of cryptographic protocols based on Diffie-Hellman related problems and Cheon's algorithm.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The security of many cryptographic systems is based on the hardness of the discrete logarithm problem (DLP). In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input, whcich works better than conventional algorithms. In recent years, we reported experimental results on Cheon's algorithm for DLP on an elliptic curve used for pairing-based cryptography. In this paper, we explain some methods of speeding Cheon's algorithm, which were not used in our past experiment. We also describe the effect of speeding Cheon's algorithm.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The security of publick-key cryptographic protocols are reduced to the infeasibility of underlying mathematical problems. More cryptographic protocols have been designed, more new mathematical problems have been introduced. Especially in paring-based protocols, a various problems related to the Diffie-Hellman problem (Diffie-Hellman related problems) have been used. Compared to the fundamental mathematical problems such as the integer factoring problem or the discrete logarithm problem, the infeasibility of these newly introduced problems are not fully evaluated yet. In 2006, Cheon proposed an algorithm to solve the discrete logarithm problem with auxiliary input (DLPwAI), however, since the problem is tightly related to the Diffie-Hellman related problems, Cheon's algorithm also solves Diffie-Hellman related problems. This manuscript discusses the relation between the security of cryptographic protocols based on Diffie-Hellman related problems and Cheon's algorithm.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The security of many cryptographic systems is based on the hardness of the discrete logarithm problem (DLP). In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input, whcich works better than conventional algorithms. In recent years, we reported experimental results on Cheon's algorithm for DLP on an elliptic curve used for pairing-based cryptography. In this paper, we explain some methods of speeding Cheon's algorithm, which were not used in our past experiment. We also describe the effect of speeding Cheon's algorithm.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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Language：English   Presentation type：Symposium, workshop panel (nominated)  

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Event date： 1 8 2022 - 4 8 2022

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Event date： 16 11 2021 - 17 11 2021

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Event date： 8 11 2021 - 10 11 2021

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