Faculty Profiles - NOGAMI Yasuyuki

MISC - NOGAMI Yasuyuki

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Classification of MRCPs and Type-I CVMA Modified for Its Prime Field Multiplication

TAKAI Yusuke, NEKADO Kenta, NOGAMI Yasuyuki, MORIKAWA Yoshitaka, KAGOTANI Hiroto

IEICE technical report 110 ( 137 ) 19 - 24 2010.7

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

Cyclic vector multiplication algorithm (CVMA) has been originally proposed as a vector multiplication algorithm for elements in a certain extension field. Recently, Granger et al. have proposed the primes called Minimal Redundancy Cyclotomic Primes (MRCPs) and they have applied CVMA for the modular multiplications with MRCPs. This paper shows that several detailed classes of MRCPs and their customized multiplication algorithms.

Cost Estimates of CNTW Attack against EMV Signatures

SAKEMI Yumi, IZU Tetsuya, TAKENAKA Masahiko, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 110 ( 114 ) 195 - 201 2010.6

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

Specification of EMV signatures is an ISO/IEC 9796-2 compliant format with extra redundancy, and used for certifying credit cards. At CRYPTO 2009, Coron, Naccache, Tibouchi, and Weinmann proposed a new forgery attack against the signature ISO/IEC 9796-2. They also discussed the possibility when the attack is applied to the EMV signatures. As a results, they concluded that the attack can not forge them for operational reason. However, since they estimated the attack's cost under a specific condition, it is difficult to evaluate the attack's threat under other conditions. This paper gives the detailed cost of the attack under all conditions based on the fixed data in a message. Then, the conditions under which the attack can forge EMV signature with low costs are shown.

Cost Estimates of CNTW Attack against EMV Signatures

SAKEMI Yumi, IZU Tetsuya, TAKENAKA Masahiko, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 110 ( 113 ) 195 - 201 2010.6

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

Specification of EMV signatures is an ISO/IEC 9796-2 compliant format with extra redundancy, and used for certifying credit cards. At CRYPTO 2009, Coron, Naccache, Tibouchi, and Weinmann proposed a new forgery attack against the signature ISO/IEC 9796-2. They also discussed the possibility when the attack is applied to the EMV signatures. As a results, they concluded that the attack can not forge them for operational reason. However, since they estimated the attack's cost under a specific condition, it is difficult to evaluate the attack's threat under other conditions. This paper gives the detailed cost of the attack under all conditions based on the fixed data in a message. Then, the conditions under which the attack can forge EMV signature with low costs are shown.

Existing Probability of Gauss Period Normal Basis

NEKADO Kenta, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 109 ( 446 ) 403 - 407 2010.2

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

Recently, for several pairing-based cryptographic applications, convenient basis which can construct extension field for every pair of characteristic p and extension degree m has been required. Kato et al. have focused on Gauss period normal basis(GNB)as the basis, and proposed cyclic vector multiplication algorithm(CVMA)as an efficient multiplication algorithm in an extension field constructed by GNB. This paper considers how to elicite existing probability of GNB theoretically, and estimates the efficiency of CVMA by using the elicitation method.

Anonymous IEEE802.1X Authentication System Using Group Signatures

A. Sudarsono, T. Nakanishi, Y. Nogami, and N. Funabiki

IPSJ Journal 51 ( 3 ) 691 - 704 2010

Mixed Bases for Efficient Inversion in F(((22)2)2) and Conversion Matrices of Sub Bytes of AES

Yasuyuki Nogami, Kenta Nekado, Tetsumi Toyota, Naoto Hongo, Yoshitaka Morikawa

CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2010 6225 234 - 247 2010

Language：English Publisher：SPRINGER-VERLAG BERLIN

A lot of improvements and optimizations for the hardware implementation of Sub Bytes of Rijndael, in detail inversion in F(28) have been reported. Instead of the Rijndael original F(28) it is known that its isomorphic tower field F(((22)2)2) has a more efficient inversion. For the towerings, several kinds of bases such as polynomial and normal bases can be used in mixture. Different from the meaning of this mixture of bases, this paper proposes another mixture that contributes to the reduction of the critical path delay of SubBytes. To the F((22)2)-inversion architecture, for example, the proposed mixture inputs and outputs elements represented with normal and polynomial bases, respectively.

DOI： 10.1007/978-3-642-15031-9_16

Other Link： https://dblp.uni-trier.de/db/conf/ches/ches2010.html#NogamiNTHM10

Anonymous IEEE802.1X Authentication System Using Group Signatures

A. Sudarsono, T. Nakanishi, Y. Nogami, N. Funabiki

IPSJ Journal 51 ( 3 ) 691 - 704 2010

Mixed Bases for Efficient Inversion in F(((22)2)2) and Conversion Matrices of Sub Bytes of AES

Yasuyuki Nogami, Kenta Nekado, Tetsumi Toyota, Naoto Hongo, Yoshitaka Morikawa

CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2010 6225 234 - 247 2010

Authorship：Lead author Language：English Publisher：SPRINGER-VERLAG BERLIN

A lot of improvements and optimizations for the hardware implementation of Sub Bytes of Rijndael, in detail inversion in F(28) have been reported. Instead of the Rijndael original F(28) it is known that its isomorphic tower field F(((22)2)2) has a more efficient inversion. For the towerings, several kinds of bases such as polynomial and normal bases can be used in mixture. Different from the meaning of this mixture of bases, this paper proposes another mixture that contributes to the reduction of the critical path delay of SubBytes. To the F((22)2)-inversion architecture, for example, the proposed mixture inputs and outputs elements represented with normal and polynomial bases, respectively.

DOI： 10.1007/978-3-642-15031-9_16

GLV Method for Non-Supersingular Paring-Friendly Curves of Embedding Degree 1

TAKEUCHI Shoichi, IZUTA Tetsuya, SAKEMI Yumi, NISHII Kazushi, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 109 ( 337 ) 37 - 41 2009.12

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

Recently, some pairing-based cryptographies that uses a non-supersingular pairing-friendly curve whose order has large prime factors as RSA does have been proposed. Since it generally takes a lot of calculation time for generating such a composite order pairing-friendly curve, several efficient methods have been also proposed. Then, using such a special pairing-friendly curve, pairing-based cryptographies will be implemented with not only pairing calculations but also scalar multiplications and exponentiations over a certain finite field. This paper first introduces a non-supersingular pairing-friendly curve of embedding degree 1 whose order has two large prime factors as RSA does. Then, it is shown that GLV method and multi scalar multiplication are efficiently applied for accelerating a scalar multiplication. After that, some experimental results are shown.

A Construction Method of Basis Conversion Matrix by Using Small Multiplicative Group for Cryptographic Applications

KATO Hidehiro, NOGAMI Yasuyuki, UEHARA Satoshi, MORIKAWA Yoshitaka

IEICE technical report 109 ( 337 ) 43 - 50 2009.12

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

Several methods for finding a basis conversion matrix between two different bases in extension field F_<p^m> have been proposed. Among them, the one based on Gauss period normal basis (GNB-based method) is averagely the most efficient. However, since it needs to construct a certain tower field F_<(p^m)^n, some inefficient cases in which the towering degree becomes relatively large have been reported. It is caused from the condition of GNB. In order to overcome the inefficiency, this paper proposes a method that does not need any GNBs in the target extension field F_<p^m> but uses a certain polynomial basis in F_<p^m> derived by a certain small cyclic group in F_<(p^m)^n. Then, the condition for the towering degree is relaxed, some experimental results show that the proposed method substantially accelerates the average computation time for finding a basis conversion matrix.

An Implementation of Tate Pairing with Non-Supersingular Curves of Embedding degree 1

IZUTA Tetsuya, SAKEMI Yumi, NISHII Kazushi, TAKEUCHI Shoichi, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 109 ( 207 ) 59 - 64 2009.9

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

Recently, pairing-based cryptographic applications such as ID-based cryptography have received much attention. On the other hand, RSA cryptography has been widely used and it is defined over a certain composite order as the modulus. In detail, it generally needs to be a product of two large prime numbers. In order to apply RSA-based techniques to pairing-based cryptography, pairing friendly curve needs to have such a composite order. This paper focuses on some non-supersingular pairing friendly curves whose order r has two large prime factors and embedding degree k is equal to 1. This paper shows some experimental results on generating such a composite order curve and Tate pairing.

Integer Variable chi-Based Cross Twisted Ate Pairing and Its Optimization for Barreto-Naehrig Curve

Yasuyuki Nogami, Yumi Sakemi, Hidehiro Kato, Masataka Akane, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 8 ) 1859 - 1867 2009.8

Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log(2) r/phi(k), where phi(.) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from left perpendicularlog(2) right perpendicular to left perpendicularlog(2)(t-1)right perpendicular, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "chi." For such a curve, this paper gives integer variable chi-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve. it reduces the number of loops to left perpendicularlog(2)chi right perpendicular. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.

DOI： 10.1587/transfun.E92.A.1859

Integer Variable chi-Based Cross Twisted Ate Pairing and Its Optimization for Barreto-Naehrig Curve

Yasuyuki Nogami, Yumi Sakemi, Hidehiro Kato, Masataka Akane, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 8 ) 1859 - 1867 2009.8

Authorship：Lead author Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log(2) r/phi(k), where phi(.) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from left perpendicularlog(2) right perpendicular to left perpendicularlog(2)(t-1)right perpendicular, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "chi." For such a curve, this paper gives integer variable chi-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve. it reduces the number of loops to left perpendicularlog(2)chi right perpendicular. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.

DOI： 10.1587/transfun.E92.A.1859

Other Link： https://dblp.uni-trier.de/db/journals/ieicet/ieicet92a.html#NogamiSKAM09

Finding a Basis Conversion Matrix via Prime Gauss Period Normal Basis

Yasuyuki Nogami, Ryo Namba, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 6 ) 1500 - 1507 2009.6

Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

This paper proposes a method to construct a basis conversion matrix between two given bases in F-pm. In the proposed method, Gauss period normal basis (GNB) works as a bridge between the two bases. The proposed method exploits this property and construct a basis conversion matrix mostly faster than EDF-based algorithm on average in polynomial time. Finally, simulation results are reported in which the proposed method compute a basis conversion matrix within 30 msec on average with Celeron (2.00 GHz) when m log p approximate to 160.

DOI： 10.1587/transfun.E92.A.1500

Other Link： https://dblp.uni-trier.de/db/journals/ieicet/ieicet92a.html#NogamiNM09

A Consideration on Generating Ordinary Pairing Friendly Curve of Composite Order That Has Two Large Prime Factors

NISHII Kazushi, SAKEMI Yumi, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report 109 ( 42 ) 51 - 54 2009.5

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

Recently, pairing-based cryptographic applications such as ID-based cryptography have received much attention. On the other hand, RSA cryptography has been widely used and is defined over a certain composite order as the modulus. In detail, it generally needs to be a product of two large prime numbers. In order to apply RSA-based techniques to pairing-based cryptography, pairing-friendly elliptic curve also needs to have such a composite order. This paper proposes a method for generating ordinary pairing-friendly curves of such a composite order especially when the embedding degree k is equal to 3, the discriminant is equal to 3, in addition the elliptic curve is given in the form of y^2=x^3+a, a∈F_p.

An Implementation of a Group Signature Scheme with Efficient Verifier-Local Revocation Check

SUDARSONO Amang, NAKANISHI Toru, SAKEMI Yumi, NOGAMI Yasuyuki, FUNABIKI Nobuo

IEICE technical report 109 ( 42 ) 37 - 42 2009.5

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

A group signature scheme with efficient verifier-local revocation check has been proposed. This scheme provides a more efficient revocation check, using the multi-pairing technique for a product of pairings. However, this scheme has not been implemented and evaluated. This paper presents an implementation of the group signature scheme and the experimental results.

An Improvement of Cyclic Vector Multiplication Algorithm based on Gauss period Normal Basis

YANAGI Erika, NEKADO Kenta, NOGAMI Yasuyuki, MORIKAWA Yoshiktaka

IEICE technical report 109 ( 42 ) 55 - 60 2009.5

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

This paper first introduces cyclic vector multiplication algorithm (CVMA) that is a multiplication algorithm with Gauss period Normal Basis in extension field. Then, it is also introduced that CVMA is useful under the tight restrictions of pairing-based cryptographies. Then, this paper points out a problem about the calculation cost of CVMA. For this problem, this paper proposes an improvement. According to some simulation and experimental results, it is shown that the improvement makes CVMA much more efficient in some cases.

Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve

Masataka Akane, Yasuyuki Nogami, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 2 ) 508 - 516 2009.2

Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y(2) = x(3) + a, a is an element of F-p. For the curve, an isomorphic substitution from G(2) is an element of E(F-p(12)) into G(2)'in subfield-twisted elliptic curve E'(F-p(2)) speeds up scalar multiplications over G(2) and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.

DOI： 10.1587/transfun.E92.A.508

Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve

Masataka Akane, Yasuyuki Nogami, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 2 ) 508 - 516 2009.2

Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y(2) = x(3) + a, a is an element of F-p. For the curve, an isomorphic substitution from G(2) is an element of E(F-p(12)) into G(2)'in subfield-twisted elliptic curve E'(F-p(2)) speeds up scalar multiplications over G(2) and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.

DOI： 10.1587/transfun.E92.A.508

Other Link： https://dblp.uni-trier.de/db/journals/ieicet/ieicet92a.html#AkaneNM09

A Multiplication Algorithm in F-pm Such That p > m with a Special Class of Gauss Period Normal Bases

Hidehiro Kato, Yasuyuki Nogami, Tomoki Yoshida, Yoshitaka Morikawa

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E92A ( 1 ) 173 - 181 2009.1

Language：English Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG

In this paper, a multiplication algorithm in extension field F-pm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic 1) and extension degree in only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p > m, 4p does not divice m(p - 1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree in is small.

DOI： 10.1587/transfun.E92.A.173

Other Link： https://dblp.uni-trier.de/db/journals/ieicet/ieicet92a.html#KatouNYM09

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