Faculty Profiles - NOGAMI Yasuyuki

A Successive Extension of Degree 2 for Fast Frobenius Map

Other Link： https://dblp.uni-trier.de/db/conf/icics/icics2003.html#FengNM03

FUJII Yoshihiro, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report. Information theory 102 ( 331 ) 37 - 42 2002.9

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

Elliptic Curve Cryptosystem has attracted much attentions as a public key cryptosystem in the next generation and an extension field has been uesd as the definition field. When the degree of an extension field is the composition number, fundamental arithmetics in the field can be fast implemented by using successive extensions. On the other hand, a fast implementation of Frobenius Map in such an extension field has not been explicitly presented. In this paper, two successive extension methods, in which a binomial or a trinomial is used as the modular polynomial, are introduced, and then, we evaluate the calculation costs of the Frobenius Maps implemented by these two methods. Finally, it is clearly shown that the method using a binomial as the modular polynomial is suitable for a fast Frobenius Map implementation.

A Systematic Generation of Irreducible Polynomials of Degree 3 for Use in Elliptic Curve Cryptosystem

OKAMURA Masato, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report. Information theory 102 ( 331 ) 49 - 54 2002.9

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

The order of elliptic curve which is adopted in the elliptic curve cryptosystem is prefered to be a prime except for the characteristic of the definition field. Accordingly, some algorithms for generating such a prime-order elliptic curve has been proposed. Among these algorithms, there is an algorithm using irreducible polynomials of degree 3 effectively in order to generate no-two torsion elliptic curves in which all prime-order elliptic curves are contained. In this paper, let us consider that an irreducible polynomial of degree 3 is given, an algorithm to generate a lot of irreducible polynomials of degree 3 is proposed by use of a relation between the zeros and the coefficients of the given irreducible polynomial. And then, it is experimentally shown that the preceding algorithm can quickly generate prime order elliptic curves by using this algorithm and some properties between an elliptic curve and its twisted version. In the case of the characteristic p = 2^<24> - 3, for example, the number of possible prime-order elliptic curves for this algorithm is 164, and all kinds of these prime-order elliptic curves are generated within 3 minutes by using 10 processors, such as Pentium4 (1.7GHz).

A Fast Implementation of Elliptic Curve Addition over F_<p^8> on 16-bits Microcontroller

IKEDA Takaaki, FUJII Yoshihiro, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report. Information theory 102 ( 331 ) 43 - 48 2002.9

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

Elliptic Curve Cryptosystem(ECC) has been received much attention, and implemented on a terminal even with scarce computation resources. In this paper, by using a successive extension field as the definition field of ECC, it is shown that a scalar multiplication, which is needed in the encryption/decryption process, can be fast implemented. And, we generate an elliptic curve with a prime order defined over a successive extension field of degree 8, and then a result of an implementation of Elgamal Elliptic Curve Cryptosystem on micro-controller is reported.

Watermarking Method Using PN Diffusion and 1D-Fourier Transform of Multi-Resolution Approximation for Image

TSUGE Koichiro, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IPSJ SIG Notes 2001 ( 121 ) 49 - 54 2001.12

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

In this paper, we propose image digital watermark method which has robustness against image compression and clipping. In this method, we first at first take discrete wavelet transform of original image, and get out multi-resolution approximation (MRA). Next, we spread spectrum of the MRA by Pseudo Noise (PN) sequence, and then take 1D-discrete Fourier transform (DFT) of each column. We vary the DFT coefficients according to each bit of watermark information. This method has the features which the third eavesdropper, who don't know the PN sequence, can not decipher the information data and alter them. IN detection process, we take the DFT difference between PN-spread MRA of original image and that of watermark-embedded image and calculate shift of the DFT coefficients. Therefore, this method has the advantage that we can detect the watermark information even from the clipping image.

Watermarking Method Using PN Diffusion and 1D-Fourier Transform of Multi-Resolution Approximation for Image

Other Link： http://id.nii.ac.jp/1001/00041426/

TSUGE Koichiro, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report. Communication systems 101 ( 494 ) 49 - 54 2001.12

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

In this paper, we propose image digital watermark method which has robustness against image compression and clipping. In this method, we first at first take discrete wavelet transform of original image, and get out multi-resolution approximation(MRA). Next, we spread spectrum of the MRA by Pseudo Noise(PN)sequence, and then take 1D-discrete Fourier transform(DFT)of each column. We vary the DFT coefficients according to each bit of watermark information. This method has the features which the third eavesdropper, who don't know the PN sequence, can not decipher the information data and alter them. In detection process, we take the DFT difference between PN-spread MRA of original image and that of watermark-embedded image and calculate shift of the DFT coefficients. Therefore, this method has the advantage that we can detect the watermark information even from the clipping image.

A Consideration on Elliptic Curve Cryptosystem Using Irreducible Polynomial of Degree 3

An Image Watermarking Method Using 1-D DFT Phase of Multi-Resolution Approximation

TSUGE Koichiro, NOGAMI Yasuyuki, MORIKAWA Yoshitaka

24 ( 1 ) 215 - 218 2001.12

An Implementation of Elliptic Curve Cryptosystem Using An Extended AOPE

HIRAMOTO T., SAITO A., NOGAMI Y., MORIKAWA Y.

24 ( 1 ) 351 - 354 2001.12

Conditions of Characteristic and Trace for Rank One Elliptic Curve Twisted over F_<p^2^m>

DANNO T., NOGAMI Y., MORIKAWA Y.

SITA2001 24 ( 1 ) 355 - 358 2001.12

NOGAMI Yasuyuki, MORIKAWA Yoshitaka

IEICE technical report. Information theory 101 ( 407 ) 7 - 12 2001.11

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

For realization of the elliptic curve cryptosystem(ECC), enough considerations on its cryptological strength and implementation must be done. On cryptological strength, the elliptic curve order must have a prime factor of about 160-bits to be enough safe. In general, the ECC is estimated to be enough safe in the case that the order is a prime number which is not equal to the characteristic. Even if prime, however, it is not always safe, for example super singular elliptic curve, MOV-reduction and FR-reduction work on the elliptic curve of prime order. In this paper, we consider elliptic curve with coefficient over the prime field and defined over its extension field. Then, the parameter conditions for the elliptic curve to be enough safe and with fast implementation are given. Finally, construction examples, which satisfy all of the given conditions, are introduced.

High-Speed Algorithm for Taking Square Root in an Extension Field by Using (x^<m+1>-1)/(x-1) as the Modulus

DANNO T., SAITO A., NOGAMI Y., MORIKAWA Y.

IEICE technical report. Information theory 101 ( 234 ) 31 - 36 2001.7

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

ECC(Elliptic Curve Cryptosystem)is expected as a next generation public-key cryptosystem. Four arithmetic operations on finite field including the inverse operation, quadratic residue test, and square root derivation are necessary to implement ECC. These operations must be enough speedy to make ECC practical. In this paper, we propose a high speed algorithm for taking square root in an extension field AOPF(All One Polynomial Field)by using(x^<m+1>-1)/(x-1)as the moduls.

Steganography in Wavelet Domain by Use of Visual Complexity

TSUGE K., NOGAMI Y., MORIKAWA Y.

Technical report of IEICE. SST 100 ( 694 ) 35 - 40 2001.3

Extension Fields by Using (x^<m+1>-1)/(x-1) as the Modulus for High-Speed Arithmetic

SAITO A., HIRAMOTO T., DANNO T., NOGAMI Y., MORIKAWA Y.

Technical report of IEICE. SST 100 ( 693 ) 129 - 134 2001.3

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

Elliptic Curve Cryptosystem has attracted much attentions as a public-key cryptosystem in next generation, and an extension field has been used as the definition field. The arithmetic speed in extension feild is drastically different by the selection of characteristic, extension degree or basis, and therefore, it is necessary to pay the attention to this selection. In such meaning, OEF proposed recently is said that it is optimal. In this paper, we propose a class of finite fields which uses {ω,ω^2,…,ω^m) as a basis in order to execute multiplication and inversion faster than OEF, where ω is a zero of (x^<m+1>-1)/(x+1).

Testing Irreducibility of Polynomial of Degree 3 over GF(P)

GF(P)における3次多項式の高速既約判定アルゴリズム

平本琢士, 野上保之, 森川良孝

電子情報通信学会論文誌A 2001

Determining Minimal Polynomial of Proper Element by Using Higher Degree Traces

Y.Nogami, Y.Morikawa

MEMOIRS OF THE FACULTY OF ENGINEERING OKAYAMA UNIVERSITY 2001

HIRAMOTO T., YANO T., NOGAMI Y., MORIKAWA Y.

IEICE technical report. Information theory 99 ( 562 ) 19 - 24 2000.1

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

Properties of elliptic curve y^2=f(x)=^^△x^3+ax+b over prime field;GF(P)have been studied from many aspects, since the curve may yield a diverse of public key cryptsystems with short length key. Whereas for secure cryptststem the cublic polynomial f(x) has to be irreducible over GF(P), only the theorem of Stickelberger is known concerning decision of the reducibility. By means of the theorem, we can decide reducibility if the discriminant of f(x)is quadratic power residue, but not otherwise. In this paper, we apply Cardano's formula for solution of third order equation over complex field to the one over GF(P)and derive the condition for all solutions to be proper elements of cubic extension field GF(P^3). We also show the proposed algorithm for test of reducibility are very fast.