http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Inversion with Normal Bases in Tower Field F<SUB>((2²)²)²</SUB> for S–Box of AES
Yasuyuki Nogami,Masami Hagio,Erika Yanagi,Yoshitaka Morikawa 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7
For the inversion of S?Box of AES, this paper proposes a method for constructing tower field F((2²)²)² with normal bases and shows a vector conversion matrix.
A Method for Distinguishing the Two Candidate Elliptic Curves in the Complex Multiplication Method
Yasuyuki Nogami,Mayumi Obara,Yoshitaka Morikawa 한국전자통신연구원 2006 ETRI Journal Vol.28 No.6
In this paper, we particularly deal with no Fp-rational two-torsion elliptic curves, where Fp is the prime field of the characteristic p. First we introduce a shift productbased polynomial transform. Then, we show that the parities of (#E − 1)/2 and (#E΄− 1)/2 are reciprocal to each other, where #E and #E΄ are the orders of the two candidate curves obtained at the last step of complex multiplication (CM)-based algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transform. For a 160 bits prime number as the characteristic, the proposed method carries out the parity check 25 or more times faster than the conventional checking method when 4 divides the characteristic minus 1. Finally, this paper shows that the proposed method can make CM-based algorithm that looks up a table of precomputed class polynomials more than 10 percent faster.
Determining Basis Conversion Matrix without Gauss Period Normal Basis
Yasuyuki Nogami,Erika Yanagi,Masami Hagio,Yoshitaka Morikawa 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7
This paper proposes a more efficient basis conversion matrix calculation method than a method using GNB (Gauss period Normal Basis). The method is not using GNB, thus it is possible to calculate a basis conversion matrix when GNB does not exist.
Efficient Exponentiation in Extensions of Finite Fields without Fast Frobenius Mappings
Yasuyuki Nogami,Hidehiro Kato,Kenta Nekado,Yoshitaka Morikawa 한국전자통신연구원 2008 ETRI Journal Vol.30 No.6
This paper proposes an exponentiation method with Frobenius mappings. The main target is an exponentiation in an extension field. This idea can be applied for scalar multiplication of a rational point of an elliptic curve defined over an extension field. The proposed method is closely related to so-called interleaving exponentiation. Unlike interleaving exponentiation methods, it can carry out several exponentiations of the same base at once. This happens in some pairing-based applications. The efficiency of using Frobenius mappings for exponentiation in an extension field was well demonstrated by Avanzi and Mihailescu. Their exponentiation method efficiently decreases the number of multiplications by inversely using many Frobenius mappings. Compared to their method, although the number of multiplications needed for the proposed method increases about 20%, the number of Frobenius mappings becomes small. The proposed method is efficient for cases in which Frobenius mapping cannot be carried out quickly.
Basis Translation Matrix between Two Isomorphic Extension Fields via Optimal Normal Basis
Yasuyuki Nogami,Ryo Namba,Yoshitaka Morikawa 한국전자통신연구원 2008 ETRI Journal Vol.30 No.2
This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field Fpm where p is characteristic. As a brute force method, when pm is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when pm is large, it becomes too difficult. The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when mlog2 p = 160.