A High-Speed Square Root Algorithm for Extension fields -Especially for Fast Extension Fields-

A square root (SQRT) algorithm in extension field F(p(m))(m = r(0)r(1)･･･r(n−1)･2(d), r(i) : odd prime, d : positive integer) is proposed in this paper. First, a conventional SQRT algorithm, the Tonelli-Shanks algorithm, is modified to compute the inverse SQRT in F(p(2d)), where most of the computations are performed in the corresponding subfields F(p(2i)) for 0 ≤ i ≤ d-1. Then the Frobenius mappings with addition chain are adopted for the proposed SQRT algorithm, in which a lot of computations in a given extension field F(p(m)) are also reduced to those in a proper subfield by the norm computations. Those reductions of the field degree increase efficiency in the SQRT implementation. The Tonelli-Shanks algorithm and the proposed algorithm in F(p(6)) and F(p(10)) were implemented on a Core2 (2.66 GHz) using the C++ programming language. The computer simulations showed that, on average, the proposed algorithm accelerated the SQRT computation by 6 times in F(p(6)), and by 10 times in F(p(10)), compared to the Tonelli-Shanks algorithm

Fast Exponentiation in Extension Field with Frobenius Mappings

This paper proposes an exponentiation method with Frobenius mappings. Our method is closely related to so-called interleaving exponentiation. Different from the interleaving exponentiation methods, our method can carry out several exponentiations using same base at the same time. The efficiency to use Frobenius mappings for an exponentiation in extension field is well introduced by Avanzi and Mihailescu. This exponentiation method is based on so-called simultaneous exponentiation and uses many Frobenius mappings. Their method more decreased the number of multiplications; however, the number of Frobenius mappings inversely increased. Compared to their method , the number of multiplications needed for the proposed method becomes about 20% larger; however, that of Frobenius mappings becomes small enough

Extension Field for Xate Pairing with Freeman Curve

Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field must be efficiently carried out. The authors show efficient arithmetic operations of extension field for Xate pairing especially with Freeman curve

Model-based analyses of trends over time in the age corresponding to the transition phase for Antarctic minke whales in the JARPA research area

This study applies a model-based approach similar to that of Thomson et al. (1999) to the transition phase data obtained from JARPA surveys to examine trends in the age at maturity for the I and P stocks of Antarctic minke whales. The results, which takes into account various potential biases related to examining trend in transition phase data (i.e. truncation and fringe effects, differences between readers, and readers learning over time) suggest that the age at maturity of Antarctic minke whales declined from about 11 years in the late 1940s to 7 years in the late 1960s for both stocks, and these declining trends are statistically significant at the 5% level. The analyses also suggest that the age at maturity increased slightly from the late 1960s to the late 1970s and has stabilized thereafter. These trends are consistent with the results obtained from VPA (Mori et al. 2006), which suggest that for both the I and P stocks, abundance increased from the 1940s to the late 1960s and thereafter has been stable or declined somewhat. This consistency enhances the confidence to be placed in estimates of parameters (such as natural mortality and MSYR) from such VPA analyses that may be of value for management purposes. It also serves to demonstrate the utility of age-at-maturity as an index to monitor stock status, and suggests that continued monitoring of this parameter is desirable both for this purpose and for contributing to the understanding of the dynamics of the Antarctic ecosystem

Sulfonylurea-resistant biotypes of Monochoria vaginalis generate higher ultraweak photon emissions than the susceptible ones

All living organisms spontaneously generate ultraweak photon emissions, which originate from biochemical reactions in cells. Current research uses the ultraweak photon emission from organisms as a novel indicator in nondestructive analyses of an organisms living state. This study indicates that ultraweak photon emissions from Monochoria vaginalis are different between resistant biotypes (R) to sulfonylurea (SU) and susceptible biotypes (S). In SU-R biotypes, distinct increases in photon emissions were observed, but there was little increase in SU-S biotypes. In addition, photon emissions from the resistant biotypes of M. vaginalis were suppressed by treatment with P450 inhibitors. This suggests that cytochrome P450 monooxygenase, which plays a crucial role in the metabolic detoxification of SUs, could be associated with the generation of ultraweak photon emissions. Ultraweak photon emissions have a potential use in a novel diagnosis system as an indicator in a nondestructive testing of weeds resistant to SUs

Cost Evaluation of The Improvement of Twisted Ate Pairing That Uses Integer Variable X of Small Hamming Weight

Barreto–Naehrig (BN) curve has been introduced as an efficient pairing-friendly elliptic curve over prime field F(p) whose embedding degree is 12. The characteristic and Frobenius trace are given as polynomials of integer variable X. The authors proposed an improvement of Miller's algorithm of twisted Ate pairing with BN curve by applying X of small hamming weight in ITC–CSCC2008; however, its cost evaluation has not been explicitly shown. This paper shows the detail of the cost evaluation