• Convergence Security Journal
• /
• v.18 no.1
• /
• pp.13-18
• /
• 2018

Efficiency is one of the most important factors in cryptographic systems. Cheon et al. proposed a new exponent form for speeding up the exponentiation operation in discrete logarithm based cryptosystems. It is called split exponent with the form $e_1+{\alpha}e_2$ for a fixed element ${\alpha}$ and two elements $e_1$, $e_2$ with low Hamming weight representations. They chose $e_1$, $e_2$ in two unbalanced subsets $S_1$, $S_2$ of $Z_p$, respectively. We achieve efficiency improvement making $S_1$, $S_2$ balanced subsets of $Z_p$. As a result, speedup for exponentiations on binary fields is 9.1% and speedup for scalar multiplications on Koblitz Curves is 12.1%.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.14 no.6
• /
• pp.125-134
• /
• 2004

When cryptosystem designers implement devices that computing power or memory is limited such as smart cards, PDAs and so on, not only he/she has to be careful side channel attacks(SCA) but also the cryptographic algorithms within the device has to be efficient using small memory. For this purpose, countermeasures such as Moiler's method, Okeya-Takagi's one and overlapping window method, based on window method to prevent SCA were proposed. However, Moiler's method and Okeya-Talngi's one require additional cost to prevent other SCA such as DPA, Second-Order DPA, Address-DPA, and so on since they are immune to only SPA. Also, overlapping window method has a drawback that requires big memory. In this paper, we analyze existing countermeasures and propose an efficient and secure countermeasure that is immune to all existing SCA using advantages of each countermeasure. Moreover, the proposed countermeasure can enhance the efficiency using mixed coordinate systems.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.17 no.3
• /
• pp.17-25
• /
• 2007

Delegation of signing capability is a common practice in various applications. Mambo et al. proposed a proxy signatures as a solutions for delegation of signing capability. Proxy signatures allow a designated proxy signer to sign on behalf of an original signer. After the concept of proxy signature scheme is proposed, many variants are proposed to support more general delegation setting. To capture all possible delegation structures, the concept of delegation network was proposed by Aura. ID-based cryptography, which is suited for flexible environment, is desirable to construct a delegation network. Chow et al proposed an ID-based delegation network. In the computational point of view, their solution requires E pairing operations and N elliptic curve scalar multiplications where E and N are the number of edges and nodes in a delegation structure, respectively. In this paper, we proposed an efficient ID-based delegation network which requires only E pairing operations. Moreover, we can design a modified delegation network that requires only N pairing operations.

• The Mathematical Education
• /
• v.61 no.3
• /
• pp.441-456
• /
• 2022

The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students' units coordination and K-12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax². To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students' ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

• The Journal of the Acoustical Society of Korea
• /
• v.39 no.5
• /
• pp.441-446
• /
• 2020

In this paper, we propose the α-Feature Map Scaling (α-FMS) method which extends the FMS method that was designed to enhance the discriminative power of feature maps of deep neural networks in Speaker Verification (SV) systems. The FMS derives a scale vector from a feature map and then adds or multiplies them to the features, or sequentially apply both operations. However, the FMS method not only uses an identical scale vector for both addition and multiplication, but also has a limitation that it can only add a value between zero and one in case of addition. In this study, to overcome these limitations, we propose α-FMS to add a trainable parameter α to the feature map element-wise, and then multiply a scale vector. We compare the performance of the two methods: the one where α is a scalar, and the other where it is a vector. Both α-FMS methods are applied after each residual block of the deep neural network. The proposed system using the α-FMS methods are trained using the RawNet2 and tested using the VoxCeleb1 evaluation set. The result demonstrates an equal error rate of 2.47 % and 2.31 % for the two α-FMS methods respectively.