• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.7
• /
• pp.3455-3474
• /
• 2018

As a unique form of signed-digit representation, non-adjacent form (NAF) minimizes Hamming weight by removing a stream of non-zero bits from the binary representation of positive integer. Thanks to this strong point, NAF has been used in various applications such as cryptography, packet filtering and so on. In this paper, to improve the NAF conversion speed of the $NAF_w$ algorithm, we propose a new NAF conversion algorithm, called w-bit Shifting Non-Adjacent Form($SNAF_w$), where w is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the $NAF_w$ algorithm. To verify the excellence of the $SNAF_w$ algorithm, the $NAF_w$ algorithm and the $SNAF_w$ algorithm are implemented in the 8-bit microprocessor ATmega128. By measuring CPU cycle counter for the NAF conversion under various input patterns, we show that the $SNAF_2$ algorithm not only increases the NAF conversion speed by 24% on average but also reduces deviation in the NAF conversion time for each input pattern by 36%, compared to the $NAF_2$ algorithm. In addition, we show that $SNAF_w$ algorithm is always faster than $NAF_w$ algorithm, regardless of the size of w.

• Journal of KIISE
• /
• v.44 no.5
• /
• pp.537-544
• /
• 2017

As a special form of the signed-digit representation, the NAF(non-adjacent form) minimizes the hamming weight by reducing the average density of the non-zero bits from the binary representation of the positive integer k. Due to this advantage, the NAF is used in various fields; in particular, it is actively used in cryptology. The existing NAF-conversion algorithm, however, is problematic because the conversion speed decreases when the LSB(least significant bit) frequently becomes "1" during the binary positive integer conversion process. This paper suggests a method for the improvement of the NAF-conversion speed for which the problems that occur in the existing NAF-conversion process are solved. To verify the performance improvement of the algorithm, the CPU cycle for the various inputs were measured on the ATmega128, a low-performance 8-bit microprocessor. The results of this study show that, compared with the existing algorithm, the suggested algorithm not only improved the processing speed of the major patterns by 20% or more on average, but it also reduced the NAF-conversion time by 13% or more.

• Journal of Internet Computing and Services
• /
• v.4 no.3
• /
• pp.1-8
• /
• 2003

The power analysis attack is a physical attack which can be applied to the cryptosystems such as smartcard. We try to experimental attack to a smart card which implemented Elliptic Curve Cryptosystem adopting NAF algorithm as a secret key recording method. Our differential power analysis attack is a potential threat to that implementation. The attacker measures the power traces during the multiplication with secret key bits in a target smart card and the multiplication with the guessed bits in other experimental one. The comparison of these two traces gives a secret bit, which means that attacker can find all secret key bits successively.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.27 no.2
• /
• pp.195-203
• /
• 2017

This paper is concerned with the active vibration control of shell structure that is subjected to internal unbalanced excitation by using active mounts and accelerometers. The unbalanced excitation is caused by a rotating unbalanced mass. The control algorithm considered in this study is the negative acceleration feedback (NAF) control. A simplified dynamic model was derived to verify the effectiveness of the NAF control. Four actuators and four accelerometers were mounted on the shell structure, so that the multiple-input and multiple-output (MIMO) NAF controller was designed by both centralized and decentralized ways. Numerical results show that both the decentralized and centralized NAF controllers are effective. Based on the numerical simulation, the proposed decentralized NAF controller was applied to the real shell structure. Experimental results show that the proposed decentralized NAF controller can effectively suppress vibrations of the shell structure.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.34 no.1C
• /
• pp.21-27
• /
• 2009

We present an efficient exponentiation algorithm for a finite field $GF(2^n)$ determined by an optimal normal basis of type II using signed digit representation of the exponents. Our signed digit representation uses a non-adjacent form (NAF) for $GF(2^n)$. It is generally believed that a signed digit representation is hard to use when a normal basis is given because the inversion of a normal element requires quite a computational delay. However our result shows that a special normal basis, called an optimal normal basis (ONB) of type II, has a nice property which admits an effective exponentiation using signed digit representations of the exponents.

• The KIPS Transactions:PartC
• /
• v.15C no.6
• /
• pp.507-512
• /
• 2008

At a recent, enterprises based on online-service are established because of rapid growth of information network. These enterprises collect personal information and do customer management. If customers use a paid service, company send billing information to customer and customer pay it. Such circulation and management of information is big issue but most companies don't care of information security. Actually, personal information that was managed by largest internal open-market was exposed. For safe customer information management, this paper proposes the method that decrease load of RSA cryptography algorithm that is commonly used for preventing from illegal attack or hacking. The method for decreasing load was designed by Binary NAF Method and it can operates modular Exponentiation rapidly. We implemented modular Exponentiation algorithm using existing Binary Method and Windows Method and compared and evaluated it.

• Proceedings of the IEEK Conference
• /
• 2001.06b
• /
• pp.305-308
• /
• 2001

This paper describes the design of elliptic curve cryptographic (ECC) coprocessor over binary fields for the If card. This coprocessor is implemented by the shift-and-add algorithm for the field multiplication algorithm. And the modified almost inverse algorithm(MAIA) is selected for the inverse multiplication algorithm. These two algorithms is merged to minimize the hardware size. Scalar multiplication is performed by the binary Non Adjacent Format(NAF) method. The ECC we have implemented is defined over the field GF(2$^{163}$), which is a SEC-2 recommendation［7］..

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.14 no.2
• /
• pp.394-402
• /
• 2010

At a recent, enterprises based on online-service are established because of rapid growth of information network. These enterprises collect personal information and do customer management. If customers use a paid service, company send billing information to customer and customer pay it. Such circulation and management of information is big issue but most companies don't care of information security. Actually, personal information that was managed by largest internal open-market was exposed. For safe customer information management, this paper proposes the method that decrease load of RSA cryptography algorithm that is commonly used for preventing from illegal attack or hacking. The method for decreasing load was designed by Binary NAF Method and it can operates modular Exponentiation rapidly. We implemented modular Exponentiation algorithm using existing Binary Method and Windows Method and compared and evaluated it.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.8 no.6
• /
• pp.1212-1217
• /
• 2004

The main back-bone operation in elliptic curve cryptosystems is scalar point multiplication. The most frequently used method implementing the scalar point multiplication, which is performed in the upper level of GF multiplication and GF division, has been the double-and-add algorithm, which is recently challenged by NAF(Non-Adjacent Format) algorithm. In this paper, we propose a more efficient and novel scalar multiplication method than existing double-and-add by applying redundant receding which originates from radix-4 Booth's algorithm. After deriving the novel quad-and-add algorithm, we created a new operation, named point quadruple, and verified with real application calculation to utilize it. Derived numerical expressions were verified using both C programs and HDL (Hardware Description Language) in real applications. Proposed method of elliptic curve scalar point multiplication can be utilized in many elliptic curve security applications for handling efficient and fast calculations.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.13 no.10
• /
• pp.2154-2162
• /
• 2009

This paper describes a scalar multiplier for Elliptic curve cryptography for smart card security. The scaler multiplier has 163-bits key size which supports the specifications of smart card standard. To reduce the computational complexity of scala multiplication on finite field, the non-adjacent format (NAF) conversion algorithm which is based on complementary recoding is adopted. The scalar multiplier core synthesized with a 0.35-${\mu}m$ CMOS cell library has 32,768 gates and can operate up to 150-MHz@3.3-V. It can be used in hardware design of Elliptic curve cryptography processor for smartcard security.