• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.573-584
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• 2016

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on ${\mathbb{Z}}_{2^n}$ which generates an n-bit word sequence without consecutive elements of period $2^n$.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1984-1987
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• 2002

This paper describes the design and implementation of a single-chip digitally synthesized 0-35MHz agile function generator. The chip comprises an integrated direct digital synthesizer (DDS) with a 10-bit on- chip digital-to-analog converter (DAC) using an n-well single-poly triple-metal 0.5-$\mu\textrm{m}$ CMOS technology. The main features of the chip include maximum clock frequency of 100 MHz at 3.3-V supply voltage, 32-bit frequency tuning word resolution, 12-bit phase tuning word resolution, and an on-chip 10-bit DAC. The chip provides sinusoidal, ramp, saw-tooth, and random waveforms with phase and frequency modulation, and power-down function. At 100-MHz clock frequency, the chip covers a bandwidth from dc to 35 MHz in 0.0233-Hz frequency steps with 190-ns frequency switching speed. The complete chip occupies 12-mm$^2$die area and dissipates 0.4 W at 100-MHz clock frequency.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.10
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• pp.2209-2216
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• 2011

In this paper, we design a 32-bit eFuse OTP memory for PMICs using MagnaChip's $0.18{\mu}m$ process. We solve a problem of an electrical shortage between an eFuse link and the VSS of a p-substrate in programming by placing an n-well under the eFuse link. Also, we propose a WL driver circuit which activates the RWL (read word-line) or WWL (write word-line) of a dual-port eFuse OTP memory cell selectively when a decoded WERP (WL enable for read or program) signal is inputted to the eFuse OTP memory directly. Furthermore, we reduce the layout area of the control circuit by removing a delay chain in the BL precharging circuit. We'can obtain an yield of 100% at a program voltage of 5.5V on 94 manufactured sample dies when measured with memory tester equipment.

• Journal of Korea Multimedia Society
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• v.9 no.12
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• pp.1607-1616
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• 2006

The growing market of multimedia and digital signal processing requires significant data-path portions of SoCs. However, the common models for verification are not suitable for SoCs. A novel model--WGL (Weighted Generalized List) is proposed, which is based on the general-list decomposition of polynomials, with three different weights and manipulation rules introduced to effect node sharing and the canonicity. Timing parameters and operations on them are also considered. Examples show the word-level WGL is the only model to linearly represent the common word-level functions and the bit-level WGL is especially suitable for arithmetic intensive circuits. The model is proved to be a uniform and efficient model for both bit-level and word-level functions. Then Based on the WGL model, a backward-construction logic-verification approach is presented, which reduces time and space complexity for multipliers to polynomial complexity(time complexity is less than $O(n^{3.6})$ and space complexity is less than $O(n^{1.5})$) without hierarchical partitioning. Finally, a construction methodology of word-level polynomials is also presented in order to implement complex high-level verification, which combines order computation and coefficient solving, and adopts an efficient backward approach. The construction complexity is much less than the existing ones, e.g. the construction time for multipliers grows at the power of less than 1.6 in the size of the input word without increasing the maximal space required. The WGL model and the verification methods based on WGL show their theoretical and applicable significance in SoC design.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.3
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• pp.637-647
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• 2010

This paper suggested an algorithm that uses a multiplier, 'w bit $\times$ w bit = 2w bit', to process $\frac{N}{D}$ integer division of 2w bit integer N and w bit integer D. An algorithm suggested of the research, when the divisor D is '$D=0.d{\times}2^L$, 0.5 < 0.d < 1.0', approximate value of $\frac{1}{D}$, '$1.g{\times}2^{-L}$', which satisfies '$0.d{\times}1.g=1+e$, e < $2^{-w}$', is defined as over reciprocal number and the dividend N is segmented in small word more than 'w-3' bit, and partial quotient is calculated by multiplying over reciprocal number in each segmented word, and quotient of double precision integer division is evaluated with sum of partial quotient. The algorithm suggested in this paper doesn't require additional correction, because it can calculate correct reciprocal number. In addition, this algorithm uses only multiplier, so additional hardware for division is not required to implement microprocessor. Also, it shows faster speed than the conventional SRT algorithm. In conclusion, results from this study could be used widely for implementation SOC(System on Chip) and etc. which has been restricted to microprocessor and size of the hardware.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.927-934
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• 2011

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large (e.g., n = 64) such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we study T-functions which are probably invertible and are very useful in stream ciphers. In this paper we study some conditions on a T-function h(x) such that f(x) = x + h(x) has a single cycle on ${\mathbb{Z}}_{2^n}$.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.331-343
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• 2015

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we study T-functions which are probably invertible transformations and are very useful in stream ciphers. In this paper we study the number of single cycle T-functions satisfying some conditions and characterize single cycle T-functions on $(\mathbb{Z}_2)^n$ generated by some elements in $(\mathbb{Z}_2)^{n-1}$.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.4
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• pp.127-135
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• 1994

In this paper we propose an EWLD(Enhanced Weighted Levenshtein Distance) algorithm to organize code-string pattern matching linear array processor based on the mappting to an one-dimensional array from a two-dimensional matching matrix, and design a processing element(PE) of the processor, N PEs are required instead of NS02T in the processor because of the mapping. Data input and output between PEs and all internal operations of each PE are performed in bit-serial fashion. The bit-serial operation consists of the computing of word distance (WD) by comparison and the selection of optimal code transformation path, and takes 22 clocks as a cycle. The layout of a PE is designed based on the double metal $1.5\mu$m CMOS rule. About 1,800 transistors consistute a processing element and 2 PEs are integrated on a 3mm$\times$3mm sized chip.

• Journal of Korea Multimedia Society
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• v.11 no.8
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• pp.1093-1100
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• 2008

Feistel and SPN are the two main structures in designing a block cipher algorithm. Unlike Feistel, an SPN has an asymmetric structure in encryption and decryption. In this paper we propose an SPN algorithm which has a symmetric structure in encryption and decryption. The whole operations in our SPN algorithm are composed of the even numbers of N rounds where the first half of them, 1 to N/2, applies function and the last half of them, (N+1)/2 to N, employs inverse function. Symmetry layer is executed to create a symmetry block in between function layer and inverse function layer. AES encryption and decryption algorithm, whose safety is already proved, are exploited for function and inverse function, respectively. In order to be secure enough against the byte or word unit-based attacks, 32bit rotation and simple logical operations are performed in symmetry layer. Due to the simplicity of the proposed encryption and decryption algorithm in hardware configuration, the proposed algorithm is believed to construct a safe and efficient cipher in Smart Card and RFID environments where electronic chips are built in.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.7
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• pp.1218-1226
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• 2008

With the development of semiconductor integrated technology and with the increasing use of multimedia functions in computer, more functions have been implemented as hardware. Nowadays, most microprocessors beyond 32 bits generally implement an integer multiplier as hardware. However, as for a divider, only specific microprocessor implements traditional SRT algorithm as hardware due to complexity of implementation and slow speed. This paper suggested an algorithm that uses a multiplier, 'w bit $\times$ w bit = 2w bit', to process $\frac{N}{D}$ integer division. That is, the reciprocal number D is first calculated, and then multiply dividend N to process integer division. In this paper, when the divisor D is '$D=0.d{\times}2^L$, 0.5 < 0.d < 1.0', approximate value of ' $\frac{1}{D}$', '$1.g{\times}2^{-L}$', which satisfies ' $0.d{\times}1.g=1+e$, $e<2^{-w}$', is defined as over reciprocal number and then an algorithm for over reciprocal number is suggested. This algorithm multiplies over reciprocal number '$01.g{\times}2^{-L}$' by dividend N to process $\frac{N}{D}$ integer division. The algorithm suggested in this paper doesn't require additional revision, because it can calculate correct reciprocal number. In addition, this algorithm uses only multiplier, so additional hardware for division is not required to implement microprocessor. Also, it shows faster speed than the conventional SRT algorithm and performs operation by word unit, accordingly it is more suitable to make compiler than the existing division algorithm. In conclusion, results from this study could be used widely for implementation SOC(System on Chip) and etc. which has been restricted to microprocessor and size of the hardware.