• Journal of the Korea Institute of Information Security & Cryptology
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• v.27 no.6
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• pp.1295-1305
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• 2017

There is SEED cryptosystem in domestic block cipher standard. This code was drafted by the Korea Information Security Agency (KISA) in October 1998 and underwent a public verification process in December of the same year, which resulted in the final amendment to improve safety and performance. Unlike DES, it is a 128-bit block cipher that has been passed through various processes and established in 2005 as an international standard. It is a block cipher with a pastel structure like DES, but the input bit block has been increased to 128 bits, double DES. In this paper, first, we introduce the general algorithm of SEED cryptosystem and analyzed mathematically generating principle of key-value which is used in F-function. Secondly, we developed a table that calculates the exponent of the primitive element ${\alpha}$ corresponding to the 8-bit input value of the S-function and finally analyzed calculating principle of S-function designed in G-function through the new theorem and example. Through this course, we hope that it is to be suggest the ideas and background theory needed in developing new cryptosystem to cover the weakness of SEED cryptosystem.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.2
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• pp.333-342
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• 2022

Cellular Automata (CA) is a discrete and abstract computational model that is being applied in various fields. Applicable as an excellent pseudo-random sequence generator, CA has recently developed into a basic element of cryptographic systems. Several studies on CA-based stream ciphers have been conducted and it has been observed that the encryption strength increases when the radius of a CA's neighbor is increased when appropriate CA rules are used. In this paper, among CAs that can be applied as a one-dimensional pseudo-random number sequence generator (PRNG), one-dimensional 5-neighbor CAs are classified according to the connection state of their neighbors, and the ignition relationship of the characteristic polynomial is obtained. Also this paper propose a synthesis algorithm for an asymmetric 1-D linear 5-neighbor MLCA in which the radius of the neighbor is increased by 2 using the one-dimensional 3-neighbor 90/150 CA state transition matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.6
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• pp.590-603
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• 1989

In tnis paper, the CRC-CCITT code and primitive polynomial CRC code are selected for analysing error detecting performance. However, general formulas for obtaining the weight distribution of these two CRC codes are not so far dericed. So, a new method for calculating the weight distribution of the shortened cyclic Hamming code is presented and an undetected error probability of these two codes is obtained when used in cell of ATM for broadband ISDN user-network interface. Consequently, we show that CRC code too much does affect its error detection performance. All the computer simulation is performed by IBM PC/AT.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.4
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• pp.3-10
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• 2005

Every cell position of a maximum-length 90/150 cellular automata(CA) generates the same pseudo-noise(PN) sequence corresponding to the characteristic polynomial of the CA with a phase shift. Unlike LFSRs, the phase shift is generally different between stages of a CA. In this paper, we propose an algorithm to compute relative phase shifts between stage of a CA. Our algorithm does not need Shank's algorithm to compute relative phase shifts and does not need any previous phase shifts to compute a phase shift. Moreover it is done in time $O(2^n)$.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.6
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• pp.1105-1112
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• 2020

One-dimensional 3-neighborhood Cellular Automata (CA)-based pseudo-random number generators are widely applied in generating test patterns to evaluate system performance and generating key sequence generators in cryptographic systems. In this paper, in order to design a CA-based key sequence generator that can generate more complex and confusing sequences, we study a one-dimensional symmetric 5-neighborhood CA that expands to five neighbors affecting the state transition of each cell. In particular, we propose an n-cell one-dimensional symmetric 5-neighborhood CA synthesis algorithm using the algebraic method that uses the Krylov matrix and the one-dimensional 90/150 CA synthesis algorithm proposed by Cho et al. [6].

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.8
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• pp.35-45
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• 1999

In this paper, the addition and the multiplicative algorithm of two polynomials over finite field $GF(p^m)$ are presented. The 4-valued arithmetic processor of the serial input-parallel output modular structure on $GF(4^3)$ to be performed the presented algorithm is implemented by current mode CMOS. This 4-valued arithmetic processor using current mode CMOS is implemented one addition/multiplication selection circuit and three operation circuits; mod(4) multiplicative operation circuit, MOD operation circuit made by two mod(4) addition operation circuits, and primitive irreducible polynomial operation circuit to be performing same operation as mod(4) multiplicative operation circuit. These operation circuits are simulated under $2{\mu}m$ CMOS standard technology, $15{\mu}A$ unit current, and 3.3V VDD voltage using PSpice. The simulation results have shown the satisfying current characteristics. The presented 4-valued arithmetic processor using current mode CMOS is simple and regular for wire routing and possesses the property of modularity. Also, it is expansible for the addition and the multiplication of two polynomials on finite field increasing the degree m and suitable for VLSI implementation.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.93-101
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• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.123-136
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• 2004

In this paper, complexity and regularity of polynomial multiplication over $GF({2^n})$ are defined by using Hamming weight of rows and columns of the matrix ever GF(2) which represents polynomial multiplication. It is shown experimentally that in order to construct the block cipher robust against differential cryptanalysis, polynomial multiplication of substitution layer and the permutation layer should have high complexity and high regularity. With result of the experiment, a way of constituting S box and G function is suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with a nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over $GF({2^8})$ which has neither a fixed pout, whose input and output are the same except 0 and 1, nor an opposite fixed number, whose output is one`s complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes linear transform with 4 S-box outputs using the matrix of 4${\times}$4 over $GF({2^8})$. The components in the matrix of linear transformation have high complexity and high regularity. Furthermore, G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, and there can be no weak input where a fixed point an opposite fixed point, and output can be two`s complement of input. The primitive polynomials of nonlinear function affine transform and linear transformation are different each other. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.