• Convergence Security Journal
• /
• v.18 no.4
• /
• pp.27-33
• /
• 2018

Stream cipher is an one-time-pad type encryption algorithm that encrypt plaintext using simple operation such as XOR with random stream of bits (or characters) as symmetric key and its security depends on the randomness of used stream. Therefore we can design more secure stream cipher algorithm by using mathematical analysis of the stream such as period, linear complexity, non-linearity, correlation-immunity, etc. The key stream in stream cipher is generated in linear feedback shift register(LFSR) having characteristic polynomial. The primitive polynomial is the characteristic polynomial which has the best security property. It is used widely not only in stream cipher but also in SEED, a block cipher using 8-degree primitive polynomial, and in Chor-Rivest(CR) cipher, a public-key cryptosystem using 24-degree primitive polynomial. In this paper we present the concept and various properties of primitive polynomials in Galois field and prove the theorem finding the number of irreducible polynomials and primitive polynomials over $F_p$ when p is larger than 2. This kind of research can be the foundation of finding primitive polynomials of higher security and developing new cipher algorithms using them.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.11 no.1
• /
• pp.35-42
• /
• 2001

The primitive polynomial on GF(q) is used in the area of the scrambler, the error correcting code and decode, the random generator and the cipher, etc. The algorithm that generates efficiently the primitive polynomial on GF(q) was proposed by A.D. Porto. The algorithm is a method that generates the sequence of the primitive polynomial by repeating to find another primitive polynomial with a known primitive polynomial. In this paper, we propose the algorithm that is improved in the A.D. Porto algorithm. The running rime of the A.D. Porto a1gorithm is O($\textrm{km}^2$), the running time of the improved algorithm is 0(m(m+k)). Here, k is gcd(k, $q^m$-1). When we find the primitive polynomial with m odor, it is efficient that we use the improved algorithm in the condition k, m>>1.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2006.05a
• /
• pp.393-396
• /
• 2006

In this paper, we analyze the characteristic polynomials of 90/150 cellular automata which uses only 90, 150 rules as state-transition rules. In particular, we propose the method which the characteristic polynomial is represented as the exponential type of a primitive polynomial by synthesizing 90/150 CA.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2009.05a
• /
• pp.433-436
• /
• 2009

Many researchers had made a diversity of attempts for generating pseudorandom sequences such as the method of using LFSR whose characteristic polynomial is a primitive polynomial, of using Cellular Automata and of using quadratic functions. In this paper, we can analyze and characterize the methods for generating maximal period pseudorandom sequences constructed by quadratic functions.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.6 no.1
• /
• pp.13-19
• /
• 2011

Games gave the calculation method for the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial. In this paper, we calculate the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial with the periodic crosscorrelation function of two base sequences. Our method is different from the Games's method.

• Aerospace Engineering and Technology
• /
• v.6 no.2
• /
• pp.157-163
• /
• 2007

The purpose of this study is to design and simulate Reed Solomon encoder(255,223) in PCM/FM communication system in order to transmit the KSLV-I onboard video data. Especially in the compressed video data transmission applications, the communication system is required to have a very low BER performance because of interframe or interframe compression techniques. We have used the primitive polynomial of CCSDS standard and calculated the various coefficients and then the encoder have been simulated as a part of RF interface FPGA hardware in a video compression unit.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2004.05a
• /
• pp.1071-1074
• /
• 2004

최대길이를 갖는 선형유한상태기계(LFSM)가 패턴생성, 신호분석, 암호, 오류정정 부호에 응용되면서 n차 원시다항식을 특성다항식으로 갖는 선형유한상태기계에 관한 연구가 활발하게 이루어지고 있다. 본 논문은 최대길이를 갖는 다양한 셀룰라 오토마타의 효과적인 생성방법을 제안한다. 특성다항식이 n 차 원시다항식인 선형 MLCA로부터 유도된 여원 CA가 MLCA임을 밝히며 여원 MLCA의 여러 가지 성질들을 분석한다. 또한 n-셀 MLCA를 ${\phi}(2^n-1)2^{n+1}/n$개 생성할 수 있음을 보인다.

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 1990.10a
• /
• pp.219-224
• /
• 1990

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.14 no.3
• /
• pp.41-48
• /
• 2004

Finite field multiplication and division are important arithmetic operation in error-correcting codes and cryptosystems. The elements of the finite field GF($2^m$) are represented by bases with a primitive polynomial of degree m over GF(2). We can be easily realized for multiplication or computing multiplicative inverse in GF($2^m$) based on a normal basis representation. The number of product terms of logic function determines a complexity of the Messay-Omura multiplier. A normal basis exists for every finite field. It is not easy to find the optimal normal element for a given primitive polynomial. In this paper, the generating method of normal basis is investigated. The normal bases whose product terms are less than other bases for multiplication in GF($2^m$) are found. For each primitive polynomial, a list of normal elements and number of product terms are presented.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
• /
• 2002.11a
• /
• pp.88-91
• /
• 2002

자기 수축 발생기(self-shrinking generator)는 Meier와 Staffelbach에 의해 제안되었으며[4], 구조가 간단하고 키수열을 생성하는 속도가 빠르기 때문에 스트림 암호시스템으로 각광받고 있다 [5]. 본 논문에서는 자기 수축 발생기의 새로운 구성방법을 제안한다. 제안된 자기 수축 발생기는 하나의 선형귀환회로와 주어진 짝수 m에 의하여 정의되며 일반적으로 선형귀환회로의 귀환다항식으로 원시다항식을 사용한다. 이 경우 키수열은 균형성을 만족하며, 선형귀환회로의 귀환다항식의 차수를 $d_{Y}$ 라고 하면 주기는 $d_{Y-2}$ 이다. m을 $2^{η}$ζ로 표현하면 선형복잡도 Lz는 $d_{Y}$ ＋η-3/$\leq$ $L_{Z}$ $\leq$m/2($d_{Y}$ -1 - ($d_{Y}$ -2))이다. 따라서 제안된 자기 수축 발생기는 기존의 자기 수축 발생기에 비하여 암호학적으로 우수한 성질을 갖는다.다.