Publications (39)10.22 Total impact
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ABSTRACT: In this paper, we study the autocorrelation property of quaternary sequences. Firstly, we will determine the minimum bound for the maximum magnitude of nontrivial autocorrelation values according to its weight function and period. Secondly, we derive necessary and sufficient conditions for balance property with respect to the correlation values and the weight function of quaternary sequences.01/2011;  [Show abstract] [Hide abstract]
ABSTRACT: A Construction of Quaternary Low Correlation Zone Sequence Sets from Binary Low Correlation Zone Sequence Sets Improving OptimalityIEICE Transactions. 01/2011; 94A:17681771.  [Show abstract] [Hide abstract]
ABSTRACT: Large prime numbers are one of inevitable ingredients in the public key cryptosystems. However, the decision of the primality requires significant computational resources. In this paper, we proposed two efficient methods to generate large prime numbers. Firstly, an accelerating method by utilizing preinstalled modular multiplier which is used to calculate public key algorithm is proposed. Secondly, new improved algorithm which reduces computational resources is presented. In the latter algorithm, the requirement for the related parameters are reinforced in order to prevent generating random numbers with small prime factors. In addition, by slightly releasing the requirement for the parameters, it is possible to remove the unit generation procedure in Joye and Paillier's scheme. Through these modifications, it is possible to obtain new efficient prime number generation algorithm.2011 IEEE AsiaPacific Services Computing Conference, APSCC 2011, Jeju, Korea (South), December 1215, 2011; 01/2011  [Show abstract] [Hide abstract]
ABSTRACT: We propose an extension method of quaternary low correlation zone (LCZ) sequence set with odd period. From a quaternary LCZ sequence set with parameters (N , M, L, 1), the proposed method constructs a new quaternary LCZ sequence set with parameters (2N, 2M, L, 2), where N is odd. If the employed LCZ sequence set in the construction is optimal, the extended LCZ sequence set becomes also optimal where N = kL, L > 4, and k >2.IEICE Transactions. 01/2010; 93A:557560.  [Show abstract] [Hide abstract]
ABSTRACT: The periodic complementary sequence (PCS) set is a set of periodic sequences such that the sum of all nontrivial periodic autocorrelation functions of sequences in the set is zero. This paper proposes two ways to construct quaternary periodic complementary sequence sets from any binary periodic complementary sequence set with even period. It is well known that a quaternary sequence {u(t)} can be constructed from two binary sequences {r(t)},{s(t)} of the same period using a Gray mapping ϕ, i.e., u(t)=ϕ[r(t),s(t)]. Let ℬ={b i (t)∣0≤i≤M1} be a binary PCS set with M sequences of period N. The first result in this paper (Theorem 1) constructs a quaternary PCS set 𝒢={g i (t)∣0≤i≤M1} where each quaternary sequence g i (t) is defined by g i (t)=ϕ[b i (t),b i (t+N/2)]. Instead of using a single binary sequence in the Gray mapping construction in Theorem 1, the second method (Theorem 2) uses every two adjacent binary periodic complementary sequences in set ℬ to construct each pair of quaternary sequences in the quaternary PCS set 𝒬={q i (t)∣0≤i≤M1}, by taking phase shift for each binary PCS in ℬ respectively. Namely, q 2k (t)=ϕ[b 2k (t),b 2k+1 (t+N/2)] and q 2k+1 (t)=ϕ[b 2k+1 (t),b 2k (t+N/2)]. However, in the case that M is odd, the last quaternary sequence in 𝒬 is constructed from the last binary PCS in ℬ using the first construction. The proofs of theorems rely on Krone and Sarwate’s result (Lemma 1) of crosscorrelation functions of quaternary sequences constructed by Gray mappings. Two examples are also given in the paper.Reviewer: Qiang (Steven) Wang (Ottawa)Advances in Mathematics of Communications 01/2010; 4(1):6168. · 0.60 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper provides two construction methods of sequence using the Gray mapping. In the first method, a quaternary sequence with Rmax = 2 for N ≡ 2 (mod 4) which is the same as the best known Rmax, is proposed. The sequence is constructed by the Gray mapping of a binary sequence with even period and its halfperiod shift. The resulting quaternary sequence has the same autocorrelation distribution with that of the employed binary sequence. From binary sequences with optimal autocorrelation for even period such as Sidel'nikov sequences, DingHellesethMartinsen (DHM) sequences, and sequences from the images of polynomials, etc., we can construct quaternary sequences with Rmax = 2 for period N ≡ 2 (mod 4) and Rmax = 4 for period N ≡ 4 (mod 4). In constrast to the previous quaternary sequences separately designed, new quaternary sequences are constructed from many existing binary sequences with optimal autocorrelation. In the second construction, optimal quaternary LCZ sequence sets are derived from binary LCZ sequence sets which are not necessarily optimal. To the best of our knowledge, it is the first result to obtain an optimal LCZ sequence set from a nonoptimal LCZ sequence set, while there are constructions to obtain LCZ sequence sets from another LCZ sequence set. Moreover, since the parameters of new quaternary LCZ sequence set in the second method are determined by the parameters of the binary LCZ sequence set, it is possible to obtain flexible quaternary LCZ sequence sets by using flexible binary LCZ sequence sets.01/2010;  [Show abstract] [Hide abstract]
ABSTRACT: A true random number generator (TRNG) is widely used to generate secure random numbers for encryption, digital signatures, authentication, and so on in cryptosystems. Since TRNG is vulnerable to environmental changes, a deterministic function is normally used to reduce bias and improve the statistical properties of the TRNG output. In this paper, we propose a linear corrector for secure TRNG. The performance of a linear corrector is bounded by the minimum distance of the corresponding linear error correcting code. However, we show that it is possible to construct a linear corrector overcoming the minimum distance limitation. The proposed linear corrector shows better performance in terms of removing bias in that it can enlarge the acceptable bias range of the raw TRNG output. Moreover, it is possible to efficiently implement this linear corrector using only XOR gates, which must have a suitable hardware size for embedded security systems.Etri Journal 01/2010; 32(3). · 0.74 Impact Factor 
Conference Paper: New quaternary sequences with ideal autocorrelation constructed from binary sequences with ideal autocorrelation
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ABSTRACT: In this paper, a new generation method of quaternary sequences of period 2(2<sup>n</sup>1) with ideal autocorrelation and balance property is proposed using the binary sequences of period 2<sup>n</sup>  1 with ideal autocorrelation and reverse Gray mapping. The autocorrelation distribution of the proposed quaternary sequences is also derived.Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009 
Conference Paper: New quaternary sequences with optimal autocorrelation
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ABSTRACT: We propose a new construction of quaternary sequences using the reverse Gray mapping of a pair of binary Sidel'nikov sequences. The proposed construction provides sequences of even period N with the maximum nontrivial autocorrelation magnitude, R<sub>max</sub> = 2. For N Â¿ 0 mod 4, the new quaternary sequences have the optimal R<sub>max</sub> = 2 and are almostbalanced in contrast to the only earlier optimal construction S<sub>j</sub>.Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009 
Conference Paper: New construction of quaternary sequences with ideal autocorrelation from Legendre sequences
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ABSTRACT: In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the Legendre sequences of period p. The distribution of autocorrelation function of the proposed quaternary sequences is also derived.Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, using the binary (N,M,L,1) low correlation zone(LCZ) sequence set with specific property, we propose the construction method of a quaternary LCZ sequence set with parameters (2N,2M,L,2). The binary LCZ sequence using this method must have period mod 4, balance property, and specific correlation property. The proposed method is modified from the construction method of binary LCZ sequence set by using binary LCZ sequence with specific condition proposed by Kim, Jang, No, and Chung[4].The Journal of Korea Information and Communications Society. 01/2009; 34(1C).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, for even integer N, we propose a new construction method of quaternary low correlation zone(LCZ) sequence set from a binary LCZ sequence set with parameters (N,M,L,). Proposed method applies the inverse gray mapping from Krone and Sarwate to binary LCZ sequences and their phase shifts. The only needed condition of binary LCZ sequence set used in this construction is even period.The Journal of Korea Information and Communications Society. 01/2009; 34(2C).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we propose a quaternary sequence with good autocorrelation property. New quaternary sequence is generated by using inverse Gray mapping and binary sequence with ideal autocorrelation. And the maximum magnitude of nontrivial correlation value is 3. Proposed quaternary sequence has only one 1 in one period, so called almost binary sequence. Therefore the balance property is not good, but value of its weight function is nearly 0.The Journal of Korea Information and Communications Society. 01/2009; 34(2C).  [Show abstract] [Hide abstract]
ABSTRACT: A quaternary sequence is constructed by Gray mapping of a binary sequence with even period and its shift. The autocorrelation of the new quaternary sequence is the same as that of the binary sequence employed. Quaternary sequences with the maximum autocorrelation 2 can be obtained by the construction for period N ≡ 2 (mod 4).IEICE Transactions. 01/2009; 92A:21392140.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we propose a new construction method of binary low correlation zone (LCZ) sequence set. New construction method applies Gray mapping to conventional quaternary LCZ sequence set that has specific property. The period of new binary sequence set is twice as that of used sequence set in construction, and maximum magnitude of correlation value within the LCZ and cardinality of new set is also twice as those of used quaternary sequence set. But the LCZ size is the same with that of used sequence set. If the used Quaternary sequence set is optimal, the constructed binary sequence set is optimal with high probability.The Journal of Korea Information and Communications Society. 01/2009; 34(2C).  Advances in Mathematics of Communications  ADV MATH COMMUN. 01/2009; 3(2):115124.
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ABSTRACT: The path key establishment phase in the wireless sensor network is vulnerable to Byzantine attack. Huang and Hedhi proposed a Byzantine resilient multikey establishment scheme using a systematic RS code, which has shortcomings of exposing a part of message symbols and inefficient transmission. In this paper, we propose a new Byzantine resilient multipath key establishment scheme in which direct message symbols are not exposed to an adversary and are more efficiently transmitted the RSencoded symbols to the destination node. In the Proposed scheme, a nonsystematic RS code is used to transmit a generated indirect secret key and each encoded symbol is relayed through available paths between two sensor nodes. If enough symbols are collected at the destination node, it is possible to reconstruct the secret message through RS decoding.The Journal of Korea Information and Communications Society. 01/2009; 34(9C). 
Conference Paper: Quaternary low correlation zone sequence set with flexible parameters
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ABSTRACT: In this paper, we proposed a new quaternary low correlation zone(LCZ) sequence set with parameters (2(2<sup>n</sup>  1),M, L, 2). The new LCZ sequence set is constructed from the binary sequence with ideal autocorrelation of period 2<sup>n</sup>  1. The proposed construction method corresponds to the generalization of the construction method of binary LCZ sequence set by using binary sequence with ideal autocorrelation proposed by Kim, Jang, No, and Chung [1].Information Theory, 2008. ISIT 2008. IEEE International Symposium on; 08/2008 
Conference Paper: Generalized extending method for construction of qary low correlation zone sequence sets
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ABSTRACT: In this paper, a new extending method of qary low correlation zone(LCZ) sequence sets is proposed, which is a generalization of binary LCZ sequence set by Kim, Jang, No, and Chung. Using this method, qary LCZ sequence set with parameters (N,M,L, isin) is extended as a qary LCZ sequence set with parameters (pN, pM, plfloor(L + 1)/plfloor  1, pisin), where p is prime and pq.Information Theory, 2008. ISIT 2008. IEEE International Symposium on; 08/2008  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, using the binary (N,M,L,1) low correlation zone(LCZ) sequence set with specific properties, we propose a construction method of quaternary LCZ sequence sets with parameters (2N,2M,L,2). Binary LCZ sequences for the construction must have period N equiv 3 mod 4, the balance property, and proper correlation property. The new method is modified from the construction of binary LCZ sequence set by using binary LCZ sequence with the condition proposed by Kim, Jang, No, and Chung.01/2008;
Publication Stats
110  Citations  
10.22  Total Impact Points  
Top Journals
Institutions

2009

University of California, San Diego
 Department of Electrical and Computer Engineering
San Diego, CA, United States


2003–2008

Seoul National University
 • School of Electrical Engineering and Computer Sciences
 • Department of Electrical and Computer Engineering
 • School of Computer Science and Engineering
Seoul, Seoul, South Korea
