We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseu...We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.展开更多
In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and pr...In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.展开更多
Under Kerckhoff principle,this paper discusses the security property of an image encryp-tion scheme with a pseudorandom permutation.Some findings on the security problems of the algo-rithm are reported in the followin...Under Kerckhoff principle,this paper discusses the security property of an image encryp-tion scheme with a pseudorandom permutation.Some findings on the security problems of the algo-rithm are reported in the following:(1) If each row or column of the plain-image matrix is the same,the receiver cannot decrypt correctly.(2) Each plain-text word is correlated with single cipher-text word,but independent of other cipher-text word,which cannot meet the principles of algorithm design-diffusion and confusion.(3) If the cycle numbers are relatively small,statistics attack can be used to reveal some visual information of any other plain-images encrypted with the same secret key.Con-sidering the above problems,we propose an improved algorithm and then analyze its performance.Theoretical analysis and simulation results show that the improved algorithm can obtain better cryptographic properties,such as statistical characteristics,difference characteristics,and so on.展开更多
The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we ...The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.展开更多
This paper presents a fast pseudorandom generation algorithm,which is based on the BLAKE hash function and can pass the random test of the NIST(National Institute of Standards and Technology)Statistical Test Suite.Thr...This paper presents a fast pseudorandom generation algorithm,which is based on the BLAKE hash function and can pass the random test of the NIST(National Institute of Standards and Technology)Statistical Test Suite.Through theoretical analysis and experimental imitation,our new algorithm is proven to be more secure and efficient than G-SHA1.Simultaneously,we introduce and discuss the BLAKE in detail.Its security shows that can be utilized to generate pseudorandom bit sequences,which the experimental results show the BLAKE hash function has excellent pseudorandomness.Therefore,we believe the BLAKE is one of the most potential candidate algorithms of SHA-3 program.展开更多
In this paper we analyse the security of a multiple pseudorandom-bit generator based on the coupled map lattice and suggest an improved model. Utilizing the error function attack, the multiple pseudorandom-bit generat...In this paper we analyse the security of a multiple pseudorandom-bit generator based on the coupled map lattice and suggest an improved model. Utilizing the error function attack, the multiple pseudorandom-bit generators which can be realized by the three digitization methods are analysed and the effective key spaces are estimated. We suggest an improved multiple pseudorandom-bit generator with 128-bit secret key, and analyse the key sensitivity and statistical properties of the system.展开更多
This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2n?for n-bit shift register with a nonlinear feedback function. The developed met...This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2n?for n-bit shift register with a nonlinear feedback function. The developed method is illustrated by constructing a nonlinear function feedback shift register. It is proved that the offered method requires the realization of a memory size proportional to n2?that allows making successful use of suitable generators for practical use on the shift register of the longer word.展开更多
Luby and Rackoff idealized DES by replacing each round function with one large random function. In this paper, the author idealizes Camellia by replacing each S-box with one small random function, which is named Camel...Luby and Rackoff idealized DES by replacing each round function with one large random function. In this paper, the author idealizes Camellia by replacing each S-box with one small random function, which is named Camellialike scheme. It is then proved that five-round Camellia-like scheme is pseudorandom and eight-round Camellia-like scheme is super-pseudorandom for adaptive adversaries. Further the paper considers more efficient construction of Camellia-like scheme, and discusses how to construct pseudorandom Camellia-like scheme from less random functions.展开更多
A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and...A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and the run-length properties of the FRDS-sequences are investigated . By transformation, a new kind of pseudorandom sequences with optimal auto-correlation functions is suggested.展开更多
Let A ■ ■_(N),and f_(A)(s)={1-|A/N,-|A|/N,for s ∈A,for s■ A.We define the pseudorandom measure of order k of the subset A as follows,P _(k)(A,N)=max D|∑n∈■_(N)|f_(A)(n+c_(1))f_(A)(n+c_(2))…f_(A)(n+c_(k))|where...Let A ■ ■_(N),and f_(A)(s)={1-|A/N,-|A|/N,for s ∈A,for s■ A.We define the pseudorandom measure of order k of the subset A as follows,P _(k)(A,N)=max D|∑n∈■_(N)|f_(A)(n+c_(1))f_(A)(n+c_(2))…f_(A)(n+c_(k))|where the maximum is taken over all D=(c_(1),c_(2),…,C_(K))∈■^(k) with 0≤c_(1)<c_(2)<…ck≤N-1.The subset A ■ ■_(N) is considered as a pseudorandom subset of degree k if P_(k)(A,N)is“small”in terms of N.We establish a link be tween the Gowers norm and our pseudorandom measure,and show that“good”pseudorandom subsets must have“small”Gowers norm.We give an example to suggest that subsets with"small" Gowers norm may have large pseudorandom measure.Finally,we prove that the pseudorandom subset of degree L(k)contains an arithmetic progression of length k,where L(k)=2·lcm(2,4,…,2|k/2|),for k≥4,and lcm(a1,a2,…,al)denotes the least common multiple of a1,a2,…,al.展开更多
The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying b...The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying boundary evaluations. Experimental tests prove that range errors caused by the fluctuation of the number of photon counts in the laser echo pulse leads to the range drift of the time point spread function. The function relationship between the range error and the photon counting ratio is determined by using numerical fitting.Range errors due to a different echo energy is calibrated so that the corrected range root mean square error is improved to 1 cm.展开更多
基金Supported by the National Natural Science Foundation of China (61063041)the Program for New Century Excellent Talents in Fujian Province University (JK2010047)the Open Funds of State Key Laboratory of Information Security (01-01-1)
文摘We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60973162)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009GM037)+1 种基金the Science and Technology of Shandong Province, China(Grant No. 2010GGX10132)the Key Program of the Natural Science Foundation of Shandong Province, China (Grant No. Z2006G01)
文摘In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.
基金Supported by the National Natural Science Foundation of China (No. 60874091)the Six Projects Sponsoring Talent Summits of Jiangsu Province (No. SJ209006)+2 种基金the Foundation for Doctoral Program of High Education of China(No. 20103223110003)the Natural Science Foundation of Jiangsu Province (No. 08KJD510022)the Post-graduate Scientific Innovation Project for Universities of Jiangsu Province (No. CXZZ11-0401)
文摘Under Kerckhoff principle,this paper discusses the security property of an image encryp-tion scheme with a pseudorandom permutation.Some findings on the security problems of the algo-rithm are reported in the following:(1) If each row or column of the plain-image matrix is the same,the receiver cannot decrypt correctly.(2) Each plain-text word is correlated with single cipher-text word,but independent of other cipher-text word,which cannot meet the principles of algorithm design-diffusion and confusion.(3) If the cycle numbers are relatively small,statistics attack can be used to reveal some visual information of any other plain-images encrypted with the same secret key.Con-sidering the above problems,we propose an improved algorithm and then analyze its performance.Theoretical analysis and simulation results show that the improved algorithm can obtain better cryptographic properties,such as statistical characteristics,difference characteristics,and so on.
基金supported by Overseas Scholars Research Fund of Heilongjiang Provinicial Education Department
文摘The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.
基金Supported by the National High Technology Research and Development Program of China (863 Program) ( 2007AA01Z411)the National Natural Science Foundation of China ( 60673071, 60970115 )
文摘This paper presents a fast pseudorandom generation algorithm,which is based on the BLAKE hash function and can pass the random test of the NIST(National Institute of Standards and Technology)Statistical Test Suite.Through theoretical analysis and experimental imitation,our new algorithm is proven to be more secure and efficient than G-SHA1.Simultaneously,we introduce and discuss the BLAKE in detail.Its security shows that can be utilized to generate pseudorandom bit sequences,which the experimental results show the BLAKE hash function has excellent pseudorandomness.Therefore,we believe the BLAKE is one of the most potential candidate algorithms of SHA-3 program.
基金Project supported by the National Natural Science Foundation of China(Grant No.60973109)
文摘In this paper we analyse the security of a multiple pseudorandom-bit generator based on the coupled map lattice and suggest an improved model. Utilizing the error function attack, the multiple pseudorandom-bit generators which can be realized by the three digitization methods are analysed and the effective key spaces are estimated. We suggest an improved multiple pseudorandom-bit generator with 128-bit secret key, and analyse the key sensitivity and statistical properties of the system.
文摘This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2n?for n-bit shift register with a nonlinear feedback function. The developed method is illustrated by constructing a nonlinear function feedback shift register. It is proved that the offered method requires the realization of a memory size proportional to n2?that allows making successful use of suitable generators for practical use on the shift register of the longer word.
基金Supported partially by the National Natural Science Foundation of China under Grants No, 60373047 and No, 90304007 the National Basic Research 973 Program of China under Grant No. 2004CB318004 the National High-Technology Development 863 Program of China under Grant No. 2003AA144030.
文摘Luby and Rackoff idealized DES by replacing each round function with one large random function. In this paper, the author idealizes Camellia by replacing each S-box with one small random function, which is named Camellialike scheme. It is then proved that five-round Camellia-like scheme is pseudorandom and eight-round Camellia-like scheme is super-pseudorandom for adaptive adversaries. Further the paper considers more efficient construction of Camellia-like scheme, and discusses how to construct pseudorandom Camellia-like scheme from less random functions.
文摘近日,西安电子科技大学数学与交叉科学研究院菁英副教授李哲与上海交通大学教授邢朝平、博士研究生姚逸洲和副教授袁晨合作,在伪随机关联生成器(Pseudorandom Correlation Generator,PCG)方面取得重要进展,相关论文“Efficient Pseudorandom Correlation Generators for Any Finite Field”被EUROCRYPT(欧密会)2025录用发表。
文摘A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and the run-length properties of the FRDS-sequences are investigated . By transformation, a new kind of pseudorandom sequences with optimal auto-correlation functions is suggested.
基金supported in part by the National Natural Science Foundation of China(Grant No.11571277).
文摘Let A ■ ■_(N),and f_(A)(s)={1-|A/N,-|A|/N,for s ∈A,for s■ A.We define the pseudorandom measure of order k of the subset A as follows,P _(k)(A,N)=max D|∑n∈■_(N)|f_(A)(n+c_(1))f_(A)(n+c_(2))…f_(A)(n+c_(k))|where the maximum is taken over all D=(c_(1),c_(2),…,C_(K))∈■^(k) with 0≤c_(1)<c_(2)<…ck≤N-1.The subset A ■ ■_(N) is considered as a pseudorandom subset of degree k if P_(k)(A,N)is“small”in terms of N.We establish a link be tween the Gowers norm and our pseudorandom measure,and show that“good”pseudorandom subsets must have“small”Gowers norm.We give an example to suggest that subsets with"small" Gowers norm may have large pseudorandom measure.Finally,we prove that the pseudorandom subset of degree L(k)contains an arithmetic progression of length k,where L(k)=2·lcm(2,4,…,2|k/2|),for k≥4,and lcm(a1,a2,…,al)denotes the least common multiple of a1,a2,…,al.
基金supported by the National Natural Science Foundation of China(Nos.61101196 and 61271332)the Natural Science Research Foundation of Jiangsu Province(No.168JB510015)
文摘The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying boundary evaluations. Experimental tests prove that range errors caused by the fluctuation of the number of photon counts in the laser echo pulse leads to the range drift of the time point spread function. The function relationship between the range error and the photon counting ratio is determined by using numerical fitting.Range errors due to a different echo energy is calibrated so that the corrected range root mean square error is improved to 1 cm.
