Abstract: Disclosed is a random sequence generating apparatus for generating a sequence of integers. A seed receiving section receives a sequence of integers as a seed. An initialization section provides a transformation section with the received sequence of integers. The transformation section performs predetermined transformation on each of the provided integer sequence to acquire a sequence of integers. A rotation section acquires the number of rotation bits from a part of the acquired sequence of integers, performs a rotation operation on the acquired number of rotation bits with respect to all of or part of the sequence of integers taken as a bit sequence, and acquires a sequence of integers. An updating section provides the transformation section with the sequence of integers. An output section outputs part of a sequence of integers obtained last as a random sequence in case where transformation and rotation are repeated a predetermined number of times.

Abstract: A filter (201) accepts spreading code sequences or the like as input sequences of a chip rate 1/D, the accepted spreading code sequences are sequentially delayed and distributed by delay circuits (202) connected in series, delay times of individual signals are an arithmetical progression with a chip length D being a common difference D, the individual signals are amplified with spreading codes by amplifiers (203), amplification factors for the individual signals are a geometrical progression of a common ratio r, the sum of the amplified signals is obtained by addition in an adder (204), and the result is sequentially output as an output sequence.

Abstract: A first storage in an apparatus for outputting a sequence of vectors stores vector x having the dimension at least 1, a first calculator calculates vector function x′=f(x) which utilizes a first rational vector map f to which the stored vector x is input, a second storage stores vector y having the dimension at least 1, a second calculator calculates vector function y′=g(x, y) which utilizes a second rational vector map g to which the stored vectors x and y are input, an output outputs vector z′ which is association of the resultant vectors x′ and y′, a first update updates the first storage by storing the resultant vector x′, and a second update updates the second storage by storing the resultant vector y′.

Abstract: A first storage in an apparatus for outputting a sequence of vectors stores vector x having the dimension at least 1, a first calculator calculates vector function x′=f(x) which utilizes a first rational vector map f to which the stored vector x is input, a second storage stores vector y having the dimension at least 1, a second calculator calculates vector function y′=g(x, y) which utilizes a second rational vector map g to which the stored vectors x and y are input, an output outputs vector z′ which is association of the resultant vectors x′ and y′, a first update updates the first storage by storing the resultant vector x′, and a second update updates the second storage by storing the resultant vector y′.

Abstract: A PN sequence output apparatus outputs a PN sequence which is generated by using a Chebyshev polynomial T(a, cos &thgr;)=cos(a &thgr;) for an integer a (2≦a) and which has a length N (1≦N). An accepting section accepts an S (1≦S) number of initial values X1, X2, . . . , Xs each of which is a real number larger than −1 and less than 1, and an S number of degrees p1, p2, . . . , ps each of which is an integral number equal to or larger than 2. A calculation section calculates a Pseudorandom Noise sequence, having a length N, z[1], z[2], . . . , z[N], using the initial values, the degrees, and recurrence formulas xj[1]=Xj, xj[m+1]=T (pj, xj[m]), and z[n]=Πj=1s T(pj, xj[n]), for integers j (1≦j≦S), m (1≦m≦N−1) and n (1≦n≦N). An output section outputs a PN sequence.

Abstract: A system for outputting pseudorandom noise sequences comprises a plurality of output apparatuses.

Abstract: An observation unit of an authentication apparatus and an observation unit of an authentication target apparatus observe a radio wave from a common radio star at a common observation time. A sending unit sends information message including information on the observed radio wave, and an information reception unit receives it. An estimation unit estimates a position of the authentication target apparatus based on “the information on the radio wave observed by the observation unit” and “information on the radio wave observed by the observation unit”. A retaining unit pre-retains positions of one or more authentication target apparatus(s). A determination unit checks whether a position of the authentication target apparatus pre-retained in the retaining unit and the estimated position correspond within a predetermined error range, and settles authentication for the information message as a success in a case where the positions correspond.

Abstract: Four optical interferometers are arranged in parallel. Optical path length differences of the optical interferometers are set to L, r×L, r×r×L, and r×r×r×L, respectively, where L is a unit optical path length difference (constant). A coefficient r by which the unit optical path length difference L is multiplied is any non-integer real number for example an irrational number. An irrational number is for example a surd ({square root}2, {square root}3, etc.), ratio of circumference D, or base e of a natural logarithm. When such optical path length differences are set in such a manner, a chaotic dynamical system, an addition theorem, and a chaotic map are not satisfied with respect to the intensities of light which is output from the optical interferometers. In other words, a thoroughly unpredictable sequence can be generated. The sequence is spectrum spread as spread codes.

Abstract: A converter uses a predetermined parameter a. A generating unit accepts generated inputs x1, . . . , xn, and generates generated outputs, y1, . . . , yn, using recurrence formulas, y1=F1 (x1, a) and yi+1=Fi+1 (xi+1, yi) (1≦i≦n−1). A key accepting unit accepts key inputs, k1, . . . , kn, and gives them as generated inputs to said generating unit. A repetition controller gives the generated outputs as generated inputs to said generating unit, for an “m” (m≧0) number of times, and sets one of the generated outputs to be given at the end as a random number string, r1, . . . , rn. The data accepting unit accepts data inputs, dl, . . . , dn. The converting unit converts data using, ei=di☆ri, and, outputs data outputs, el, . . . , en. The converter can be used both for encrypting and decrypting data.

Abstract: A key sharing system is disclosed which uses a public key X&egr;GF(n) (2≦X<n) which belongs to a Galois finite field GF(n) for an integer n (n≧2), and a polynomial T(•, •) defined in GF(n) by T(a, x)≡S(a, x)mod n where S(•, •) is a Chebyshev polynomial defined by S(a, cos&thgr;)=cos(a&thgr;) where a is an integer (a≧2). In a key sharing apparatus of this system, an integer obtaining unit obtains an integer p (2≦p<n), a transmission key calculation unit calculates a transmission key Y&egr;GF(n) using the integer p based on Y=T(p, X), a transmission key sending unit sends the transmission key Y to another key sharing apparatus, a transmission key reception unit receives a transmission key W from another key sharing apparatus, and a common key calculation unit calculates a common key Z&egr;GF(n) using the transmission key W based on Z=T(p, W).

Abstract: A device for outputting stochastic process according to the present invention comprises a plurality of random variable output units, a normalizing unit, and a result output unit. Each of the random variable output units outputs a sequence of random variables whose limiting distribution obeys an explicit density function. The normalizing unit normalizes the sum of the random variables in the same row over the random variable sequences output by the random variable output units, and sequentially outputs the normalized values. The result output unit integrates the values sequentially output by the normalizing unit, and sequentially outputs the integrated values as result values in stochastic process. The random variable output units utilize a recurrence formula obtained by an addition formula of a tangent function, thus, efficient high speed simulation of the Lévy's stable processes is realized.

Abstract: A transmitter, receiver, and communication system that utilize a pseudo-random number sequence (PRNS) output unit that provides a PRNS of length N. The PRNS output unit generates the PRNS responsive to a number (s) of prescribed positive integers (qx), a prescribed real impulse constant (r), and a prescribed non-zero real constant (C), where 1<x<s. The PRNS output unit includes an input acceptance section that accepts the number (s) of real number sequence initial values (Yx), and the number (s) of integer parameters (px); and a calculation section that uses the prescribed real impulse constant (r), the prescribed non-zero real constant (C), the real number sequence initial values (Yx), the integer parameters (px), and the prescribed positive integers (qx) to calculate a recurrence formula that is used to generate a PRNS (z′[y]) of length N, and that outputs the PRNS (z′[y]), where 1<y<N.

Abstract: A method for simulating a stochastic phenomenon, particularly one employing a Monte Carlo method, includes a step for generating random numbers having a nonuniform density function &rgr;(x) based on an ideal model of a chaotic dynamic system in the form Xn+1=f(Xn). The ideal model of chaotic map F(x) is a class of an algebraic map derived from an addition theorem of an elliptic function. The nonuniform density function &rgr;(x) is expressed by an algebraic function of a dynamical variable x. Examples of the ideal model of the chaotic map F(x) include a generalized Ulam-von Neumann map and a generalized cubic map. The nonuniform density function &rgr;(x) of the chaotic maps has the form Xn+1=F(Xn). The class of chaotic dynamical systems is ideal in the sense that the invariant measure &rgr;(x)dx satisfies the ergodic property required by the Monte Carlo method. Thus, a statistical simulation can be performed in the same manner as the conventional Monte Carlo method.

Abstract: An apparatus for optically generating chaotic random numbers to obtain chaotic random numbers satisfying a chaotic dynamical system expressed by X(n+1)=F(X(n)) includes an optical signal splitting device for splitting light from a light source into a predetermined number of beams with identical optical power; an optical chaotic signal generating device comprising the same number of interferometers as the beams, each having a pair of optical paths for receiving the beams from the optical signal splitting device, splitting each of the beams, interfering the splitted beams and outputting optical chaotic signals; optical path length difference data memory device for memorizing data on a difference between the lengths of the pair of optical paths at portions thereof between splitting and interfering; optical output signal measuring device for measuring optical power of the optical chaotic signals output from the interferometers as chaotic random numbers; and an optical output signal memory device for m

Abstract: When numerically integrating an integrand function A over an unbounded domain, a vector map f converts an m (m≧1)-dimensional vector into an m-dimensional vector wherein a multidimensional density function &rgr; of the limiting distribution resulting from repeatedly applying the map f to a predetermined m-dimensional vector u is analytically solvable. A first storage unit stores an m-dimensional vector x, a second storage unit stores a scalar value w, a first computing unit computes a vector x′=f(x), a second computing unit computes a scalar value w′=A(x)/&rgr;(x), an update unit updates values in the first and second storage units and by storing the vector x′ on the first storage unit and adding the scalar value w′ to a value to be stored in the second storage unit, and an output unit computes a scalar value s=w/(c+1) when the number of update times by the update unit becomes c (c≧1) and outputs the result.