B.A. Francis, A Course in H" Control TheoH. Berlin: SpringerVerlag, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the field of elliptic curves is their applicability to cryptography. The points of an elliptic curve E over a finite field form an abelian group. Hence the group E can be used to implement analogs of the Diffie Hellman key exchange scheme and the ElGamal public key cryptosystem, as explained in [9]. The security of these analogous systems rests on the difficulty of the discrete logarithm problem on an elliptic curve. In this paper, we propose new TOFs (or public key cryptographic schemes) based on elliptic curves over a ring Z n , although an elliptic curve E over Z n does not form a ....

....but this algorithm is quite impractical for large p. It is known that E p (a; b) is either cyclic or the product of two cyclic groups. In the latter case, E p (a; b) ZN 1 Theta ZN 2 where N 1 Delta N 2 = #E p (a; b) where N 2 divides N 1 and where N 2 also divides p Gamma 1. We refer to [9] for a more detailed introduction to elliptic curves, and to [8] for some further cryptographically useful properties of elliptic curves. If the forms of elliptic curve E p (a; b) and prime p are restricted, the order #E p (a; b) and the group structure are known as follows. Lemma 1. Let p be an ....

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N. Koblitz, A Course in Number Theory and Cryptography, Berlin: Springer-Verlag, 1987.

....Prime numbers, Primality proof, MillerRabin test, RSA cryptosystem, Number theory. 1 Some results of this paper were presented at EUROCRYPT 89, Houthalen, Belgium, April 10 13, 1989. 1. Introduction A variety of cryptographic systems, including public key distribution systems [28] [45], 58] public key cryptosystems [30] 36] 47] 79] digital signature schemes [30] 79] 80] 82] 90] and identification protocols [32] 39] and a large number of variations of some of these systems have recently been proposed. The security of most public key schemes is based on the ....

N. Koblitz, A Course in Number Theory and Cryptography, Berlin: Springer-Verlag, 1987.

....its precise definition. Such a problem in the linear state feedback setting has been completely solved in [18] 19] by using a Riccati equation approach. In the case of output fcedback, sufficient conditions t0r designing robust H controllers with a fixed ordcr have been derived in [11] while [16] has developed 4 controllers for systems with uncertainty in the state matrix only. The focal point of this note is the linear dynamic output feedback and we consider uncertain systems with parameter uncertainties appcaring in 1 the state, input, and output matrices. It should be noted that a ....

....given. The system (2.4) is stable with disturbance attenuation 3, if and only if there cxists asymmctric matrix P 0 such that ArP PA 3, 2PBB[P C[C 0. 2.5) When there is parameter uncertainty A(t) in the state matrix of (2.43, the system reads ( 33: t) A A(t) x(t) Blw(t ) 2. 6a) z(t) Cx(t) 2.6b) Definition 2.2 [1] The system (2.6) is said to be quadraticall 3, stable if there exists a positivc dcfinite symmetric matrix P such that for all admissible uncertainty hA( A AA(t) TP P[A AA(t) 0. 2.7) Similarly, the uncertain system (2.13 is said to be ....

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B.A. Francis, A Course in H" Control TheoH. Berlin: SpringerVerlag, 1987.

....P , design a controller C such that the closed loop system is stable and satisfies some given (optimal) performance criteria. When the optimal performance criterion is the H1 norm (H 2 norm or l 1 norm respectively) of the closed loop transfer function based on the Youla parameterization [1] a parameterization of the class of controllers which stabilize the plant, the controller synthesis problem can be changed into the H1 norm (H 2 norm or l 1 norm respectively) model matching problem the problem of finding the optimal stable free parameter which minimizes the H1 norm ....

B.A. Francis, A Course in H1 Control Theory. Berlin: SpringerVerlag, 1987.

.... P , design a controller C such that the closed loop system is stable and satis es some given (optimal) performance criteria. When the optimal performance criterion is the H1 norm (H 2 norm or l 1 norm respectively) of the closed loop transfer function based on the Youla parameterization [1] a parameterization of the class of controllers which stabilize the plant, the controller synthesis problem can be changed into the H1 norm (H 2 norm or l 1 norm respectively) model matching problem the problem of nding the optimal stable free parameter which minimizes the H1 norm (H 2 ....

B.A. Francis, A Course in H1 Control Theory. Berlin: Springer-Verlag, 1987.

....uncertainties is investigated. 1 Introduction The H1 control problem for dynamical systems with external disturbances is to design feedback controllers which make the resulting systems to have small L 2 gains (or H1 norms for linear systems) such that the external disturbances are attenuated [9, 8, 39, 4, 36, 3, 13, 18]. In this paper, the H1 control problem for nonlinear systems which additionally depend on unknown parameters is considered by the use of adaptive control schemes with full information feedback. It is known from dissipation theory that a dynamical system has bounded L 2 gain if the system is ....

B.A. Francis, A Course in H1 -Control Theory, Berlin: Springer-Verlag, 1986.

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