Certificateless signature: a new security model and an improved generic construction

Certificateless cryptography involves a Key Generation Center (KGC) which issues a partial key to a user and the user also independently generates an additional public/secret key pair in such a way that the KGC who knows only the partial key but not the additional secret key is not able to do any cryptographic operation on behalf of the user; and a third party who replaces the public/secret key pair but does not know the partial key cannot do any cryptographic operation as the user either. We call this attack launched by the third party as the key replacement attack. In ACISP 2004, Yum and Lee proposed a generic construction of digital signature schemes under the framework of certificateless cryptography. In this paper, we show that their generic construction is insecure against key replacement attack. In particular, we give some concrete examples to show that the security requirements of some building blocks they specified are insufficient to support some of their security claims. We then propose a modification of their scheme and show its security in a new and simplified security model. We show that our simplified definition and adversarial model not only capture all the distinct features of certificateless signature but are also more versatile when compared with all the comparable ones. We believe that the model itself is of independent interest.A conventional certificateless signature scheme only achieves Girault’s Level 2 security. For achieving Level 3 security, that a conventional signature scheme in Public Key Infrastructure does, we propose an extension to our definition of certificateless signature scheme and introduce an additional security model for this extension. We show that our generic construction satisfies Level 3 security after some appropriate and simple modification. A preliminary version of the extended abstract of partial results appeared in ACISP 2006 [9].     

An algebraic construction of the generic singularities of Boardman-Thom

In this paper we study some of the functorial properties of the infinite jet space in order to give a coordinate free algebraic definition of the generic singularities of Boardman-Thom. More precisely, suppose thatk is a commutative ring with an identity and suppose that A is a commutative ring with an identity which is ak-algebra. An A-k-Lie algebra L is ak-Lie algebra with ak-Lie algebra map ? from L to the algebra ofk-derivations of A to itself such that ford, d′εL anda, a′εA, then $$[ad'],a 'd'] = a(\varphi (d')ad' - a'(\varphi (d')a)d' + aa'[d',\;d'].$$ . There is a universal enveloping algebra for such Lie algebras which we denote by E(L). Denote byL-alg the category of A-algebras B which have L and hence E(L) acting as left operators such that foraεA,dεL, (da)i _B=d(a.i _B). If F is the forgetful functor fromL-alg to the category of A-algebras, we show that F has a left adjoint J(L, ·) which is the natural algebraic translation of the infinite jet space. In the third section of this paper we construct a theory of singularities for a derivation from a ring to a module and then we apply this construction to J(L, C) where C is an A-algebra. These singularities are subschemas with defining sheaf of ideals given by Fitting invariants of appropriately chosen modules when A and B are polynomial rings over a fieldk and C=A? _k B; these are the generic singularities of Boardman-Thom. Finally we show that, under some rather general conditions on the structure of C as an A-algebra, the generic singularities are regular immersions in the sense of Berthelot.     

Reflections on the security proofs of Boneh-Franklin identity-based encryption scheme

In this paper, we first review the existing proofs of the Boneh-Franklin identity-based encryption scheme (BF-IBE for short), and show how to admit a new proof by slightly modifying the specifications of the hash functions of the original BF-IBE. Compared with prior proofs, our new proof provides a tighter security reduction and minimizes the use of random oracles, thus indicates BF-IBE has better provable security with our new choices of hash functions. The techniques developed in our proof can also be applied to improving security analysis of some other IBE schemes. As an independent technical contribution, we also give a rigorous proof of the Fujisaki-Okamoto (FO) transformation in the case of CPA-to-CCA, which demonstrates the efficiency of the FO-transformation (CPA-to-CCA), in terms of the tightness of security reduction, has long been underestimated. This result can remarkably benefit the security proofs of encryption schemes using the FO-transformation for CPA-to-CCA enhancement.     

A generic construction of low correlation zone sequences based on interleaved technique

Low correlation zone (LCZ) sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, a generic construction of LCZ sequences based on inter-leaved technique is investigated. Firstly, the shift sequence is shown to correspond to two-tuple balanced d-form function essentially, which results in new shift sequence. Secondly, an optimal design of p2-ary sequences over the integer residue class ring Zp2 is proposed, which improves the previous construction when p is an odd prime.     

构造正交表的一种替换模式

A method of constructing orthogonal arrays is presented by Zhang, Lu and Pang in 1999. In this paper,the method is developed by introducing a replacement scheme on the construction of orthogonal arrays ,and some new mixed-level orthogonal arrays of run size 36 are constructed.     

An algebraic construction of k-balanced multiwavelets via the lifting scheme

Multiwavelets have been revealed to be a successful generalization within the context of wavelet theory. Recently Lebrun and Vetterli have introduced the concept of “balanced” multiwavelets, which present properties that are usually absent in the case of classical multiwavelets and do not need the prefiltering step. In this work we present an algebraic construction of biorthogonal multiwavelets by means of the well-known “lifting scheme”. The flexibility of this tool allows us to exploit the degrees of freedom left after satisfying the perfect reconstruction condition in order to obtain finite k-balanced multifilters with custom-designed properties which give rise to new balanced multiwavelet bases. All the problems we deal with are stated in the framework of banded block recursive matrices, since simplified algebraic conditions can be derived from this recursive approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pure Picard-Vessiot extensions with generic properties

Given a connected linear algebraic group over an algebraically closed field of characteristic 0, we construct a pure Picard-Vessiot extension for , namely, a Picard-Vessiot extension , with differential Galois group , such that and are purely differentially transcendental over . The differential field is the quotient field of a -stable proper differential subring with the property that if is any differential field with field of constants and is a Picard-Vessiot extension with differential Galois group a connected subgroup of , then there is a differential homomorphism such that is generated over as a differential field by .

     

Hilbert spaces with generic groups of automorphisms

Let G be a countable group. We prove that there is a model companion for the theory of Hilbert spaces with a group G of automorphisms. We use a theorem of Hulanicki to show that G is amenable if and only if the structure induced by countable copies of the regular representation of G is existentially closed.     

The centers of generic division algebras with involution

The main goal of this paper is a study of the centers of the generic central simple algebras with involution. These centers are shown to be invariant fields under finite groups in a way analagous to the center of the generic division algebras. The centers of the generic central simple algebras with involution are also described as generic splitting fields (i.e. function fields of Brauer-Severi varieties) over the centers of generic division algebras. Finally, a generic central simple algebra is described for the class of central simple algebras with subfields of a certain dimension. The first author would like to thank the Department of Mathematics of The University of Texas at Austin for its hospitality and the NSF for its support under grant DMS 585-05767. The second author would like to thank the NSF for its support under grants DMS 8303356 and DMS 8601279.     

Preimages of CR submanifolds with generic holomorphic maps

We investigate the notion of CR transversality of a generic holomorphic map f: ℂ ⁿ → ℂ ^m to a smooth CR submanifold M of ℂ ^m . We construct a stratification of the set of non-CR transversal points in the preimage M′ = f ⁻¹ (M) by smooth submanifolds, consisting of points where the CR dimension of M′ is constant. We show the existence of a Whitney stratification for sets which are locally diffeomorphic to the product of an open set and an analytic set. Work on this paper was supported by ARRS, Republic of Slovenia.     

The construction of an iterative fractional scheme: the case of Joe

In his paper on A New Hypothesis Concerning Children’s Fractional Knowledge, Steffe (2002) demonstrated through the case study of Jason and Laura how children might construct their fractional knowledge through reorganization of their number sequences. He described the construction of a new kind of number sequence that we refer to as a connected number sequence (CNS). A CNS can result from the application of a child’s explicitly nested number sequence, ENS (Steffe, L. P. (1992). Learning and Individual Differences, 4(3), 259–309; Steffe, L. P. (1994). Children’s multiplying schemes. In: G. Harel, & J. Confrey (Eds.), (pp. 3–40); Steffe, L. P. (2002). Journal of Mathematical Behavior, 102, 1–41) in the context of continuous quantities. It requires the child to incorporate a notion of unit length into the abstract unit items of their ENS. Connected numbers were instantiated by the children within the context of making number-sticks using the computer tool TIMA: sticks. Steffe conjectured that children who had constructed a CNS might be able to use their multiplying schemes to construct composite unit fractions. (In the context of number-sticks a composite unit fraction could be a 3-stick as 1/8 of a 24-stick.) In the case of Jason and Laura, his conjecture was not confirmed. Steffe attributed the constraints that Jason and Laura experienced as possibly stemming from their lack of a splitting operation for composite units. In this paper we shall demonstrate, using the case study of Joe, how a child might construct the splitting operation for composite units, and how such a child was able to not only confirm Steffe’s conjecture concerning composite unit fractions, but also give support to our reorganization hypothesis by constructing an iterative fractional scheme (and consequently, a fractional connected number sequence (FCNS)) as a reorganization of his ENS.     

Modal analysis reduction of multi-body systems with generic damping

Modal analysis of multi-body systems is broadly used to study the behavior and controller design of dynamic systems. In both cases, model reduction that does not degrade accuracy is necessary for the efficient use of these models. Previous work by the author addressed the reduction of modal representations by eliminating entire modes or individual modal elements (inertial, compliant, resistive). In that work, the bond graph formulation was used to model the system and the modal decomposition was limited to systems with proportional damping. The objective of the current work is to develop a new methodology such that model reduction can be implemented to modal analysis of multi-body systems with non-proportional damping that were not modeled using bond graphs. This extension also makes the methodology applicable to realistic systems where the importance of modal coupling terms is quantified and potentially eliminated. The new methodology is demonstrated through an illustrative example.     

On generic families of cyclic polynomials with even degree

 We construct generic cyclic polynomials of even degree with two parameters. Our result, which is based on an affirmative solution for linear Noether's problem, corresponds to ``two-dimensional' Kummer theory with base field descended to the maximal real subfield of the cyclotomic field. Received: 17 September 2001 / Revised version: 31 October 2001     

Minimizing singularities of generic plane disks with immersed boundaries

A cooriented circle immersion into the plane can be extended to a stable map of the disk which is an immersion in a neighborhood of the boundary and with outward normal vector field along the boundary equal to the given coorienting normal vector field. We express the minimal number of fold components of such a stable map as a function of its number of cusps and of the normal degree of its boundary. We also show that this minimum is attained for any cooriented circle immersion of normal degree not equal to one. The first author is a research fellow of the Royal Swedish Academy of Sciences sponsored by the Knut and Alice Wallenberg foundation.     

Spaces appearing in the construction of infinite-dimensional analysis according to the biorthogonal scheme

We study properties of annihilation operators of infinite order that act in spaces of test functions. The results obtained are used for establishing the coincidence of spaces of test functions.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 977–990, July, 2004.     

Riemannian 3-metrics with a generic Codazzi Ricci tensor

We determine a large family of explicit metrics, defined on open subsets of \mathbb R ³{\mathbb R ^3} , having a Codazzi Ricci tensor and three distinct Ricci eigenvalues.     

Symmetries of a generic coaction

If B is -algebra of dimension $4leq n<infty$ then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say , have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for in the case where B is a matrix algebra (2) if then the dual is not amenable (3) if then the fixed point subfactor has index n and principal graph . Received: 3 December 1998 / in final form: 8 January 1999