fast normal basis multiplication using general purpose processors for cryptographic applications normal bases have received considerable attention especially for hardware implementation we consider fast software algorithms for normal basis multiplication over the extended binary field gf 2 sup m we present a vector level algorithm which essentially eliminates the bit wise inner products needed in the conventional approach to the normal basis multiplication we then present another algorithm which significantly reduces the dynamic instruction counts both algorithms utilize the full width of the data path of the general purpose processor on which the software is to be executed we also consider composite fields and present an algorithm which can provide further speed ups and an added flexibility toward hardware software codesign of processors for very large finite fields

assouad nagata dimension of connected lie groups we prove that the asymptotic assouad nagata dimension of a connected lie group g equipped with a left invariant riemannian metric coincides with its topological dimension of g c where c is a maximal compact subgroup to prove it we will compute the assouad nagata dimension of connected solvable lie groups and semisimple lie groups as a consequence we show that the asymptotic assouad nagata dimension of a polycyclic group equipped with a word metric is equal to its hirsch length and that some wreath type finitely generated groups can not be quasi isometrically embedded into any cocompact lattice on a connected lie group

a hurewicz type theorem for asymptotic dimension and applications to geometric group theory we prove an asymptotic analog of the classical hurewicz theorem on mappings that lower dimension this theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension as applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their hirsch length we are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups amalgamated free products and the hyperbolization of metric spaces possessing the higson property

a search of minimal key functions for normal basis multipliers the circuit complexity of a massey omura normal basis multiplier for a finite field gf 2 sup m depends on the key function for multiplication key functions with minimum complexity called minimal key functions are desirable this paper investigates the complexity of a key function and reports search results of minimal key functions a table of minimal key functions for m up to 31 is included

limit operators compactness and essential spectra on bounded symmetric domains abstract this paper is a follow up to a recent article about the essential spectrum of toeplitz operators acting on the bergman space over the unit ball as mentioned in the said article some of the arguments can be carried over to the case of bounded symmetric domains and some cannot the aim of this paper is to close the gaps to obtain comparable results for general bounded symmetric domains in particular we show that a toeplitz operator on the bergman space a p is fredholm if and only if all of its limit operators are invertible even more generally we show that this is in fact true for all band dominated operators an algebra that contains the toeplitz algebra moreover we characterize compactness and explain how the berezin transform comes into play in particular we show that a bounded linear operator is compact if and only if it is band dominated and its berezin transform vanishes at the boundary for p 2 band dominated can be replaced by contained in the toeplitz algebra

deformation of canonical morphisms and the moduli of surfaces of general type in this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space among other things we prove a criterion that determines when a finite map can be deformed to a one to one map we use this criterion to construct new surfaces of general type with birational canonical map for different c 1 2 and the canonical map of the surfaces we construct is in fact a finite birational morphism our general results enable us to describe some new components of the moduli of surfaces of general type we also find infinitely many moduli spaces open image in new window having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism

vlsi architectures for computing multiplications and inverses in gf 2 m finite field arithmetic logic is central in the implementation of reed solomon coders and in some cryptographic algorithms there is a need for good multiplication and inversion algorithms that can be easily realized on vlsi chips massey and omura 1 recently developed a new multiplication algorithm for galois fields based on a normal basis representation in this paper a pipeline structure is developed to realize the massey omura multiplier in the finite field gf 2m with the simple squaring property of the normal basis representation used together with this multiplier a pipeline architecture is also developed for computing inverse elements in gf 2m the designs developed for the massey omura multiplier and the computation of inverse elements are regular simple expandable and therefore naturally suitable for vlsi implementation

the integral k theoretic novikov conjecture for groups with finite asymptotic dimension the integral assembly map in algebraic k theory is split injective for any geometrically finite discrete group with finite asymptotic dimension

on homological coherence of discrete groups abstract we explore a weakening of the coherence property of discrete groups studied by f waldhausen the new notion is defined in terms of the coarse geometry of groups and should be as useful for computing their k theory we prove that a group of finite asymptotic dimension is weakly coherent in particular there is a large collection of r modules of finite homological dimension when r is a finite dimensional regular ring this class contains word hyperbolic groups coxeter groups and as we show the cocompact discrete subgroups of connected lie groups

efficient multiplication beyond optimal normal bases in cryptographic applications the use of normal bases to represent elements of the finite field gf 2 sup m is quite advantageous especially for hardware implementation in this article we consider an important field operation namely multiplication which is used in many cryptographic functions we present a class of algorithms for normal basis multiplication in gf 2 sup m our proposed multiplication algorithm for composite finite fields requires a significantly lower number of bit level operations and hence can reduce the space complexity of cryptographic systems

an etale approach to the novikov conjecture we show that the rational novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the higson compactification of an e we then show that for groups of finite asymptotic dimension the higson compactification is mod p acyclic for all p and deduce the integral novikov conjecture for these groups 2007 wiley periodicals inc

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

efficient algorithms and architectures for field multiplication using gaussian normal bases recently implementations of normal basis multiplication over the extended binary field gf 2 sup m have received considerable attention a class of low complexity normal bases called gaussian normal bases has been included in a number of standards such as ieee and nist for an elliptic curve digital signature algorithm the multiplication algorithms presented there are slow in software since they rely on bit wise inner product operations in this paper we present two vector level software algorithms which essentially eliminate such bit wise operations for gaussian normal bases our analysis and timing results show that the software implementation of the proposed algorithm is faster than previously reported normal basis multiplication algorithms the proposed algorithm is also more memory efficient compared with its look up table based counterpart moreover two new digit level multiplier architectures are proposed and it is shown that they outperform the existing normal basis multiplier structures as compared with similar digit level normal basis multipliers the proposed multiplier with serial output requires the fewest number of xor gates and the one with parallel output is the fastest multiplier

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension