Structure of the sialylated L3 lipopolysaccharide of Neisseria meningitidis.

The L3 immunotype lipopolysaccharide (LPS) of Neisseria meningitidis was subjected to degradation procedures, which produced a number of different oligosaccharide fragments. The high resolution 1H and 13C NMR spectroscopic analyses of these oligosaccharides yielded structural information on a number of different regions of the LPS. For example, from one oligosaccharide, it was found that the endogenous sialylation of the meningococcal LPS occurs at O-3 of the terminal beta-D-galactopyranosyl residue of its lacto-N-neotetraose antenna in the alpha-D-configuration. From another, it was also established that the dominant structural feature responsible for L3 epitope specificity is the presence of a phosphorylethanolamine substituent at O-3 of the penultimate heptopyranosyl residue of its other antenna. In addition from information obtained with another oligosaccharide the structure of the 3-deoxy-D-manno-octulosonic acid disaccharide region of the L3 LPS was also elucidated. From all the above cumulative data plus some published data, it was then possible to reconstruct the complete structure of the entire native L3 LPS

Automorphismes projectifs et polynômes binaires irréductibles

Cette thèse porte sur l'étude de certaines propriétés structurelles de l'ensemble des polynômes irréductibles à coefficients dans F2. La première partie classifie ces polynômes par rapport à l'action du groupe des automorphismes de la droite projective P1(F2), à savoir PGL2(F2) S3. Nous btenons quatre familles de polynômes invariants par l'action des quatre sous-groupes non triviaux de S3, ce qui généralise la notion de polynôme réciproque. De plus, nous donnons une formule de dénombrement qui complète celle de Carlitz (qui a traité le cas réciproque). Dans la seconde partie, nous donnons des transformations permettant de générer nos polynômes invariants ainsi que le théorème général décrivant leur action précise sur les polynômes irréductibles. Cela donne deux partitions différentes par des relations simples sur leurs coefficients. Nous proposons également des moyens de construire des suites infinies explicites d'irréductibles invariants en généralisant ce qui existait pour les réciproques. Dans la troisième partie, nous étudions plus en détail nos transformations. En particulier, nous retrouvons deux d'entre elles au travers d'opérations sur les points de deux courbes elliptiques.This Ph.D. is a study of some structural properties of the set of irreducible polynomials with coefficients in F2. The first part classify these polynomials under the action of the automorphisms group of the projective line P1(F2), i.e. PGL2(F2) S3. We obtain four families of invariant polynomials under each non trivial subgroup of S3, which generalize the notion of self-reciprocal polynomials. Moreover, we give an enumeration formula that completes Carlitz' one (which concerns the self-reciprocal polynomials). In the second part, we give transformations that generate our invariant polynomials and the general theorem describing their action on the irreducible polynomials. That gives two different partitions by easy relations on their coefficients. We also propose ways to construct infinite sequences of irreducible invariant polynomials, generalizing what was known for self-reciprocal polynomials. In the third part, we study more deeply our transformations. In particular, we show that we can find two of them through operations on the points of two elliptic curves.ROUEN-BU Sciences Madrillet (765752101) / SudocSudocFranceF

Sur différentes familles de polynômes binaires irréductibles

International audienceUsing a natural action of the permutation group S3 on the set of irreducible polynomials, we attach to each subgroup of S3 the family of its invariant polynomials. Enumeration formulas for the trivial subgroup and for one transposition subgroup were given by Gauss (for prime fields) [1] and Carlitz (for all finite base fields) [2]. Respectively, they allow to enumerate all irreducible and self reciprocal irreducible polynomials. In our context, the last remaining case concerned the alternating subgroup A3. We give here the corresponding enumeration formula restricted to F2 base field. We wish this will give an interesting basis for subsequent developments analogous to those of Meyn [3] and Cohen [4]

Transformations sur les polynômes binaires irréductibles

International audienceUsing the natural action of GL2(F2) S3 over F2[X], one can define different classes of polynomials strongly analogous to selfreciprocal irreducible polynomials. We give transformations to construct polynomials of each kind of invariance and we deal with the question of explicit infinite sequences of invariant irreducible polynomials in F2[X]. We generalize results obtained by Varshamov, Wiedemann, Meyn and Cohen and we give sequences of invariant irreducible polynomials. Moreover we explain what happens when the given constructions fail. We also give a result on the order of the polynomials of one of the classes: the alternate irreducible polynomials

On Maximal QROBDD's of Boolean Functions

We investigate the structure of ``worst-case'' quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of ``hard'' Boolean functions as functions whose QROBDD are ``worst-case'' ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer)

Mahler's expansion and boolean functions

International audienceThe substitution of X by X2 in binomial polynomials generates sequences of integers by Mahler's expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) associated with boolean functions

HFE and BDDs: A Practical Attempt at Cryptanalysis

HFE (Hidden Field Equations) is a public key cryptosystem using univariate polynomials over finite fields. It was proposed by J. Patarin in 1996. Well chosen parameters during the construction produce a system of quadratic multivariate polynomials over GF(2) as the public key. An enclosed trapdoor is used to decrypt messages. We propose a ciphertext-only attack which mainly consists in satisfying a boolean formula. Our algorithm is based on BDDs (Binary Decision Diagrams), introduced by Bryant in 1986, which allow to represent and manipulate, possibly efficiently, boolean functions. This paper is devoted to some experimental results we obtained while trying to solve the Patarin's challenge. This approach was not successful, nevertheless it provided some interesting information about the security of HFE cryptosystem

On Maximal QROBDD's of Boolean Functions

We investigate the structure of ``worst-case'' quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of ``hard'' Boolean functions as functions whose QROBDD are ``worst-case'' ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer)

Boolean Functions: Cryptography and Applications.

ISBN: 2-87775-403-0Proceedings of BFCA'0