Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

Business-friendly contracting : how simplification and visualization can help bring it to practice

One thesis of this book is that the legal function within businesses will shift from a paradigm of security to one of opportunity. This chapter embraces that likelihood in the context of business contracting, where voices calling for a major shift are starting to surface. It explores how contracts can be used to reach better outcomes and relationships, not just safer ones. It introduces the concept of business-friendly contracting, highlighting the need for contracts to be seen as business tools rather than exclusively as legal tools, and working as business enablers rather than obstacles. By changing the design of contracts and the ways in which those contracts are communicated—through simplification and visualization, for example—legal and business operations can be better integrated. Contracts can then be more useful to business, and contract provisions can actually become more secure by becoming easier to negotiate and implement.fi=vertaisarvioitu|en=peerReviewed

Two-Face: New Public Key Multivariate Schemes

We present here new multivariate schemes that can be seen as HFE generalization having a property called `Two-Face\u27. Particularly, we present five such families of algorithms named `Dob\u27, `Simple Pat\u27, `General Pat\u27, `Mac\u27, and `Super Two-Face\u27. These families have connections between them, some of them are refinements or generalizations of others. Notably, some of these schemes can be used for public key encryption, and some for public key signature. We introduce also new multivariate quadratic permutations that may have interest beyond cryptography

The Resultant via a Koszul Complex

Abstract. As noticed by Jouanolou, Hurwitz proved in 1913 ([Hu]) that, in the generic case, the Koszul complex is acyclic in positive degrees if the number of (homogeneous) polynomials is less than or equal to the number of variables†. It was known around 1930 that resultants may be calculated as a Mc Rae invariant of this complex. This expresses the resultant as an alternate product of determinants coming from the differentials of this complex. Demazure explained in a preprint ([De]), how to recover this formula from an easy particular case of deep results of Buchsbaum and Eisenbud on finite free resolutions. He noticed that one only needs to add one new variable in order to do the calculation in a non generic situation. I have never seen any mention of this technique of calculation in recent reports on the subject (except the quite confidential one of Demazure and in an extensive work of Jouanolou, however from a rather different point of view). So, I will give here elementary and short proofs of the theorems needed—except the well-known acyclicity of the Koszul complex and the “Principal Theorem of Elimination”—and present some useful remarks leading to the subsequent algorithm. In fact, no genericity is needed (it is not the case for all the other techniques). Furthermore, when the resultant vanishes, some information can be given about the dimension of the associated variety. As an illustration of this technique, we give an arithmetical consequence on the resultant: if the polyno