This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancement in problems solved using quantum annealing, does not guarantee privacy for all possible cases. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example illustrates how to retrieve the original problem from that transformed by SRT. Moreover, we show that our method is efficient also for full-scale problems.

This article describes a system that can significantly improve the candidate selection process for media casting. It allows the impresario company to recommend an optimal set of performers by selecting people who are most likely to fit specific role demands. Several mechanisms interoperate to provide an innovative recommendation system. These include Osgood semantic scale, various NLP techniques and searching in an embedding space. The Polish language corpus for NLP was created using PolishSubtitles, Dictionary of Synonyms, and Dictionary created from Personnel Consulting Agency Database, provided for the authors by cast recruitment company. Before artificial intelligence training, data had to be segmented, lemmatized, and disambiguated in the morph syntactic domain using the Morpheus 2.0 analyzer. The recommendation system described in the paper is very promising due to the applicability of machine learning algorithms and the intelligent user interface. A test, performed by a cast recruitment company, was performed to confirm proposed model viability. Test was concluded in comparision to manual selection process and provided more adequate set of candidates in shorter timeframe.

This paper presents method for obtaining high-degree compression functions using natural symmetries in a given model of an elliptic curve. Such symmetries may be found using symmetry of involution $[-1]$ and symmetry of translation morphism $\tau_T=P+T$, where $T$ is the $n$-torsion point which naturally belongs to the $E(\mathbb K)$ for a given elliptic curve model. We will study alternative models of elliptic curves with points of order $2$ and $4$, and specifically Huff's curves and the Hessian family of elliptic curves (like Hessian, twisted Hessian and generalized Hessian curves) with a point of order $3$. We bring up some known compression functions on those models and present new ones as well. For (almost) every presented compression function, differential addition and point doubling formulas are shown. As in the case of high-degree compression functions manual investigation of differential addition and doubling formulas is very difficult, we came up with a Magma program which relies on the Gr\"obner basis. We prove that if for a model $E$ of an elliptic curve exists an isomorphism $\phi:E \to E_M$, where $E_M$ is the Montgomery curve and for any $P \in E(\mathbb K)$ holds that $\phi(P)=(\phi_x(P), \phi_y(P))$, then for a model $E$ one may find compression function of degree $2$. Moreover, one may find, defined for this compression function, differential addition and doubling formulas of the same efficiency as Montgomery's. However, it seems that for the family of elliptic curves having a natural point of order $3$, compression functions of the same efficiency do not exist. Comment: 33 pages

Let E be an elliptic curve given by any model over a field K. A rational function f : E → K of degree 2 such that f(P) = f(Q) ⇔ Q = ±P can be used as a point compression on E. Then there exists induced from E multiplication of values of f by integers given by [n]f(P) := f([n]P), which can be comput ed using the Montgomery ladder algorithm. For this algorithm one needs the generalized Montgomery formulas for differential addition and doubling that is rational functions A(X1, X2, X3) ∈ K(X1, X2, X3) and [2] ∈ K(X) such that f(P + Q) = A(f(P), f(Q), f(Q − P)) and [2]f(P) = f([2]P) for generic P,Q ∈ E. For most standard models of elliptic curves generalized Montgomery formulas are known. To use compression for scalar multiplication [n]P for P ∈ E, one can compute after compression [n]f(P), which is followed by [n + 1]f(P) in the Montgomery ladder algorithm, then one can recover [n]P on E, since there exists a rational map B such that [n]P = B(P, [n]f(P), [n + 1]f(P)) for generic P ∈ E and n ∈ Z. Such a map B is known for Weierstrass and Edwards curves, but to our knowledge it seems that it was not given for other models of elliptic curves. In this paper for an elliptic curve E and the above compression function f we give an algorithm to search for generalized Montgomery formulas, functions on K induced after compression by endomorphisms of E, and the above map B for point recovering. All these tasks require searching for solutions of similar type problems for which we describe an algorithm based on Gröbner bases. As applications we give formulas for differential addition, doubling and the above map B for Jacobi quartic, Huff curves, and twisted Hessian curves.

The GLV method allows to improve scalar multiplication on an elliptic curve E/𝔽 q with an efficiently computable endomorphism Φ : E → E over 𝔽 q . For points in a subgroup of large prime order r this requires decomposition of scalar k = k 0 + k 1 λ mod r, where Φ acts on the subgroup of order r as multiplication by λ ∈ 𝔽 r and k 0 , k 1 are integers O ( r ) . In this note we consider the case when λ is of the form λ = 2 s + a, where a is a small integer and λ = O ( r ) , which allows very easy and fast decomposition of k especially in hardware implementations. We give a method to construct such elliptic curves based on the complex multiplication method, and give examples of elliptic curves for λ ∈ {2 s , 2 s − 1} and various security levels.