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- W6894421 abstract "Megmutattuk, hogy a normaforma fuggvenyt modulo pq redukalva, ahol p es q nagy primszamok, utkozesmentes fuggvenyt kapunk. Tobb konstrukciot elemeztunk kriptografiai alkalmazasok szempontjabol relevans veletlen sorozatcsaladra. Ha Gn(x) egy algebrailag zart test feletti linearis rekurziv polinomsorozat es x,y algebrailag fuggőek, akkor bebizonyitottuk, hogy a Gn(x)=Gm(y) egyenletnek altalanos feltetelek mellett csak veges sok megoldasa van n,m-ben. Bebizonyitottuk, hogy egy normaforma egyenletnek altalaban csak veges sok olyan megoldasa van, ahol a megoldasok koordinatai egy szamtani sorozatot alkotnak. Megadtuk a klasszikus ?-reprezentacio es a kanonikus szamrendszerek egy kozos altalanositasat es tobb dolgozatban vizsgaltuk ezen SRS-nek elnevezett fogalom tulajdonsagait. Elemzesunk valaszt ad arra, hogy miert nehez a harmadfoku CNS polinomok, illetve az (F) tulajdonsagu Pisot szamok jellemzese. Megfogalmaztuk a kovetkező sejtest: Legyen |?|<2 es {an} egesz szamok olyan sorozata, amelyre 0 ? an-1+ ? an + an+1 <1 minden n-re. Akkor {an} periodikus. Szamos korabbi eredmenyt messzemenően altalanositva, mely eredmenyeket ertunk el ket klasszikus, Fermat-ig es Eulerig visszanyulo diofantikus temakorben, nevezetesen szamtani sorozatokban, illetve hatvanyosszegekben talalhato teljes hatvanyokra vonatkozoan. Tobbek kozott megmutattuk, hogy egeszekből allo k-tagu szamtani sorozat tagjainak szorzata k ? 11-re altalaban nem lehet teljes hatvany. | Considering the reduction modulo pq, where p and q are big primes we constructed collision resistant hash functions. We studied some construction of cryptography relevant pseudo random number sequences. If Gn(x) denotes a linear recursive polynomial sequence over an algebraically closed field and x,y are algebraically dependent, then we proved that the equation Gn(x)=Gm(y) has under quite general assumptions only finitely many solutions in n,m. We proved that a norm form equation has only finitely many solutions, which coordinates form an arithmetical progression. We realized a common generalization, called shift radix system, of the classical ?-reprezentation and the canonical number systems and studied its properties in several papers. Our investigation showed that the characterization problem of cubic CNS polynomials and Pisot numbers of proprty (F) is complicated. We made rise the conjecture: Let |?|<2 and {an} a sequence of integers staisfying the inequality 0 ? an-1+ ? an + an+1 <1 for all n. Then {an} is periodical. Generalyzing essentially several earlier results, we achieved deep results in two classical diophantine topics: perfect powers in arithmetical progressions and in power sums, which are going back to Farmat and Euler. We proved among others that the product of members of an arithmetical progression of length at most 11 apart from trivial cases cannot be a perfect power." @default.
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- W6894421 date "2006-01-01" @default.
- W6894421 modified "2023-10-18" @default.
- W6894421 title "Algoritmikus számelmélet és alkalmazásai a kriptográfiában = Computational number theory and its applications in cryptography" @default.
- W6894421 hasPublicationYear "2006" @default.
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