. "V\u00FDpo\u010Detn\u00ED n\u00E1ro\u010Dnost faktorizace velk\u00FDch \u010D\u00EDsel stoj\u00ED v cest\u011B p\u0159i \u00FAtoc\u00EDch na v\u011Bt\u0161inu asymetrick\u00FDch \u0161ifer. Metoda eliptick\u00FDch k\u0159ivek (ECM) je pova\u017Eov\u00E1na za jednu z nejlep\u0161\u00EDch pokud jde o \u010D\u00EDsla \u0159\u00E1dov\u011B kolem 200b, co\u017E p\u0159\u00EDmo neumo\u017E\u0148uje \u00FAtok na RSA, av\u0161ak lze tuto metodu vyu\u017E\u00EDt nap\u0159\u00EDklad jako stavebn\u00ED prvek n\u011Bkter\u00E9 ze sofistikovan\u011Bj\u0161\u00EDch metod \u0159e\u0161en\u00ED, jakou je nap\u0159\u00EDklad GNFS. V tomto \u010Dl\u00E1nku p\u0159edstavujeme novou metodu p\u0159\u00EDstupu k \u0159e\u0161en\u00ED faktorizace velk\u00FDch \u010D\u00EDsel s vyu\u017Eit\u00EDm ECM, zam\u011B\u0159enou na HPC syst\u00E9my TIER. Na\u0161e metoda SPHERE ( Scalable Parallel HPC Efficient Realization of ECM ), kombinuje v sou\u010Dasn\u00E9 dob\u011B nov\u00FD v\u00FDpo\u010Detn\u00ED postup vyu\u017E\u00EDvaj\u00EDc\u00ED afinn\u00EDch sou\u0159adnic se zn\u00E1m\u00FDm algoritmem na inverzi Left-Shift. Navrhovan\u00E1 metoda SPHERE je v sou\u010Dasn\u00E9 dob\u011B v pokro\u010Dil\u00E9m st\u00E1diu v\u00FDvoje a prob\u00EDh\u00E1 optimalizace pou\u017Eit\u00FDch algoritm\u016F pro pot\u0159eby nasazen\u00ED na HPC syst\u00E9mech. Na\u0161\u00EDm c\u00EDlem je rychlostn\u011B p\u0159ekonat ostatn\u00ED pou\u017E\u00EDvan\u00E9 sou\u0159adn\u00E9 syst\u00E9my jako jsou projektivn\u00ED, \u010Di Jacobiho a vyvr\u00E1tit tak domn\u011Bnku, \u017Ee razantn\u00ED zv\u00FD\u0161en\u00ED po\u010Dtu v\u0161ech matematick\u00FDch operac\u00ED jako cena za odstran\u011Bn\u00ED inverze z v\u00FDpo\u010Dtu, je v\u00FDhodn\u00E9." . "RIV/68407700:21240/14:00219442" . . "Faktorizace p\u0159irozen\u00FDch \u010D\u00EDsel metodou eliptick\u00FDch k\u0159ivek vyu\u017E\u00EDvaj\u00EDc\u00ED HPC syst\u00E9my"@cs . "1"^^ . "N" . . "V\u00FDpo\u010Detn\u00ED n\u00E1ro\u010Dnost faktorizace velk\u00FDch \u010D\u00EDsel stoj\u00ED v cest\u011B p\u0159i \u00FAtoc\u00EDch na v\u011Bt\u0161inu asymetrick\u00FDch \u0161ifer. Metoda eliptick\u00FDch k\u0159ivek (ECM) je pova\u017Eov\u00E1na za jednu z nejlep\u0161\u00EDch pokud jde o \u010D\u00EDsla \u0159\u00E1dov\u011B kolem 200b, co\u017E p\u0159\u00EDmo neumo\u017E\u0148uje \u00FAtok na RSA, av\u0161ak lze tuto metodu vyu\u017E\u00EDt nap\u0159\u00EDklad jako stavebn\u00ED prvek n\u011Bkter\u00E9 ze sofistikovan\u011Bj\u0161\u00EDch metod \u0159e\u0161en\u00ED, jakou je nap\u0159\u00EDklad GNFS. V tomto \u010Dl\u00E1nku p\u0159edstavujeme novou metodu p\u0159\u00EDstupu k \u0159e\u0161en\u00ED faktorizace velk\u00FDch \u010D\u00EDsel s vyu\u017Eit\u00EDm ECM, zam\u011B\u0159enou na HPC syst\u00E9my TIER. Na\u0161e metoda SPHERE ( Scalable Parallel HPC Efficient Realization of ECM ), kombinuje v sou\u010Dasn\u00E9 dob\u011B nov\u00FD v\u00FDpo\u010Detn\u00ED postup vyu\u017E\u00EDvaj\u00EDc\u00ED afinn\u00EDch sou\u0159adnic se zn\u00E1m\u00FDm algoritmem na inverzi Left-Shift. Navrhovan\u00E1 metoda SPHERE je v sou\u010Dasn\u00E9 dob\u011B v pokro\u010Dil\u00E9m st\u00E1diu v\u00FDvoje a prob\u00EDh\u00E1 optimalizace pou\u017Eit\u00FDch algoritm\u016F pro pot\u0159eby nasazen\u00ED na HPC syst\u00E9mech. Na\u0161\u00EDm c\u00EDlem je rychlostn\u011B p\u0159ekonat ostatn\u00ED pou\u017E\u00EDvan\u00E9 sou\u0159adn\u00E9 syst\u00E9my jako jsou projektivn\u00ED, \u010Di Jacobiho a vyvr\u00E1tit tak domn\u011Bnku, \u017Ee razantn\u00ED zv\u00FD\u0161en\u00ED po\u010Dtu v\u0161ech matematick\u00FDch operac\u00ED jako cena za odstran\u011Bn\u00ED inverze z v\u00FDpo\u010Dtu, je v\u00FDhodn\u00E9."@cs . . . . . . . . "16409" . "RIV/68407700:21240/14:00219442!RIV15-MSM-21240___" . . "1"^^ . . "2014-09-04+02:00"^^ . "Faktorizace p\u0159irozen\u00FDch \u010D\u00EDsel metodou eliptick\u00FDch k\u0159ivek vyu\u017E\u00EDvaj\u00EDc\u00ED HPC syst\u00E9my" . "Technick\u00E1 univerzita v Liberci. Fakulta mechatroniky, informatiky a mezioborov\u00FDch studi\u00ED" . "21240" . . "http://pad2014.fm.tul.cz/code/sbornik.html" . . "Mal\u00E1 Sk\u00E1la" . "Faktorizace p\u0159irozen\u00FDch \u010D\u00EDsel metodou eliptick\u00FDch k\u0159ivek vyu\u017E\u00EDvaj\u00EDc\u00ED HPC syst\u00E9my" . "Liberec" . "Faktorizace p\u0159irozen\u00FDch \u010D\u00EDsel metodou eliptick\u00FDch k\u0159ivek vyu\u017E\u00EDvaj\u00EDc\u00ED HPC syst\u00E9my"@cs . "6"^^ . . "Sborn\u00EDik p\u0159\u00EDsp\u011Bvk\u016F PAD 2014" . . "Computing difficulty of factorization of large numbers is what stands in a way during attacks on most of asymmetric ciphers. Method of Elliptic Curve (ECM) je considered to be one of the best if it comes to a numbers around 200b, which does not allow the attack on RSA, but it can be used as a building element for some more sophisticated methods for solution, which is for example GNFS. In this paper we present new method of approach to solving factorization of large numbers with usage of ECM, focused on HPC systems TIER. Our method SPHERE (Scalable Parallel HPC Efficient Realization of ECM), combines nowadays new computational approach using affine coordinates with known algorithm for modular inverse Left-Shift. Proposed method SPHERE is currently in advanced stage of developing and optimization of used algorithms is in progress for needs of deployment on HPC systems. Our goal is to overcome in speed other used coordinate systems as a projective or Jacobi and thus show, that great increase of the number of mathematical operations as a prize for no inversion, is efficient."@en . . "978-80-7494-027-9" . . . "Factorization of large integers using elliptic curve method on HPC systems"@en . . "Factorization of large integers using elliptic curve method on HPC systems"@en . "[DBB0CE327762]" . . . "Kobrle, Daniel" . "ECM; HPC; TIER; SPHERE; affine coordinates; Left-Shift; double-and-add; modular inverse; operational difficulty; factorization."@en .