b67dfea8947ffac03093c860ce9bb7bf ApuntsAritmetica.pdf 03489c27fec29b6afeb6b9a901aecb58022ad1f5 ApuntsAritmetica.pdf 6e54edf3f6b2d5fcdf3a43f03e3c011f278ca2cc1c1f2e230d41701fc6335dcd ApuntsAritmetica.pdf Title: Apunts d'Aritmètica Subject: Keywords: Author: Marc Masdeu Creator: LaTeX with hyperref package Producer: pdfTeX-1.40.18 CreationDate: Tue Jun 7 12:30:10 2022 CEST ModDate: Tue Jun 7 12:30:10 2022 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 74 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 718958 bytes Optimized: yes PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- ZVESAA+URWGothicL-Demi Type 1 Custom yes yes no 789 0 SMJAUB+NimbusRomNo9L-Regu Type 1 Custom yes yes no 791 0 JDXZLO+NimbusRomNo9L-ReguItal Type 1 Custom yes yes no 792 0 KVFRED+URWGothicL-Book Type 1 Custom yes yes no 793 0 DWOLMQ+CMMI10 Type 1 Builtin 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Item: Title: 1.4 Mètodes efectius per inversos i exponenciació Item: Title: 1.5 Aplicacions a la criptografia Children: Item: Title: 1.5.1 Diffie Hellman Item: Title: 1.5.2 El xifrat ElGamal Item: Title: 1.5.3 El xifrat RSA Item: Title: 2 La llei de reciprocitat quadràtica Children: Item: Title: 2.1 Residus quadràtics i el símbol de Legendre Item: Title: 2.2 LRQ i demostració Children: Item: Title: 2.2.1 Demostració de la LRQ Item: Title: 2.3 El símbol de Jacobi Item: Title: 2.4 Aplicació: arrels quadrades mòdul p Children: Item: Title: 2.4.1 Un primer algoritme Item: Title: 2.4.2 L'algoritme de Cipolla Item: Title: 3 Corbes el·líptiques Children: Item: Title: 3.1 Definició i llei de grup Children: Item: Title: 3.1.1 La llei de grup en coordenades Item: Title: 3.2 Punts de torsió, punts racionals Children: Item: Title: 3.2.1 Altures Item: Title: 3.2.2 La versió dèbil del teorema de Mordell Item: Title: 3.2.3 Demostració de la finitud de L/Q Item: Title: 3.3 Isogènies Item: Title: 3.4 Corbes sobre cossos finits Item: Title: 3.5 Criptografia amb corbes el·líptiques Children: Item: Title: 3.5.1 Diffie Hellman amb corbes el·líptiques Item: Title: 3.5.2 ElGamal amb corbes el·líptiques Item: Title: 3.6 Comptatge de punts: l'algoritme de Schoof Item: Title: 4 Primalitat i factorització Children: Item: Title: 4.1 Primalitat Children: Item: Title: 4.1.1 El test de Fermat Item: Title: 4.1.2 El test de Solovay-Strassen Item: Title: 4.1.3 El test de Miller Rabin Item: Title: 4.1.4 El test de Lucas Item: Title: 4.1.5 El test de Pocklington Item: Title: 4.2 Algoritmes de factorització Children: Item: Title: 4.2.1 Rho de Pollard Item: Title: 4.2.2 Mètode (p-1) de Pollard Item: Title: 4.2.3 El mètode de Lenstra Item: Title: 4.2.4 Bases de factors: l'algoritme de Dixon Item: Title: 4.2.5 Fraccions continuades Item: Title: 4.2.6 El garbell quadràtic Item: Title: 4.3 Algoritmes pel logaritme discret Children: Item: Title: 4.3.1 Pohlig Hellman Item: Title: 4.3.2 Rho de Pollard Item: 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