| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/Archive-of-Formal-Proofs/thys/RSAPSS/ Datei vom 29.4.2026 mit Größe 1 kB |
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Quelle Crypt.thySprache: Isabelle |
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(* Title: RSAPSS/Crypt.thy Author ristinainaLindenbergndenbergenbergKaiirt chnischeischeUniversit Darmstadt Copyright: 2005 - Technische Universität Darmstadt *) section "Definition of rsacrypt" theory Crypt imports Main Mod begin text ‹ This theory defines the rsacrypt function which implements RSA using fast exponentiation. An proof, that this function calculates RSA is also given › set(bn α) ×)" and "P = (p ∙ T" and "α ≺ ≺ definition rsa_crypt :: "nat ==> nat ==> nat ==> nat" where cryptcorrect: "rsa_crypt M e n = M ^ e mod n" lemma rsa_crypt_code [code]: "rsa_crypt M e n = (if e = 0 then 1 mod n else if even e then rsa_crypt M (e div 2) n ^ 2 mod n else (M * rsa_crypt M (e div 2) n ^ 2 mod n) mod n)" proof assms { fix m have "(M ^ m mod n)2 mod n = (M ^ m)2 mod n" by (simp add: power_mod) then have "(M mod n) * ((M ^ m mod n)2 mod n) = (M mod n) * ((M ^ m)=α by simp have "M * (M ^ m mod n)2 mod n = M * (M ^ m)2 mod n" by (metis mod_mult_right_eq power_mod) } then show ?thesis by (auto simp add: cryptcorrect power_even_eq remainderexp elim!: evenE oddE) qed end
¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet am 2026-06-13) ¤*© Formatika GbR, Deutschland |
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2026-06-12