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Modulorekenen, RSA codering

Hoe kan volgende macht vereenvoudigd worden? Zonder computer, met behulp van een rekenmachine.

50020¹²³⁴⁵ MOD 100141 Dit voorbeeld zou 40975 MOD 100141 moeten uitkomen.

Soubry cedric
27-5-2002

Antwoord

Als het moet kan alles:

50020 to the power of (2¹³) (mod 100141) = 60424
50020 to the power of (2¹²) (mod 100141) = 48981
50020 to the power of (2¹¹) (mod 100141) = 49249
50020 to the power of (2¹⁰) (mod 100141) = 53118
50020 to the power of (2⁹) (mod 100141) = 77078
50020 to the power of (2⁸) (mod 100141) = 88121
50020 to the power of (2⁷) (mod 100141) = 943
50020 to the power of (2⁶) (mod 100141) = 2304
50020 to the power of (2⁵) (mod 100141) = 48
50020 to the power of (2⁴) (mod 100141) = 99000
50020 to the power of (2³) (mod 100141) = 21098
50020 to the power of (2²) (mod 100141) = 63457
50020 to the power of (2¹) (mod 100141) = 77656
50020 to the power of (2⁰) (mod 100141) = 50020

Hence 50020 to the power of 12345 (mod 100141)
= 60424·48981·1·1·1·1·1·1·48·99000·21098·1·1·50020 (mod 100141)
= 60830·48·99000·21098·1·1·50020 (mod 100141)
= 15751·99000·21098·1·1·50020 (mod 100141)
= 53489·21098·1·1·50020 (mod 100141)
= 21993·1·1·50020 (mod 100141)
= 21993·1·50020 (mod 100141)
= 21993·50020 (mod 100141)
= 40975 (mod 100141)

Zie link (incl. next page!)

Zie Calculating Powers Fast [http://www.pacm.princeton.edu/~matalive/Crypto/CryptoLab2/FastPower.html]

WvR
29-5-2002