Performing RSA's en/de-cryption procedure

Taking the modulo of a power is what the RSA public-key algorithm does to data in order to either encrypt or decrypt it. Symbolically, this is what it has to do:

x^y mod n

To humans this is intuitive only for small values. RSA uses large ones. To get an idea what RSA or other software does to evaluate such an expression, do a couple of them manually. Follow the method detailed in the slides shown in class. Refer to those slides.

The assignment:

Determine the following modulos-of-powers by applying the modular arithmetic property that the modulo of a product is the modulo of the product of the multipliers’ modulos:

 (a x b) mod n = [ (a mod n) x (b mod n) ] mod n

Show your work and prominently circle your answers.

1.  3⁵⁰ mod 7

2.  287⁴⁹⁹ mod 88