CRYPTO use fast modular technique to a determiine 95 mod 20

CRYPTO

use fast modular technique to

a. determiine 9^5 mod 20 and then express the result in congruent form

b. 7^6 mod 13 do the same as a

(a)

Here b=9, e=5 and m =20 and c = remainder.

s=1: c = (1*9) mod 20 = 9 mod 20 = 9

s=2: c = (9*9) mod 20 = 81 mod 20 = 1

s=1: c = (1*9) mod 20 = 9 mod 20 = 9

s=1: c = (9*9) mod 20 = 81 mod 20 =

s=1: c = (1*9) mod 20 = 9 mod 20 = 9

So, the final answer is 9.

(b)

Here b=7, e=6 and m =13 and c = remainder.

s=2: c = (1*7) mod 13 = 7 mod 13 = 7

s=3: c = (7*7) mod 13 = 49 mod 13 = 10

s=4: c = (10*7) mod 13 = 70 mod 13 = 5

s=5: c = (5*7) mod 13 = 35 mod 13 = 9

s=6: c = (9*7) mod 13 = 63 mod 13 = 11

s=1: c = (11*7) mod 13 = 77 mod 13 = 12

So, the final answer is 12.