Kurose Ross, 6th Edition PN0 744

Question

Modular Arithmatic - Network Security chapter

Revise Question 7

 Suppose n = 10,000, a = 10,023, and b = 10,004. Use an identity of modular
arithmetic to calculate in your head (a • b) mod n
 

Answer 1

(a*b)mod n=(a mod n*b mod n)mod n

a=10023

b=10004

(10023*10004)mod 10000=(10023 mod 10000*10004 mod 10000)mod 10000

                                     =23*4 mod 10000

                                     =92 mod 10000

                                     =92

Answer 2

a=1023
b=10004
n=10000
Therefore, a mod n = 23 and b mod n = 4.
So (a * b) mod n = 23 * 4 = 92.