More Number Theory: Higher Arithmetic in Cryptography

This is a computer science engineering quiz on cryptography and network security, which includes questions on number theory in cryptography.

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Find the set of quadratic residues in the set – Z11* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

QR set = {1, 2, 4, 5, 9} of Z11* QR set = {1, 3, 6, 5, 9} of Z11* QR set = {1, 3, 4, 9,10} of Z11* QR set = {1, 3, 4, 5, 9} of Z11*

In Zp* with (p-1) elements exactly: (p – 1)/2 elements are QR and (p – 1)/2 elements are QNR.

True False

Find the set of quadratic residues in the set – Z13* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12}

QR { 1, 2, 4,5, 10, 12} QR { 2, 4, 5, 9, 11, 12} QR { 1, 2, 4,5,10, 11} QR { 1, 3, 4, 9, 10, 12}

Euler’s Criterion can find the solution to x2 ≡ a (mod n).

True False

Find the solution of x^2≡ 2 mod 11 has a solution.

True False

ᶲ(37)=

24 22 13 36

What is the period of 7m mod 19?

2 3 4 5

How many primitive roots does Z<19> have?

5 8 7 6

gcd( 18,300) =

4 12 8 6

Equations have either no solution or exactly three incongruent solutions.

True

False

Find the solution of x^2≡ 2 mod 11.

No Solution

x ≡ 9 mod 11

x ≡ 4 mod 11

x ≡ 4 mod 11 and x ≡ 7 mod 11

Find the solution of x2≡ 16 mod 23.

x = 6 and 17

x = 4 and 19

x = 11 and 12

x = 7 and 16

Find the solution of x^2≡3 mod 23.

x≡±16 mod 23

x≡±13 mod 23

x≡±22 mod 23

x≡±7 mod 23

What is the period of 11 (mod 19).

Find the solution of x^2≡ 3 mod 11.

x ≡ -9 mod 11 and x≡ 9 mod 11

x ≡ 9 mod 11

No Solution

x ≡ 5 mod 11 and x ≡ 6 mod 11

Quiz/Test Summary

Title: More Number Theory: Higher Arithmetic in Cryptography

Questions: 15

Contributed by:

james Wed, Apr 06, 2022 07:54 AM UTC

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