Q. In Zp* with (p-1) elements exactly:

(p – 1)/2 elements are QR and
(p – 1)/2 elements are QNR.

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Q. Find the set of quadratic residues in the set –

Z13* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12}

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

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Q. Find the solution of x2≡ 16 mod 23

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Q. Find the solution of x^2 ≡ 3 mod 23

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Q. Find the solution of x^2 ≡ 7 mod 19

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Q. “If we use exponentiation to encrypt/decrypt, the adversary can use logarithm to attack and this method is very efficient. “

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Q. Find the order of the group G = <Z12*, ×>?

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Q. Find the order of the group G = <Z21*, ×>?

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Q. Find the order of group G= <Z20*, x>

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Q. Find the order of group G= <Z7*, x>

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Q. “In the group G = <Zn*, ×>, when the order of an element is the same as order of the group (i.e. f(n)), that element is called the Non – primitive root of the group.”

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Q. In the order of group G= <Z20*, x>, what is the order of element 17?

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Q. 1 2 3 4 5 6 7 order7. The order of group G= <Z9, x> , primitive roots of the group are –

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Q. Which among the following values: 17, 20, 38, and 50, does not have primitive roots in the group G = <Zn*, ×>?

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Q. Find the number of primitive roots of G=<Z11*, x>?

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Q. Find the primitive roots of G=<Z11*, x>?.

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Q. “If a group has primitive roots, it is a cyclic group”

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Q. Find the primitive roots of G = <Z10*, ×>.

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Q. “The group G = <Zp*, ×> is always cyclic.”

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