Cryptography

1. Calculate 216 mod 123.

2. Calculate 314 mod 30.

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3. Use the modular exponentiation algorithm to calculate 1519 mod 37.

4. Find gcd(143, 227), gcd(8, 182), gcd(125, 87) using Euclidean method.

5. Find the values of x2 and y2 from the given values (a, b) = (8, 182) by using extended Euclidean algorithm.

1. Find the value of x2 and y2 from the given values (a, b) = (16, 10374) by using extended Euclidean algorithm.

2. Find the x value for the equation x2 ≡ 1 (mod 35) using CRT.

3. Find the x value for the system of congruences.

x ≡34 mod

x ≡25 mod

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