use algorithm modular exponentiation to find 11^644 mod 645

Expert Solution

Colby Messinger answered 1 year ago

2. (16 pts) Use binary modular exponentiation to find 45 mod 84. (Use either table approach...

2. (16 pts) Use binary modular exponentiation to find 45 mod 84. (Use either table approach taught in slides or the pseudocode algorithm.) 3. (20 pts) Use the Euclidean Algorithm to find the greatest common divisor of the integers

Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11

1. Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11 2. Use the...

1. Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11 2. Use the max function to calculate max3(x, y, z) if x = 2, y = 6, z = 5. Show your work!

Use Recursive Algorithm to compute 5^23 Mod 8

a) Use Fermat’s little theorem to compute 52003 mod 7, 52003 mod 11, and 52003 mod 13.

a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13. b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod 1001. (Note that1001 = 7 ⋅ 11 ⋅ 13.)

We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this...

We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this algorithm to compute the following values. Show all of the steps involved. 9570-1(mod 12935) 550-1 (mod 1769)

use ELGMAL algorithm. let p = 11. find a generator number for p in case of...

use ELGMAL algorithm. let p = 11. find a generator number for p in case of elgmal algorithm. alice selects an integer number x = 5. calculate public and private key for alice in elgmal algorithm. alice wants to send plaintext "AGE" to Bob. assume that Alice selects random k values as 6, 4, 7 respectively for encryption. what is the ciphertext???

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19) 2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20. 3. Find the order of the element 5 in (z/7z)

Write a program(Java) to compute modular exponentiation: take g (base), e (exponent), and, N (modulas) as...

Write a program(Java) to compute modular exponentiation: take g (base), e (exponent), and, N (modulas) as input from the user and output the result. Use an online compiler. Do not use the inbuilt functions to compute this. Also, try to make the program as efficient as possible. In particular, please implement the square and multiply algorithm discussed in the class. 

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at...

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at least one successive squaring in detail, and at least one instance of the Chinese Remainder Theorem.

Question