QUESTION 1 If modular n = 74, e = 5, what is the multiplicative inverse of...
if modular n = 137, e = 100, what is the additive inverse of e? if modular n = 74, e =5, what is the multiplicative inverse of e?
QUESTION 7 If modular n = 137, e = 100, what is the additive Inverse of
5. Suppose n > 0 Show that if ā is the (multiplicative) inverse of a modulo n then erpn(а)-erph (a). (Hint. Consider ākak-Ga)k-1k-1 (mod n)) 5. Suppose n > 0 Show that if ā is the (multiplicative) inverse of a modulo n then erpn(а)-erph (a). (Hint. Consider ākak-Ga)k-1k-1 (mod n))
If n = 456917 and p and q are its two factors, find the multiplicative inverse of 101 mod n-p-q.
(b) Uniqueness of multiplicative inverse. Prove: If y E R is any real number with the property that ry 1 and yx1 for all E R with 0, then y 1/x
Find the multiplicative inverse of [x + 1] in Q[x]/(x4 + x + 1) Format BIU ...
a. b. c. What does the ciphertext ONL decode to with the modular inverse matrix from Question b? d. We use an encoded text using a Caesar cipher. The ciphertext was intercepted which is: THUBYLDH. What is the word? How did you work this out? Encode the uppercase letters of the English alphabet as A-0, B-1, C-2 and so on. Encrypt the word BUG with the block cipher matrix 16 4 11] 10 3 2 using modulo arithmetic with modulus...
6.12. For the affine cipher in Chapter 1 the multiplicative inverse of an element modulo 26 can be found as aamod 26. Derive this relationship by using Euler's Theorem.
A. Find the multiplicative inverse of 52 mod 77. Your answer should be an integer s in the range from 0 through 76. Check your solution by verifying that 52s mod n = 1. Show that for all integers a, b, and c, if aſb and alc, then a-|bc.
5. Let Zli_ {a + bi l a,b E Z. i2--1} be the Gaussian integers. Define a function for all a bi E Zi]. We call N the norm (a) Prove that N is multiplicative. This is, prove that for all a bi, c+di E Z[i] (b) Prove that if a + r є z[i] is a unit of Zli], then Ma + bi)-1. (c) Find all of the units in Zli 5. Let Zli_ {a + bi l a,b...