Answered: b.Given Bob's public key of (85, 7) and…

b.Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=5 to send to Bob. Show the ciphertext.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Question

a. Given p=17, q=7, and e=11, generate the public key (n,e) and the private key (n,d) using RSA Key generation algorithm.

b.Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=5 to send to Bob. Show the ciphertext.

c.Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertetx y=6 received from Alice. Show the plaintext.

d.Using the fast exponentiation method (page 182), determine 430 mod 47. Show your work.

Square-and-Multiply for Modular Exponentiation
Input:
base element x
exponent H = E-o h;2' with h; E 0,1 and h; = 1
and modulus n
„H
Output: x" mod n
Initialization: r=x
Algorithm:
1
FOR i =t – 1 DOWNTO 0
r= r² mod n
1.1
IF h; = 1
1.2
r=r•x mod n
RETURN (r)

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