>
>
Math 470/501 Spring 2011
Exam 1
Hand work ONLY
Name:
UIN:
#1.
A Linear Feedback Shift Register with initialization vector
00100 and
recursion
mod 2
is used to encrypt a binary string.
The encrypted string is
011010001110.
Find the plaintext.
We compute the encryption string:
001001
010010
100100
001001
010010
100100
001001
The 12 digit encryption string is 001001001001, the initial vector and 7 more bits
constructed down the right hand side.
We XOR that with the crypttext
011010001110
001001001001
to get the plaintext:
010011000111.
#2.
When asked to raise 65535 to the 65536000007th power mod the prime
65537, Joe Ag grabs a copy of Maple and writes "65535^65536000007 mod
65537;"
but Maple replies
Error, numeric exception: overflow
.
a)
What
went wrong, and how should the command be modified to make it work?
b)
The correct answer is 65409.
Compute that result by hand, justifying each step.
Maple does, indeed, give that response.
65535^65536000007 mod 65537;
Error, numeric exception: overflow
The problem is that Maple cannot store
in memory. It is too large.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
(2.1)
>
>
>
>
(2.2)
We modify the command using the inert operator & so that the mod is performed
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Cryptography, Encryption, Primitive root modulo n

Click to edit the document details