The University of Sydney
MATH2988 Number Theory and Cryptography (Adv)
(http:/www.maths.usyd.edu.au/u/UG/IM/MATH2988/)
Semester 2, 2013
Lecturer: A.Fish
Extra Solutions 10
6.
It was shown in Exercise 5 of Tutorial 2 that if 2n + 1 is prime then n must be
Chapter 8 Notes
Public Key cryptography: The basic idea is to do away with the necessity of a secure key
exchange, which is necessary for all private key encryption schemes. The idea is as
follows:
1) Bob creates two keys, a public key, E and a private ke
Some classical cryptography
MATH2068/2988 Number Theory & Cryptography
Week 3 Lecture 1
University of Sydney
NSW 2006
Australia
August 11th 2014
Why do we study classical cryptography?
Our main objective in cryptography is to understand
the RSA and Elgama
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of Sydney
Some more classical cryptography
MATH2068 Number Theory & Cryptography
Week 3 Lecture 2
University of Sydney
NSW 2006
Australia
August 12th 2014
Afne ciphers
Recall that a translation cipher is a substitution cipher of the
form i
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of Sydney
The Rivest-Shamir-Adleman Cryptosystem
MATH2068 Number Theory & Cryptography
Week 6 Lecture 3
University of Sydney
NSW 2006
Australia
3rd September 2014
Number theory prerequisites
Proposition: Let e, m Z with gcd(e, m)=1. Then e
The University of Sydney
MATH2068/2988 Number Theory and Cryptography
(http:/www.maths.usyd.edu.au/u/UG/IM/MATH2068/)
Semester 2, 2014
Lecturer: A. Fish
Computer Tutorial 1
The purpose of this introductory computer tutorial is to introduce you to MAGMA. S
2
these by starting at 1 and repeatedly multiply by 14 and reduce modulo 101. We get
1, 14, 95, 17, 36, 100, 87, 6, 84, 65.
The University of Sydney
MATH2068/2988 Number Theory and Cryptography
(http:/www.maths.usyd.edu.au/u/UG/IM/MATH2068/)
Semester 2, 2
2
and this is the rst component of the ciphertext. Next we must compute the
scrambling multiplier, which is the residue of 28 modulo 47. We have that
28 = 162 = 256 21 (mod 47)
and so we must multiply each term of the plaintext by 21. We nd that
21 12 = 2
The University of Sydney
MATH2068/2988 Number Theory and Cryptography
(http:/www.maths.usyd.edu.au/u/UG/IM/MATH2068/)
Semester 2, 2013
Lecturer: A.Fish
Tutorial 12
1.
In this exercise we use residue arithmetic modulo the prime 941.
(i)
As we shall see in
2
Assuming that the above table is correct, evaluate 3470 (reduced mod 941)
without using your calculator. [Is 97 a square root of 1?]
The University of Sydney
MATH2068/2988 Number Theory and Cryptography
(iii) Find all the solutions of y4 1 (mod 941).
(h
The University of Sydney
MATH2068/2988 Number Theory and Cryptography
(http:/www.maths.usyd.edu.au/u/UG/IM/MATH2068/)
Semester 2, 2014
Lecturer: A. Fish
Computer Tutorial 2
Start MAGMA. Note that it automatically loads a le called MagmaProcedures.txt (spe
The University of Sydney
School of Mathematics and Statistics
Solutions to Tutorial 9 (Week 11)
MATH2068/2988: Number Theory and Cryptography
Semester 2, 2016
Web Page: http:/www.maths.usyd.edu.au/u/UG/IM/MATH2068/
Lecturer: Anthony Henderson
Tutorial Exe
Last login: Tue Oct 18 23:47:26 on ttys000
vlan-2661-10-16-250-209:~ liangfengyi$ /Applications/Magma/magma ; exit;
Magma V2.19-8 (STUDENT) Wed Oct 19 2016 15:46:20 [Seed = 1560543116]
Type ? for help. Type <Ctrl>-D to quit.
> ChangeDirectory("MATH2068")