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## Cryptographic teaching tools

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### It is difficult to construct exercises by hand with the following properties: Sound examples ... Experimentation with data sets to study sound/diagnostic examples. ... – PowerPoint PPT presentation

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Title: Cryptographic teaching tools

1
Cryptographic teaching tools
• Presented by Suan Khai Chong
• Supervisor Assoc. Prof. Graham Farr

2
Background
• Need to securely transmit information between two
or more parties.
• Methods have been devised to meet this need.
• Cryptography is the study of these methods.

3
Cryptography
Plain text
Original Plain text
Cipher text
Cipher text
4
Cryptography (cont)
• A very long history
• Recent emergence of public key cryptography
spurred interest in it.

5
Public-key cryptography
private key
public key
message
Bob
Alice
6
Public key cryptography (cont)
• Cryptosystems which involve use of public and
private keys for encryption and decryption.
• Some types of public-key cryptosystems RSA,
Diffie Hellman and Shamir.

7
Learning Teaching Cryptography
Success of public-key cryptosystems
Growing popularity of cryptography
promotes
Interest in learning cryptography
creates need for
Effective ways of teaching cryptography
8
General Aim
Automated Cryptographic Teaching Tools
• As an aid to teaching and learning several public
key cryptosystems
• NOT writing secure implementations of
cryptosystems.

9
Correct RSA calculation
Decryption
N77, e7, p11, q7, c5(Encrypted msg)
Extended Euclidean algorithm
de(-1) mod ((p-1)(q-1))
Fast modular exponentiation
Msg, mcd mod N
RSA a public-key cryptosystem
10
Error paths in RSA exercise
N77, e7, p11, q7, c5(Encrypted msg)
Decryption key d
11
10
17
43
7
2
23
3
9
31
55
3
31
23
75
67
5
• 5

wrong path
correct path
RSA is a type of public-key cryptosystem
11
Doing exercises by hand
• An important part of learning cryptography is
doing exercises by hand. However
• It is difficult to construct exercises by hand
with the following properties
• Sound examples
• Diagnostic examples

12
Sound/Diagnostic examples
• Sound example
• Student must do the correct calculation to arrive
• Diagnostic example
• All paths give different answers.
• Students answer indicates the type of mistake

13
Existing work
• Example generators have been built by Laura Frost
and Simon Hawley (2002-3) for the following
cryptosystems
• RSA
• Diffie-Hellman
• Shamir
• ElGamal
• Chaums e-cash

14
RSA example generator
random keys
correct path
All paths
Diagnostic?
15
Project Justification
A fair question to ask would be
How useful are these example generators?
• Useful for the person constructing examples.
• Provides guidance to person doing examples.
• Statistics are helpful for researching in the
properties of
• examples.

Useful!!!
16
Deliverables
• Refining of existing programs to enhance
structure and usability.
• Experimentation with data sets to study
sound/diagnostic examples.
• Construction of web interfaces.

17
Results Overview
• System Functionalities.
• Web-based interface.
• Example probabilities table.
• Evaluation of table results.

18
1. System Functionalities
• Three main modes of operation
• Random mode
• Interactive mode
• Calculate mode

19
Main modes Random
• Generates example without tweaking parameters.
• How this works?
• Select parameters to be small enough for pen and
paper.
• Parameters must have suitable mathematical
characteristics. ( e.g. not self-inverses in RSA)
• Extra options displaying working or path tree.

20
Main modes Interactive
• Requires information from user for individual
keys.
• How this works?
• Show user appropriate inputs i.e. small with
suitable properties.
• Let user select from inputs.
• Generate example with those inputs
• Display output depending on extra options.

21
Main modes Calculate
• Functionality
• Loops over existing examples to calculate
probabilities
• Determines percentage of sound/diagnostic
examples.
• How it works ?
• User specifies parameters to be fixed or looped.
• Several examples are generated and compared.
• Program outputs example types, probabilities.

22
Display Path Selection
• Selection of paths that users want considered.
• Rationale
• Some error paths are more probable than others.
• Students become expert with parts of
cryptosystems over time.

23
Path Select Interface
24
Display Path Tree Display
• A visual representation of path table.

25
• Knapsack
• RSA signature scheme

26
Design considerations
• How is an example generator built?
• Work out possible paths by pen and paper.
• Determine characteristics unique to cryptosystem.
• Implement with some code reuse.

27
3. Web interface
Consistent input layout for all cryptosystems
28
Input Interface Key Input Dialog
Figure RSA Calc. Mode Input dialog
29
Generated Output
Web output scrollpane
30
4. Probabilities table
N.B. Probabilities table similar for other
cryptosystems
31
Evaluation of probabilities
• It is hard to generate examples that are
diagnostic.
• Probabilities of sound/diagnostic examples
increase as input size increases.

32
Demonstration
• Looking at everything we have talked about
• Main website
• http//www.csse.monash.edu.au/skcho5/

33
Discussion of results
• In short, this project contributes significantly
in the following ways
• Web interface lets users interact with the tool
easily.
• It is easy to generate examples with suitable
properties.
• Students can learn by example (steps through
en/decryption).

34
Future Work
• Project provides a basis for further work
• A generic path tree representation.
• Better visualization of output.
• Allowing output of encryption to be given to
decryption.
• A progress indicator.