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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
  • Second Reader Dianne Hagan

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
leads to
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
  • Wrong path leads to wrong answer.
  • Student must do the correct calculation to arrive
    at the right answer.
  • Diagnostic example
  • All paths give different answers.
  • Students answer indicates the type of mistake
    made.

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?
Answer
  • 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.
  • Support for additional cryptosystems.
  • Experimentation with data sets to study
    sound/diagnostic examples.
  • Construction of web interfaces.

17
Results Overview
  • System Functionalities.
  • Additional example generators.
  • 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
2. Additional example generators
  • The additional generators are
  • 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.
  • Support for additional generators.

35
Q A
  • Any Questions?
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