Cryptographic teaching tools Presented by: Suan Khai Chong Supervisor: Assoc. Prof. Graham Farr Second Reader: Dianne Hagan

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.

Cryptography Plain textOriginal Plain text Cipher text

Cryptography (cont…) A very long history… Recent emergence of public key cryptography spurred interest in it.

Public-key cryptography Alice Bob message public key private key

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.

Learning & Teaching Cryptography Success of public-key cryptosystems Growing popularity of cryptography leads to Interest in learning cryptography promotes Effective ways of teaching cryptography creates need for

General Aim Automated Cryptographic Teaching Tools As an aid to teaching and learning several public key cryptosystems NOT writing secure implementations of cryptosystems.

Correct RSA calculation N=77, e=7, p=11, q=7, c=5(Encrypted msg) Decryption Extended Euclidean algorithm d=e^(-1) mod ((p-1)(q-1)) Msg, m=c^d mod N *RSA: a public-key cryptosystem Fast modular exponentiation

Error paths in RSA exercise *RSA is a type of public-key cryptosystem Decryption key d N=77, e=7, p=11, q=7, c=5(Encrypted msg) correct path wrong path

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: a.Sound examples b.Diagnostic examples

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. Student’s answer indicates the type of mistake made.

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

RSA example generator random keys All paths Diagnostic? correct path

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. Answer: Useful!!!

Deliverables 1. Refining of existing programs to enhance structure and usability. 2. Support for additional cryptosystems. 3. Experimentation with data sets to study sound/diagnostic examples. 4. Construction of web interfaces.

Results Overview 1. System Functionalities. 2. Additional example generators. 3. Web-based interface. 4. Example probabilities table. 5. Evaluation of table results.

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

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.

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.

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.

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.

Path Select Interface

Display: Path Tree Display A visual representation of path table.

2. Additional example generators The additional generators are: Knapsack RSA signature scheme

Design considerations How is an example generator built? 1. Work out possible paths by pen and paper. 2. Determine characteristics unique to cryptosystem. 3. Implement with some code reuse.

3. Web interface Consistent input layout for all cryptosystems

Input Interface: Key Input Dialog Figure: RSA Calc. Mode Input dialog

Generated Output Web output scrollpane

4. Probabilities table N.B. Probabilities table similar for other cryptosystems

Evaluation of probabilities It is hard to generate examples that are diagnostic. Probabilities of sound/diagnostic examples increase as input size increases.

Demonstration Looking at everything we have talked about… Main website:

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).

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.

Q & A Any Questions?