1. Cryptographic teaching tools Presented by: Suan Khai Chong Supervisor: 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 textOriginal Plain text Cipher text

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

5. Public-key cryptography Alice Bob message public key private key Eve

6. Public key cryptography (cont…) Cryptosystems involving use of public and private keys for encryption and decryption. Some types of public-key cryptosystems: RSA, Diffie Hellman and Shamir. *Cryptosystem is a collection of algorithms

7. Learning & Teaching Cryptography Success of public-key cryptosystems Growing popularity of cryptography leads to Interest in learning cryptography promotes Effective ways of teaching cryptography encourages

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 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

10. Error paths in RSA exercise *RSA is a type of public-key cryptosystem 1110174372 Decryption key d N=77, e=7, p=11, q=7, c=5(Encrypted msg) 5 23393155331237567 correct path wrong path

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: a.Good examples b.Diagnostic examples

12. Good/Diagnostic examples Good example: Wrong path leads to wrong answer. Student must do correct calculation to arrive at the right answer. Diagnostic example: All paths give different answers. Student’s answer indicates the type of mistake made.

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

14. RSA example generator random keys All paths Diagnostic? correct path

15. Project Goals 1. Refine existing programs. 2. Implement example generators for other public- key cryptosystems (E.g. knapsack, elliptic curve cryptosystems, etc). 3. Experiment with data sets to study good/diagnostic examples. 4. Examine the possibility of quantifying the quality of an example. 5. Construct web interfaces.

16. Project Review Project Timeline 12 th May16 th Jun14 th Jul21 st Jul28 th Jul4 th Aug Example Generators Web Interface Testing *Implementation scheduled to take a period of 3 months

17. Summary of current work 1. Analysed existing programs. 2. Identified limitations of existing programs. 3. Identified modules that can be reused. E.g. Extended Euclidean Algorithm.

18. Summary of current work (cont…) Currently building example generators for other cryptosystems. Includes: 1. Identifying all possible paths in an exercise. (Similar to RSA paths shown earlier). 2. Building command line version of generator that could later be incorporated into the GUI.

19. The End Many Thanks to everyone for being here!