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ADVISER ASST. PROF. BHICHATE CHIEWTHANAKUL DR. WATIS LEELAPATRA

188499 COMPUTER ENGINEERING PROJECT COE2013-06. Ciphertext Compressed Scheme for a Cryptosystem via an Elliptic Curve over A Field of Characteristic Two. DEVELOPERS POONPUEM THAMMACHAI ID 533040461 - 9 NATWARANTORN LILAPONGGAMPANART ID 533040699 - 6. ADVISER

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ADVISER ASST. PROF. BHICHATE CHIEWTHANAKUL DR. WATIS LEELAPATRA

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  1. 188499 COMPUTER ENGINEERING PROJECT COE2013-06 Ciphertext Compressed Scheme for a Cryptosystem via an Elliptic Curve over A Field of Characteristic Two DEVELOPERS POONPUEM THAMMACHAI ID 533040461 - 9 NATWARANTORN LILAPONGGAMPANART ID 533040699 - 6 ADVISER ASST. PROF. BHICHATE CHIEWTHANAKUL DR. WATIS LEELAPATRA MARCH 4 TH 2014

  2. 1 CONTENTS ♦ MOTIVATIONS ♦ Plan ♦TOOLS AND Relevant Theories ♦Design AND development ♦TESTS AND RESULTS ♦Performances measurement ♦CONCLUSION

  3. 2 MOTIVATIONS ♦ Continuous project coe2012-14 ♦ fix expansion problem ♦ less bandwidth

  4. 3 Planning ♦ STUDY RELEVANT THEORIES ♦ Polynomial Rings and Elliptic curve ♦ Elgamal public key ♦ Ciphertext compression ,,,over a field of characteristic two ♦ Design ♦ Develop and Test ♦ RESULTS ANALYSIS

  5. 4 TOOLS ♦ SAGE (System for Algebra and Geometry Experimentation) ♦ PYTHON

  6. 5 theory What why is an elliptic curve?

  7. 6 theory

  8. 7 theory Advantages of elliptic curve ♦ uses calculus theorem solve problem ♦ various support tools ♦ tiny key (compare with rsa) From http://www.tech.uh.edu/isgrin/project/ELET6318/Turnbull.html

  9. 8 theory What is a galois field? What is an elgamol?

  10. 9 theory PICK A LARGE PRIME NUMBER RANDOM INTEGER ON FIELD DECRYPTION INSECURE CHANNEL สร้างกุญแจสาธารณะและกุญแจส่วนบุคคล • GENERATE • PUBLIC KEY • - SECRET KEY ENCRYPTION

  11. 10 theory C1 Encryption MESSAGE C2 ♦ Elgamol encryption diagram

  12. 11 theory C1 (X1,Y1) Encryption MESSAGE C2 (X2,Y2) Asymmetric Scheme by an elliptic curve over a field of characteristic two diagram

  13. 12 DESIGN - GENERATE ELLIPTIC CURVE - RANDOM A POINT FROM ELLIPTIC CURVE DECRYPTION • GENERATE • PUBLIC KEY • - SECRET KEY EXPANSION INSECURE CHANNEL ENCRYPTION COMPRESSION ♦ CIPHERTEXT COMPRESSion DIAGRAM

  14. 13 DESIGN COMPRESSION EXPANSION INSECURE CHANNEL X1 2 bits number X2, 2 bits number C1 C2 (X1,Y1) (X2,Y2) FIND Y1,Y2 VALUE X1 2 bits number X2, 2 bits number C2 C1 (X2,Y2) (X1,Y1) ♦ CIPHERTEXT COMPRESSionAnD EXPANSION DIAGRAM

  15. 14 TESTING • 2 Types of testing? • - ACCURACY TEST • - EFFICIENCY TEST

  16. 15 ACCURACY TEST FIGURE 1.1 SHOW PLAINTEXT BEFORE ENCRYTED AND COMPRESSED FIGURE 1.2 SHOW PLAINTEXT AFTER EXPANDED AND DECRYPTED

  17. 16 efficiency TEST 3 TESTINGS

  18. 17 efficiency TEST RELEVANT FUNCTIONS dumps( ) convert ciphertext to machine code LEN( ) count amount of characters in machine code

  19. 18 1st TESTING given NEW Elliptic curve public key private key primitive rooT plaintext

  20. 19 1st TESTING TABLE 1.1 SHOW TESTING RESULT OF 1nd TESTING

  21. 20 2ND TESTING given Elliptic curve from 1st test public key from 1sttest private key from 1sttest primitive rooTfrom 1sttest plaintextNEW CREATED

  22. 21 2ND TESTING TABLE 1.2 SHOW TESTING RESULT OF 2nd TESTING

  23. 22 3RD TESTING given Elliptic curve NEW CREATED public key NEW CREATED private key NEW CREATED primitive rooTNEW CREATED pLAINTEXTNEW CREATED

  24. 23 3RD TESTING TABLE 1.3 SHOW TESTING RESULT OF 3nd TESTING

  25. 24 RESULT 1st TESTING VS. 2nd TESTING RATIO ≈ 0.5 1stTESTING VS. 3RdTESTING RATIO ≈ 0.5

  26. 25 RESULT 50% CIPHERTEXT SIZE DECREASED BY

  27. 26 conclusion - decrease ciphertextsize by 50% - combined with cryptosystem and digital signature algorithm helps increase performances

  28. 27 question please feel free to ask

  29. thank you for your attentions

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