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1 Cryptographic Hash Function EDON-R Presented by Prof. Danilo Gligoroski Department of Telematics Faculty of Information Technology, Mathematics and Electrical Engineering Norwegian University of Science and TechnologyTechnology - NTNU,

  1. 1 Cryptographic Hash Function EDON-R Presented by Prof. Danilo Gligoroski Department of Telematics Faculty of Information Technology, Mathematics and Electrical Engineering Norwegian University of Science and TechnologyTechnology - NTNU, NORWAY 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  2. 2 Outline Short history of EDON-R Specific design characteristics Known attacks on EDON-R Are there any one-way bijections embedded in EDON-R? SW/HW performance and memory requirements 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  3. 3 Short history of EDON-R • Theoretical principles of EDON-R were described at the Second NIST Hash Workshop – 2006 in the presentation: Edon-R Family of Cryptographic Hash Functions – No concrete realization 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  4. 4 Short history of EDON-R • Theoretical principles of EDON-R were described at the Second NIST Hash Workshop – 2006 in the presentation: Edon-R Family of Cryptographic Hash Functions – No concrete realization • First implementation of Edon- R (256, 384, 512) published at http://eprint.iacr.org/2007/154 – Big acknowledgement for Søren Steffen Thomsen, giving me comments about zero being a fixed point in that realization 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  5. 5 Short history of EDON-R • Additionally, the following contributors joined the EDON-R (SHA-3) team: – Rune Steinsmo Ødegård – Investigating the mathematical properties of defined quasigroups – Marija Mihova – Investigating the differential properties in EDON-R operations – Svein Johan Knapskog (general comments and suggestions for improvements, proofreading) – Ljupco Kocarev (general comments and suggestions for improvements, proofreading) – Aleš Drápal (Theory of quasigroups and suggestions for improvements) – Vlastimil Klima (cryptanalysis and suggestions for improvements) 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  6. 6 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  7. 7 Specific design characteristics for EDON-R Concatenation of at least 65 bits (Merkle-Damgård strenghtening) 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  8. 8 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  9. 9 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  10. 10 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  11. 11 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  12. 12 Specific design characteristics for EDON-R Function is defined by quasigroup operations 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  13. 13 Specific design characteristics for EDON-R Quasigroup operations are defined on 256-bit or 512-bit operands. 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  14. 14 Specific design characteristics for EDON-R Quasigroup operations are defined on 256-bit or 512-bit operands. (X 0 , X 1 , …, X 7 ) (Y 0 , Y 1 , …, Y 7 ) 32-bit or 64-bit variables 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  15. 15 Specific design characteristics for EDON-R Quasigroup operations are defined on 256-bit or 512-bit operands. (X 0 , X 1 , …, X 7 ) (Y 0 , Y 1 , …, Y 7 ) 32-bit or 64-bit variables Operations: 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  16. 16 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  17. 17 Specific design characteristics for EDON-R Simple re-indexing (no computational costs) 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  18. 18 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  19. 19 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  20. 20 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  21. 21 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  22. 22 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  23. 23 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  24. 24 Specific design characteristics for EDON-R Rotations differ from each other for at least 2 positions. 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  25. 25 Specific design characteristics for EDON-R Two orthogonal Latin Squares of order 8 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  26. 26 Specific design characteristics for EDON-R Two orthogonal Latin Squares of order 8 Four corresponding nonsingular in (Z 2 , +, x ) matrices. 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  27. 27 Specific design characteristics for EDON-R Four nonsingular in (Z 2 , +, x ) matrices. 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  28. 28 Specific design characteristics for EDON-R Four nonsingular in (Z 2 , +, x ) matrices. Two diffusion (bi-stochastic) matrices 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  29. 29 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  30. 30 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  31. 31 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  32. 32 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  33. 33 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  34. 34 Specific design characteristics for EDON-R 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  35. 35 Specific design characteristics for EDON-R Theorem 3: 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  36. 36 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  37. 37 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  38. 38 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  39. 39 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  40. 40 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  41. 41 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

  42. 42 Specific design characteristics for EDON-R EDON-R is provably resistant against differential cryptanalysis 25-28 Feb 2009, Leuven, Belgium, The First SHA-3 Candidate Conference, Cryptographic Hash Function EDON-R

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