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Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks Benoit Cogliati Yevgeniy Dodis Jonathan Katz Jooyoung Lee John Steinberger John Steinberger Aishwarya Thiruvengadam Aishwarya Thiruvengadam Zhe Zhang

  1. Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks Benoit Cogliati Yevgeniy Dodis Jonathan Katz Jooyoung Lee John Steinberger John Steinberger Aishwarya Thiruvengadam Aishwarya Thiruvengadam Zhe Zhang Zhe Zhang 1

  2. Block Ciphers • Building block for many cryptographic constructions • Hash functions Hash functions • Encryption schemes • Message authentication codes • Keyed permutations • Popular Design Paradigms • Feistel Networks • Feistel Networks • Substitution-Permutation Networks 2

  3. Block Ciphers: Designs • Popular Design Paradigms • Feistel Network Feistel Network • Eg: DES • Substitution-Permutation Network (SPN) • Eg: AES

  4. Block Ciphers: Designs • Popular Design Paradigms • Feistel Network Feistel Network • Eg: DES • Long line of work analyzing provable security of Feistel [LR88, Pat03, Pat04] • Security been studied in various security models [Pat10, HR10, HKT11, Tes14, CHKPST16] • Substitution-Permutation Network (SPN) • Substitution-Permutation Network (SPN) • Eg: AES • In contrast, provable security of SPNs not as well-studied

  5. Related Work

  6. Related Work

  7. Substitution-Permutation Network (SPN)

  8. Substitution-Permutation Network (SPN) . . .

  9. Substitution-Permutation Network (SPN) . . .

  10. Substitution-Permutation Network (SPN)

  11. Substitution-Permutation Network (SPN) . . .

  12. Substitution-Permutation Networks Substitution- Permutation step

  13. Security of SPNs

  14. Security of SPNs 14

  15. Security of SPNs 15

  16. Security of SPNs 16

  17. Security of SPNs • Ideal World • Real World 17

  18. Categorizing SPNs Linear function

  19. Categorizing SPNs

  20. Categorizing SPNs Non-linear function

  21. Results: Linear SPNs

  22. Results: Non-linear SPNs

  23. Interpreting our Results

  24. Interpreting our Results

  25. Results

  26. Constructing Non-linear SPNs

  27. Constructing Non-linear SPNs: Blockwise Universal Permutations

  28. Constructing Non-linear SPNs: Blockwise Universal Permutations

  29. Constructing Non-linear SPNs: Blockwise Universal Permutations

  30. Non-linear SPNs via Blockwise Universal Permutations . . .

  31. Non-linear SPNs via Blockwise Universal Permutations . . .

  32. Non-linear SPNs via Blockwise Universal Permutations

  33. Results

  34. Security of 3-round linear SPN

  35. Security of 3-round Linear SPNs

  36. Results

  37. Takeaway

  38. Thank You

  39. Constructing Non-linear SPNs

  40. SPNs: Applications 1-round SPN

  41. Constructing Non-linear SPNs: Blockwise Universal Permutations

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