Parameters of Classic McEliece Cryptography

Post-Quantum cryptography is at the forefront of technological advancements, with the Classic McEliece cryptosystem being a notable player in this field. The presentation discusses the adaptation of Classic McEliece parameters for efficient memory usage, presented at the Institute of Cybersecurity in Occitanie on April 3, 2024 by Cyrius NUGIER. The slides cover aspects such as key sizes, encryption, decryption, and comparisons with other post-quantum cryptography schemes like Kyber, HQC, NTRU, and more.

• Cryptography
• Post-Quantum
• McEliece
• Parameters
• Key Sizes

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Presentation Transcript

1. Paramtres de Classic McEliece adapt s au calcul en m moire Demi-Journ e Cryptographie Post-Quantique Institut Cybers curit Occitanie 3 Avril 2024 Cyrius NUGIER

2. 1

3. = + 1

4. = + 1

5. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

6. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

7. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

8. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece

9. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

10. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

11. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

12. SK size PK size CT size Keygen Encrypt Decrypt Kyber SK size PK size CT size Keygen Encrypt = + Decrypt HQC SK size PK size CT size Keygen Encrypt Decrypt SK size NTRU PK size CT size Keygen Encrypt Decrypt McEliece 1

13. Central Processing Control Unit Unit Arithmetic Logical Unit Registers L1 Cache L2 / L3 Main Memory 2

14. Central Processing Control Unit Unit Arithmetic Logical Unit Registers SIMD Registers SIMD Extension L1 Cache L2 / L3 Main Memory 2

15. Bit-line ... Word-line ... ... ... L1 ... ... Cache L2 / L3 ... Column Peripheral And, Or, Xor, Not Nand, 3

16. L1 Cache 16Ko 32 Ways 4096 bits 64 Bytes 8 Banks 4

17. Central Processing Control Unit Unit Arithmetic Logical Unit Registers SK PK SIMD Registers SIMD Extension L1 Cache L2 / L3 Main Memory 5

18. Central Processing Control Unit Unit Arithmetic Logical Unit Registers SK SIMD Registers SIMD Extension PK L1 Cache L2 / L3 Main Memory 5

19. 3488 columns 1010011010 01110010 1010110 010110 768 rows 6

20. 3488 columns 10000 ... 10001010100 01000 11101111011 00100 00010011 00010 00001 768 rows 6

21. XOR AND 6

22. L1 Cache, 4096-bit parallelism 6

23. L1 Cache, 4096-bit parallelism 6

24. L1 Cache, 4096-bit parallelism 6

25. L1 Cache, 4096-bit parallelism 6

26. L1 Cache, 4096-bit parallelism 6

27. L1 Cache, 4096-bit parallelism 6

28. 32-bit RISC-V with 16KB L1 PIM cache 32-bit RISC-V 844 M total cycles 66 M total cycles 7 Classic McEliece Public Key generation - Area proportional to number of cycles

29. L1 Cache, 4096-bit parallelism A 8

30. L1 Cache, 4096-bit parallelism A B D C E 8

31. L1 Cache, 4096-bit parallelism A B D C E 8

32. L1 Cache, 4096-bit parallelism _ n - k = m x t A _n B D C E 8

33. L1 Cache, 4096-bit parallelism _ n - k = m x t B' B _n B'' 8

34. Classic McEliece Parameter Set 348864 460896 6688128 6960119 8192128 m 12 13 13 13 13 t 64 96 128 6688 119 6960 128 8192 n 3488 4608 m t n Category I III V V V 7 8 96 128 2400 4096 9

35. Classic McEliece BIKE HQC FHE ? Parameter Set 348864 460896 6688128 6960119 8192128 m 12 13 13 13 13 t 64 96 128 6688 119 6960 128 8192 n 3488 4608 m t n Category I III V V V 7 8 96 128 2400 4096 ? 9

36. = + 10

37. Paramtres de Classic McEliece adapt s au calcul en m moire Demi-Journ e Cryptographie Post-Quantique Institut Cybers curit Occitanie 3 Avril 2024 Cyrius NUGIER