what engineers don't know (but probably mathematicians do)
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Engineers can improve the performance and efficiency of cryptographic applications by applying mathematical solutions, transformations, and tricks. For example, fast exponentiation algorithms and loop unrolling optimizations can help with the computationally intensive task of using large prime numbers in public-key cryptography. While hardware constraints of some devices pose challenges, mathematicians provide approaches like these that engineers can implement to better secure systems and products.
![engineers
create
products
[sorry, pictures deleted - unknown ipr]](https://image.slidesharecdn.com/engineer-need-mathuploaded-090724174125-phpapp01/85/what-engineers-don-t-know-but-probably-mathematicians-do-2-320.jpg)
![sometimes inefficient
• Longer time to boot or process stuff
• Only work for toy problems
• Even, … they just don’t work at all
• [failed products?]](https://image.slidesharecdn.com/engineer-need-mathuploaded-090724174125-phpapp01/85/what-engineers-don-t-know-but-probably-mathematicians-do-4-320.jpg)
![[taken from a product somewhere]
There are 3 kinds of people
in this world:
– Those who can count and
– those who can’t](https://image.slidesharecdn.com/engineer-need-mathuploaded-090724174125-phpapp01/85/what-engineers-don-t-know-but-probably-mathematicians-do-5-320.jpg)
![Large (512-bit) numbers
• n = 81 5a d0 b9 0a ac 9f 4c da cc 57 6e ca a7
6a c3 46 92 a7 81 68 ec 08 ec 77 dd 40 c2 ec
97 52 cb 3b 34 2c b6 a6 e2 76 3a ed 42 84 fa
55 ac 0d 6c 10 39 a2 7e a3 09 be 40 35 38 04
7d 06 43 1f 6f
• e = 29 40 70 02 50 db 19 6b b1 f4 8a a7 b4 59
6c 4b 66 b5 94 f6 15 ae e4 69 44 95 23 f3 d0
fc ea 84 19 7c 55 e0 27 40 2d 19 18 15 08 05
51 ac f5 98 91 f0 98 5f c4 17 05 eb 3b e8 a3
04 32 d4 20 2f
• d = 59 f1 2f 29 73 d0 bc 8e 13 6e 2a 21 53 2c
b7 4d 69 82 c9 54 92 6c 64 43 0d 69 15 83 e9
44 a6 de 5e 30 e9 ae 48 f9 c8 84 a4 16 44 4d
df 50 f2 0e 96 3e 24 df a4 f4 ec 3d c6 db 61
a7 e6 dc ea cf
[64 chunks]](https://image.slidesharecdn.com/engineer-need-mathuploaded-090724174125-phpapp01/85/what-engineers-don-t-know-but-probably-mathematicians-do-8-320.jpg)
what engineers don't know (but probably mathematicians do)
- 1. what engineers don’t know (but mathematicians probably do) Budi Rahardjo School of Electical Engineering & Informatics Institut Teknologi Bandung
- 2. engineers create products [sorry, pictures deleted - unknown ipr]
- 4. sometimes inefficient • Longer time to boot or process stuff • Only work for toy problems • Even, … they just don’t work at all • [failed products?]
- 5. [taken from a product somewhere] There are 3 kinds of people in this world: – Those who can count and – those who can’t
- 6. Need ways to improve • Increase performance • Less power • Smaller in size • Cost efficiency • Always, not easy
- 7. Example • Cryptographic applications, eg. public-key cryptography c= me mod n • With large e and n (big num) integer • Straight forward software implementation is difficult
- 8. Large (512-bit) numbers • n = 81 5a d0 b9 0a ac 9f 4c da cc 57 6e ca a7 6a c3 46 92 a7 81 68 ec 08 ec 77 dd 40 c2 ec 97 52 cb 3b 34 2c b6 a6 e2 76 3a ed 42 84 fa 55 ac 0d 6c 10 39 a2 7e a3 09 be 40 35 38 04 7d 06 43 1f 6f • e = 29 40 70 02 50 db 19 6b b1 f4 8a a7 b4 59 6c 4b 66 b5 94 f6 15 ae e4 69 44 95 23 f3 d0 fc ea 84 19 7c 55 e0 27 40 2d 19 18 15 08 05 51 ac f5 98 91 f0 98 5f c4 17 05 eb 3b e8 a3 04 32 d4 20 2f • d = 59 f1 2f 29 73 d0 bc 8e 13 6e 2a 21 53 2c b7 4d 69 82 c9 54 92 6c 64 43 0d 69 15 83 e9 44 a6 de 5e 30 e9 ae 48 f9 c8 84 a4 16 44 4d df 50 f2 0e 96 3e 24 df a4 f4 ec 3d c6 db 61 a7 e6 dc ea cf [64 chunks]
- 9. Solutions, transformations, tricks, … Mathematics Programming • Fast • Loop unrolling exponentiation •… •…
- 11. Loop Unrolling for (int x = 0; x < 100; x++) { do(x);} /* before loop unroll */ for (int x = 0; x < 100; x += 5) { do(x); do(x+1); do(x+2); do(x+3); do(x+4);} /* after - less loops */
- 12. hardware • Implementation in constrained devices – Limitted memory & computing power
- 13. a short detour to crypto
- 14. Private-key crypto (secret key, symmetric) Alice Bob Shared (secret) key Encryption Decryption Plaintext Ciphertext Plaintext My phone Y$3*@8nh My phone 555-1234 klq&ajbq 555-1234 Ev e
- 15. Problems • Key exchange • Number of keys explode exponentially
- 16. n n * (n-1) / 2 ≈ n2/2 (# users) (# of keys) 10 50 100 5000 1000 500.000 10.000 50.000.000 100.000 5.000.000.000
- 17. New direction in cryptography
- 18. Public-key crypto (asymmetric) Public key repository Public key Certificate Authority (CA) Private key Encryption Decryption Plaintext Ciphertext Plaintext My phone L)8*@Hgx My phone 555-1234 uqnrpGtZ 555-1234
- 19. Concluding Remarks … engineers taketh what mathematicians giveth …
- 20. Thank You