Attacks on RSA using Lattice reduction techniques (LLL) : Coppersmith and Boneh and Durfee revisited by Howgrave-Graham and Herrmann and May.

1. Lattice Reduction
Techniques To Attack
RSA
David Wong
March 2015
University of Bordeaux

6. ATTACKS

7. Attacks on the
Implementation or the
Mathematics.
•Recover the plaintext
•Recover the private key

8. A Relaxed Model
• We know a part of the message
• We know an approximation of one of
the prime
• The private exponent is too small

9. LATTICE

16. COPPERSMITH

18. « le password du jour : cupcake »

19. « le password du jour : cupcake »

21. HOWGRAVE-GRAHAM

22. HOWGRAVE-GRAHAM

24. LLL reduction:
• It only does integer linear
operations on the basis
vectors
• The shortest vector of the
output basis is bound

27. Those polynomials achieve two things:
• They have the same root 𝑥0 but modulo 𝑁 𝑚
• Each iteration introduce a new monomial

36. COPPERSMITH

37. BONEH-DURFEE

45. HOWGRAVE-GRAHAM

50. HERRMAN AND MAY:
UNRAVELLED LINEARIZATION

53. BONEH-DURFEE BOUND

54. CONCLUSIONS