Cryptographic protocols for digital authentication and privacy

References (256)

1. 5.2 Operation of our Scheme . . . . . . . . . . . . . . . . . . . . . . . .
2. 5.3 Additional Properties . . . . . . . . . . . . . . . . . . . . . . . . . .
3. 6 Formal Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Anonymity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. 6.2 Soundness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. 7 Instantiation with the CFS scheme . . . . . . . . . . . . . . . . . . . . . . 5.7.1 CFS Distinguishability and Security . . . . . . . . . . . . . . . . . .
6. 7.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapitre 6 : Stade TA4 -Signature de groupe en métrique Rang . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Background on Rank metric and Cryptography . . . . . . . . . . . . . . .
9. 2.1 Rank Metric Codes . . . . . . . . . . . . . . . . . . . . . . . . . . .
10. 2.2 Rank-Based Cryptography . . . . . . . . . . . . . . . . . . . . . . .
11. 2.3 LRPC related cryptosystems . . . . . . . . . . . . . . . . . . . . . .
12. 3 Definition and Security Model . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13. 3.2 Security Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14. 4 Rank Concatenated Stern's protocol . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Problematic and Overview of our protocol . . . . . . . . . . . . . .
15. 4.2 Rank Concatenated Stern's protocol (RCSP) . . . . . . . . . . . .
16. 5 Our Rank-Based Group Signature Scheme . . . . . . . . . . . . . . . . . .
17. 5.1 High Level Overview of our scheme . . . . . . . . . . . . . . . . . .
18. 5.2 Algorithms KeyGen, Join and Sign . . . . . . . . . . . . . . . . . . .
19. 5.3 Algorithms Verif and Open . . . . . . . . . . . . . . . . . . . . . . .
20. 6 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21. 7 Instantiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22. 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entrée : Un profil Ω = (w 1 , w 2 , . . . , w n ).
23. S envoie un challenge c et salt à U.
24. U doit re-générer sk pour prouver sa connaissance du secret associé à pk • Il calcule sk = KDF(w 1 , w 2 . . . w n salt).
25. • Il génère pk ← authGen(sk ).
26. • Il génère π = authProve(sk, pk; c ).
27. Sa vérifie que authVerif(π , pk) = 1. Il rejette l'authentification sinon. Chapitre 4 : Stade TA3 -FEs réutilisables et adaptatifs. Instanciation pour la différence d'ensembles. Chapitre 4 : Stade TA3 -FEs réutilisables et adaptatifs. Instanciation pour la différence d'ensembles.
28. Contents 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29. 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30. 2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.2.2 On code-based theory . . . . . . . . . . . . . . . . . . . . . . . 153
31. 3 Cryptographic Primitives Revisited . . . . . . . . . . . . . . .
32. 3.1 A variation on Stern's Protocol: Concatenated Stern's protocol 155 5.3.2 Testable weak Zero Knowledge . . . . . . . . . . . . . . . . . . 156 5.3.3 From CSP to Testable weak Zero Knowledge Proofs . . . . . . 159 5.3.4 Security of the Concatenated Stern's protocol . . . . . . . . . . 161
33. 4 Definition and Security Model . . . . . . . . . . . . . . . . . . .
34. 4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 5.4.2 Security Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
35. 5 Our Code-Based Group Signature . . . . . . . . . . . . . . . .
36. 5.1 High Level Overview . . . . . . . . . . . . . . . . . . . . . . . . 168 5.5.2 Operation of our Scheme . . . . . . . . . . . . . . . . . . . . . 169 5.5.3 Additional Properties . . . . . . . . . . . . . . . . . . . . . . . 172
37. 6 Formal Security Analysis . . . . . . . . . . . . . . . . . . . . . .
38. 6.1 Anonymity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 5.6.2 Soundness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
39. 7 Instantiation with the CFS scheme . . . . . . . . . . . . . . . .
40. 7.1 CFS Distinguishability and Security . . . . . . . . . . . . . . . 177 5.7.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
41. 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42. According to λ, generate: 1.1. a RSD instance rsd = (H s , s, ω s ): -H s a trapdoor matrix; -sk s its related secret key.
43. 2. a R-PKC instance: -H c the public matrix key; -sk c its related secret key.
44. 3. two random matrices A and B and an integer ω.
45. gmsk := sk s , skO := (sk c , tr = [ ]).
46. Return (gpk, gmsk, skO).
47. Join(U i , gmsk = sk s , gpk)
48. Use the trapdoor sk s on H s to output y i solving rsd.
49. For l = 1 . . . l λ 2.1. Set c 1 , c 2 , c 3 , d 1 , d 2 , d 3 according to Figure 3, step 1.
50. ch := H λ (m, cmt, r, c) ∈ 2 lλ .
51. For i = 1 . . . l λ Generate rsp[l] according to ch[l] and Figure 3, step 3.
52. Set Π = (cmt, ch, resp).
53. Return σ = (Π, (r, c)).
54. Figure 6.5: KeyGen, Join, Sign algorithms signature along with c. The result r -A.x must be equal to some tr[i], from which the signer's identity is learnt. These two algorithms appear in Figure 6.6. (a) Verif(gpk, m, σ)
55. Parse Π = (cmt, ch, rsp)
56. ch * := H λ (m, cmt, r, c) ∈ 2 l λ . If ( ch = ch), Return 0.
57. For l = 1 . . . l λ 3.1. Check rsp[l] according to cmt[l], ch[l] and Figure 3.
58. 2. If a verification fails, Return 0.
59. Return 1. (b) Open(skO, gpk, m, σ)
60. If (Verif(gpk, m, σ) = 0) Return ⊥.
61. Parse skO = (sk c , tr).
62. Set z = r -Ax
63. For i = 1 . . . N If (tr[i] = z) Return U i .
64. Return ⊥. Figure 6.6: Verif and Open algorithms
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