1 / 29

Rafael Pass Cornell University

Constant-round Non-malleability From Any One-way Function. Rafael Pass Cornell University. Joint work with Huijia (Rachel) Lin. Receiver. Sender. Commitment. Commitment Scheme. The “ digital analogue ” of sealed envelops. One of the most basic cryptographic tasks.

nardo
Download Presentation

Rafael Pass Cornell University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Constant-round Non-malleability From Any One-way Function Rafael PassCornell University Joint work with Huijia (Rachel) Lin

  2. Receiver Sender Commitment Commitment Scheme The “digital analogue” of sealed envelops. One of the most basic cryptographic tasks. Part of essentially all more involved secure computations Can be constructed from any one way function. [N’89, HILL’ 99] Reveal

  3. Alice Bob “Right” abstraction if:

  4. But life is:

  5. MIM Sender Receiver/Sender Receiver C(v) C(v’) Possible that v’ = v+1 Even though MIM does not know v!

  6. Non-Malleable Commitments[Dolev Dwork Naor’91] MIM Sender Receiver/Sender Receiver i j C(v) C(v’) Non-malleability: Either MIM forwards : v = v’ Orv’ is “independent” of v

  7. Non-Malleable Commitments[Dolev Dwork Naor’91] MIM Sender Receiver/Sender Receiver i j C(i,v) C(j, v’) i  j Non-malleability: ifthen, v’ is “independent” of v

  8. Non-Malleable Commitments[Dolev Dwork Naor’91] Man-in-the-middle execution: i j i j Simulation: j Non-malleability: For every MIM, there exists a “simulator”, such that value committed by MIM is indistinguishable from value committed by simulator

  9. Non-Malleable Commitments[Dolev Dwork Naor’91] i j • Important in practice • “Test-bed” for other tasks • Applications to MPC

  10. Non-malleable Commitments • Original Work by [DDN’91] • OWF • black-box techniques • But: O(log n) rounds • Main question: how many rounds do we need? With set-up solved: 1-round, OWF: [DiCreczenzo-Ishai-Ostrovsky’99,DKO,CF,FF,…,DG] Without set-up: • [Barak’02]: O(1)-round Subexp CRH + dense crypto: • [P’04,P-Rosen’05]: O(1) rounds using CRH • [Lin-P’09]: O(1)^log* n round using OWF • [P-Wee’10]: O(1) using Subexp OWF • [Wee’10]: O(log^* n) using OWF Non BB

  11. Non-malleable Commitments • Original Work by [DDN’91] • OWF • black-box techniques • But: O(log n) rounds • Main question: how many rounds do we need? With set-up solved: 1-round, OWF: [DiCreczenzo-Ishai-Ostrovsky’99,DKO,CF,FF,…,DG] Without set-up: • O(1)-round from CRH or Subexp OWF • O(log^* n) from OWF • Sd • Sd

  12. Main Theorem Thm:Assume one-way functions. Then there exists a O(1)-round non-malleable commitment with a black-box proof of security. • Note: Since commitment schemes imply OWF, we have that unconditionally that any commitments scheme can be turned into one that is O(1)-round and non-malleable. • Note: As we shall see, this also weakens assumptions for O(1)-round secure multi-party computation.

  13. DDN Protocol Idea i = 01…1 j = 00..1 C(i,v) C(j, v’) • • • • • • Bluedoes not help Red and vice versa

  14. The Idea: What if we could run the message scheduling in the head? Let us focus on non-abortingand synchronizing adversaries. (never send invalid mess in left exec)

  15. Com(id,v): id = 00101 c=C(v) I know v s.t. c=C(v) Or I have “seen” sequence WI-POK

  16. Signature Chains Consider 2 “fixed-length” signature schemes Sig0, Sig1(i.e., signatures are always of length n) with keys vk0, vk1. Def: (s,id) is a signature-chain iffor all i, si+1 is a signature of “(i,s0)”using scheme idi s0 = r s1 = Sig0(0,s0) id1 = 0 s2 = Sig0(1,s1) id2 = 0 s3 = Sig1(2,s2) id3 = 1 s4 = Sig0(3,s3) id4 = 0

  17. Signature Games You have given vk0, vk1 and you have access to signing oracles Sig0, Sig1. Let denote the access pattern to the oracle; • that is i = b if in the i’th iteraction you access oracle b. Claim: If you output a signature-chain (s,id) Then, w.h.p, id is a substring of the access pattern .

  18. Com(id,v): id = 00101 vk0 r0 Sign0(r0) vk1 r1 Sign1(r1) c=C(v) I know v s.t. c=C(v) Or I have “seen” sequence WI-POK

  19. Com(id,v): id = 00101 vk0 r0 Sign0(r0) vk1 r1 Sign1(r1) c=C(v) I know v s.t. c=C(v) Or I know a sig-chain (s,id) WI-POK w.r.t id

  20. Non-malleability through dance i = 0110.. j = 00..1 vk0 vk0 r0 r0 Sign0(r0) Sign0(r0) vk1 vk1 r1 r1 Sign1(r1) Sign1(r1) c=C(v) c=C(v) WI-POK WI-POK w.r.t i w.r.t j * In actual protocol need “many” seq WIPOK a la [LP‘09]

  21. Dealing with Aborting Adversaries Problem 1: • MIM will notice that I ask him to sign a signature chain • Solution: Don’t. Ask him to sign commitments of sigs…(need to add a POK of commitment to prove sig game lemma) Problem 2: • I might have to “rewind” many times on left to get a single signature • So if I have id = 01011, access pattern on the right is 0*1*0*1*... • Solution:Use 3 keys (0,1,2); require chain w.r.t 2id12id22id3…

  22. Main Theorem Thm:Assume one-way functions. Then there exists a O(1)-round non-malleable commitment with a black-box proof of security. Main Technique Exploit rewinding pattern (instead of just location) Some applications

  23. Secure Multi-party Computation [Yao,GMW] A set of parties with private inputs. Wish to jointly compute a function of their inputs while preserving privacyof inputs (as much as possible) Security must be preserved even if some of the parties are malicious.

  24. Secure Multi-party Computation [Yao,GMW] Original work of [Goldreich-Micali-Wigderson’87] • TDP, n rounds More Recent:“Stronger assumption, less rounds” • [Katz-Ostrovsky-Smith’03] • TDP, dense cryptosystems, log n rounds • TDP, CRH+dense crypto with SubExp sec, O(1)-rounds, non-BB • [P’04] • TDP, CRH, O(1)-round, non-BB

  25. NMC v.s. MPC Holds both for stand-alone MPC and UC-MPC (in a number of set-up models) Corollary: TDP  O(1)-round MPC Thm [Lin-P-Venkitasubramaniam’09]: TPD + k-round “robust” NMC  O(k)-round MPC

  26. NM ZK Corollary: OWF O(1)-round NMZK Can also get Conc NMZK if adding ω(log n) rounds Thm [Lin-P-Tseng-Venkitasubramaniam’10]: k-round “robust” NMC  O(k)-round NMZK

  27. What’s Next – Adaptive Hardness Consider the Factoring problem: • Given the product N of 2 random n-bit primes p,q, can you provide the factorization Adaptive Factoring Problem: • Given the product N of 2 random n-bit primes p,q, can you provide the factorization, if you have access to an oracle that factors all other N’ that are products of equal-length primes Are these problems equivalent? Unknown!

  28. What’s Next – Adaptive Hardness Adaptively-hard Commitments [Canetti-Lin-P’10] • Commitment scheme that remains hiding even if Adv has access to a decommitment oracle Implies Non-malleability (and more!) Thm [CLP’10] Existence of commitments implies O(n^)-round Adaptively-hard commitments

  29. Thank You

More Related