1 / 24

Improved OT Extension for Transferring Short Secrets

Improved OT Extension for Transferring Short Secrets. Vladimir Kolesnikov (Bell Labs) Ranjit Kumaresan ( Technion ). Secure Computation. Most general problem in cryptography Moving fast from theory to practice Major research effort I mproving (asymptotic & concrete) efficiency

deon
Download Presentation

Improved OT Extension for Transferring Short Secrets

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. Improved OT Extension for Transferring Short Secrets Vladimir Kolesnikov (Bell Labs) Ranjit Kumaresan (Technion)

  2. Secure Computation • Most general problem in cryptography • Moving fast from theory to practice • Major research effort • Improving (asymptotic & concrete) efficiency • Implementation & “Systems’’ issues x y f1(x,y) f2(x,y)

  3. State of the Art (Semihonest Setting) THEORY PRACTICE • [IKOS08] • Constant overhead • [G09,BV11]: FHE • optimal communication • [LO13,GKK+12,GGH+13] • ORAM based SFE • [HEKM11,BHKR13] • Yao86+KS08,PSSW09… • [KK12] • [Yao86]+ [GMW87] • [CHKM12,SZ13,ALSZ13] • (Multiparty) [GMW87]

  4. Practical Computational Overhead • Hierarchy of efficiency • FHE >> PKE >> SKE >> one-time pad • “LHS >> RHS” ≈ cost of LHS is, and will probably always be, by orders of magnitude, bigger than cost of RHS. • OT Extension motivated by “PKE >> SKE”

  5. Talk Outline • OT Extension • Ishai et al. (IKNP) OT Extension • A New Framework for IKNP

  6. PKE >> SKE SKE PKE • E.g: KA, OT, SFE • Hard to implement heuristically • More expensive • E.g: PRG, hash functions • Easy to implement heuristically • Cheaper PKE cannot be black-box reduced toSKE[IR89] • Factor ~ 3-4 orders of magnitude slower • Intel AES-NI instruction set

  7. [IR89] ?  + The Next Best Thing: Extending Primitives  • Extending public key encryption is easy • Encrypt payload with symmetric key • Encrypt symmetric key with public key • Huge practical impact • What about extending Oblivious Transfer?

  8. Oblivious Transfer (OT) Evaluate each AND gate in the circuit r x0 , x1 ??? xr GMW Used to select one of two “garbled keys” Yao

  9. x1 x0 r Cost of OT • No blackboxredn from OT to one-way functions [IR89] • OT length extension is easy: • OT instance extension is possible [B96,IKNP03] • Needs only k “seed” OTs to perform n >> k OTs • Additional n symmetric key (cheap) operations • Huge impact on SFE efficient, black-box s0 G(s0) x0  + r s1 G(s1) x1

  10. OT Extension: Prior Work • [Beaver 96]: First OT extension • [Ishai-Kilian-Nissim-Petrank 03] (IKNP) • Random Oracle (RO) model or Correlation robust hash functions (CRHF) • Most practical OT extension • [HIKN08,NNOB12]: Malicious OT extension • [LZ13]: (In)feasibility results for OT extension This work: Improve semihonest IKNP

  11. Talk Outline • OT Extension • Ishai et al. (IKNP) OT Extension • A New Framework for IKNP

  12. sk sk s1 s2 s1 s2 x2,0 xn,0 x3,0 xn,1 x3,1 x2,1 ...  n r2 r1 r3 rn + O(n)H [IKNP03] Strategy x1,0 x1,1 ...  + O(n)H . . . . Length Extension

  13. Sender obtains Q  {0,1}nk qi= ti t1  r t2 tk  r t1 t2 tk t1  r t2  r tk  r qi= ti s 1 0 1 0 1 1 0 0 1 1 1 0 ri=0 ri=1 ... ... s1 s2 sk zi= yi,r  H(ti) i i [IKNP03] Main Reduction Receiver picks T R {0,1}nk Sender picks sR {0,1}k yi,0 = xi,0  H(qi) yi,1 = xi,1  H(qi s) • For 1 i n, Sender sends • For 1 i n, Receiver outputs

  14. IKNP Cost • Communication cost of resulting OT(n,L): • Main reduction: 2nLbits • Length extension: 2nkbits • Communication cost of resulting SFE: • [Yao86]: need to transfer keys of length L = k • [GMW87]: L= 1, cost = 2nk+2n, optimal?

  15. Talk Outline • OT Extension • Ishai et al (IKNP) OT Extension • A New Framework for IKNP

  16. 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 Our Work: A Closer Look at IKNP t2 tk t2  r tk  r t1 t1  r r r r ri=0 ri=1 ... ... ... ; = T T U R

  17. 1 1 0 0 1 0 Alternate Point of View k • Row-wise encoding • 0 → 0k • 1 → 1k R= T⊕U r r r ri=0 ri=1 ... n R IKNP uses repetition encoding Can we use other encodings?

  18. A Coding Theoretic Framework for IKNP k Suppose use code C • Say ri comes from a larger domain {1,…,m} • Row-wise encoding • ri→C(ri)∈ {0,1}k r1 C(r1) C(r2) r2 n ... C(rn) rn C(R)

  19. t1 t2 tk u1 u2 uk r1∈[m] rn∈[m] r2∈[m] ... s1 s2 sk zi= yi,r  H(i, ti) i i A Coding Theoretic Framework for IKNP C(R) = T⊕U Sender obtains Q  {0,1}nk u1 t2 uk q2= t2(C(r2) ⦿s) qn= tn(C(rn) ⦿s) q1= t1(C(r1) ⦿s) ... Bit-wise AND • For 1 in, 1 r m • Sender sends yi,r= xi,r H(i, qi(C(r) ⦿s)) • For 1 i n, Receiver outputs

  20. Analysis • Perfect security against malicious sender • Statistical security against semihonestreceiver: • No loss unless query H on (i, ti(C(r) ⦿s))for some r • Loss in security: m2-d, where d = min distance of C • Cost of 1-out-of-m OT(n, L): • Communication: (2nk+nmL)bits • OT(n,L)1-out-of-m OT(n/log m, Llog m) • Communication: (n/log m)(2k + mL log m) bits

  21. Efficiency • Concrete: • Hadamardcodes for encoding • Factor ≈ 2 for 1-out-of-2 OT and GMW for k=256 • Additional optimizations lead to factor ≈ 3.5 • Asymptotic comm. cost per OT: O(k/log k) bits

  22. Conclusions • OT Extension motivated by PKE >> SKE • Huge impact on practicality of SFE • Coding theoretic framework for [IKNP03] • RO or “code correlation robust hash functions” • Improvements for GMW, OT, 1-out-of-m OT • Rethink GMW vs. Yao? • Also [KK12], [NNOB12], [SZ13], [ALSZ13]

  23. Thank You!

  24. The research leading to these results has received funding from the European Union's Seventh Framework Programme(FP7/2007-2013)under grant agreement no. 259426 – ERC – Cryptography and Complexity

More Related