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kkrtpsi implementation

protocol

The KKRT PSI (Batched-OPRF PSI) [1] is one of the most efficient OT-extension (oblivious transfer) based PSI protocol that boasts more than 100 times speed up in single core performance (300s for DHPSI vs 3s for KKRT for a match between two 1 million records dataset). It is secure against semi-honest adversaries, a malicious party that adheres to the protocol honestly but wants to learn/extract the other party's private information from the data being exchanged.

  1. the sender generates CuckooHash parameters and exchange with the receiver.
  2. the receiver inserts his input set Y to the Cuckoo Hash Table.
  3. the receiver acts as the sender in the OPRF protocol and samples two matrices T and U such that the matrix T is a uniformly random bit matrix, and the matrix U is the Pseudorandom Code (linear correcting code) C on cuckoohashed inputs. The receiver outputs the matrix T as the OPRF evaluation of his inputs Y.
  4. the sender acts as the receiver in the OPRF protocol with input secret choice bits s, and receives matrix Q, with columns of Q correspond to either matrix T or U depending on the value of s, and outputs the matrix Q. Each row of the column Q along with the secret choice bit s serves as the OPRF keys to encode his own input X.
  5. the sender uses the key k to encode his own input X, and sends it to the receiver.
  6. the receiver receives the OPRF evaluation of X, and compares with his own OPRF evaluation of Y, and outputs the intersection.

data flow

             Sender                                                                  Receiver
             X                                                                       Y



Stage 1      Cuckoo Hash                                                              Stage 1
                                ───────────────────CukooHashParam───────────────►     cuckoo.Insert(Y)



Stage 2.1                                                                             Stage 2.1
             oprf.Receive()     ◄─────────────────────T, U───────────────────────     oprf.Send()


             K = Q              ────────────────────────────────────────────────►     OPRF(K, Y) = T



Stage 3      OPRF(K, X)         ────────────────────OPRF(K, X)──────────────────►     Stage 3


K:          OPRF keys
OPRF(K, Y): OPRF evaluation of input Y with key K

References

[1] V. Kolesnikov, R. Kumaresan, M. Rosulek, N.Trieu. "Efficient Batched Oblivious PRF with Applications to Private Set Intersection." In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (pp. 818-829),2016. Paper available here: https://dl.acm.org/doi/pdf/10.1145/2976749.2978381.

[2] M. Naor, B. Pinkas. "Efficient oblivious transfer protocols." In SODA (Vol. 1, pp. 448-457), 2001. Paper available here: https://link.springer.com/content/pdf/10.1007/978-3-662-46800-5_26.pdf

[3] T. Chou, O. Claudio. "The simplest protocol for oblivious transfer." In International Conference on Cryptology and Information Security in Latin America (pp. 40-58). Springer, Cham, 2015. Paper available here: https://eprint.iacr.org/2015/267.pdf

[4] Y. Ishai and J. Kilian and K. Nissim and E. Petrank, Extending Oblivious Transfers Efficiently. https://www.iacr.org/archive/crypto2003/27290145/27290145.pdf