Efficient Private Matching and Set Intersection (EUROCRYPT, 2004)

Efficient Private Matching and Set Intersection (EUROCRYPT, 2004) Author：Michael J.Freedman Kobbi Nissim Benny Pinkas Presentered by Chia Jui Hsu Date：2009-02-10

Outline • Introduction • Private Matching Scheme • Adversary models • Security • Conclusion • References

Introduction (1/3) Intersection A B DataSets

Introduction (2/3) • Oblivious Transfer(忘卻式傳輸/模糊傳送) 模糊傳送 OR Sender Receiver 1 out of 2 OT 1.傳送者不知道接收者是否得到密文 2.接收者只能得到他選擇的密文 M. Rabin, "How to Exchange Secrets by Oblivious Transfer", Technical Report TR-81,Aiken Computation Laboratory, Harvard Univ.,1981.

Introduction (3/3) • Homomorphic encryption system • E(m1)⊙E(m2)= E(m1 m2) • c=E(m), ck=E(km) Θ

Private Matching Scheme (1/4) • PM Scheme • client/chooser (C) and server/sender (S) • C inputs X = {x1,…,xkc} and S inputs Y = {y1,…,yks} • C learns X∩Y ：PM(X,Y) • Polynomial input of size C 讓S算的變數

Private Matching Scheme (2/4) • Horner scheme • example • 若y=3，則P(y)=5

Private Matching Scheme (3/4) • 法二 • 法三 y=3,P(y)=5

Private Matching Scheme (4/4) Server Client X={x1,…xkc} Y={y1,…yks} 1.內插法算出多項式 2.對多項式的係數做同態加密 4.選擇一個亂數值γ 5. 3.上傳至Server 6.重新排列後回傳KS個 7.解密，若一樣，則解出y 不一樣，則解出亂數

Adversary models • Semi-honest • 1.pretecting the client • indistinguishability • 2.protecting the sender • comparison to the ideal model • Malicious • adversary may behave arbitrarily • 1.拒絕參與協定(PM) • 2.用任意值代替輸入 • 3.過早中止協定(PM)

Security • Correctness • C’s privacy is preserved • S’s privacy is preserved

Conclusion • use homomorphic encryption and balanced hashing for both semi-honest (standard model) and malicious (random oracle model) environments. • list length k, communication O(k), and computation is O(klnlnk).

References • Efficient Private Matching and Set Intersection, 2004 • http://en.wikipedia.org/wiki/Horner_scheme

Efficient Private Matching and Set Intersection (EUROCRYPT, 2004)