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

2 Outline Introduction Private Matching Scheme Adversary models Security Conclusion References

3 Introduction (1/3) DataSets A B Intersection

4 Introduction (2/3) Oblivious Transfer( 忘卻式傳輸 / 模糊傳送 ) SenderReceiver 模糊傳送模糊傳送 OR 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., out of 2 OT

5 Introduction (3/3) Homomorphic encryption system E(m 1 ) ⊙ E(m 2 )= E(m 1 m 2 ) c=E(m), c k =E( k m) Θ

6 Private Matching Scheme (1/4) PM Scheme client/chooser (C) and server/sender (S) C inputs X = {x 1,…,x kc } and S inputs Y = {y 1,…,y ks } C learns X∩Y ： PM(X,Y) Polynomial 讓 S 算的變數 C input of size

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

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

9 Private Matching Scheme (4/4) Client Server X={x 1,…x kc } Y={y 1,…y ks } 1. 內插法算出多項式 2. 對多項式的係數做同態加密 3. 上傳至 Server 4. 選擇一個亂數值 γ 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

10 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)

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

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

13 References Efficient Private Matching and Set Intersection, me me