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Practical Affiliation-Hiding Authentication from Improved Polynomial Interpolation Mark Manulis, Bertram Poettering ASIACCS ‘11 Proceedings of the 6 th.

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Presentation on theme: "Practical Affiliation-Hiding Authentication from Improved Polynomial Interpolation Mark Manulis, Bertram Poettering ASIACCS ‘11 Proceedings of the 6 th."— Presentation transcript:

1 Practical Affiliation-Hiding Authentication from Improved Polynomial Interpolation Mark Manulis, Bertram Poettering ASIACCS ‘11 Proceedings of the 6 th ACM Symposium on Information, Computer and Communications Security, March 2011, Pages , Citation: 4 Presenter: 方竣民 Date: 2012/12/03 1

2 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 2

3 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 3

4 Introduction Affiliation-hiding (AH) protocols are valuable for hiding identities of communicating users behind their membership of groups. Improvements advance the area of efficient polynomial interpolation in finite fields. 4

5 Introduction You will see : Implementing polynomial interpolation by lots of mathematical ways and their pseudocode. One optimized multi-group Affiliation-hiding protocol. 5

6 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 6

7 Index-Hiding Message Encoding 7 Indices, messages Two algorithms iEncode and iDecode

8 Multi-Group AH Protocol GA creates public key (n,e,g) – n is the RSA modulus – e the public exponent – g a generator of a large subgroup of GA keeps private key d Membership credential cred = Pseudonym id, is random exponent 8 t is used to generate session key.

9 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 9

10 Interpolation Without Precomputation As Algorithm1, it has quadratic running time Algo1 already solves the problem of polynomial interpolation in reasonable time. 10

11 Algorithm1 Polynomial Interpolation 11

12 Interpolation Without Precomputation Most divisions can be replaced by multiplications, e.g. It is solved by algorithm2 with performance: But, algorithm2 needs extra storage for n-1 variables 12

13 Algorithm2 Interpolation with Deferred Inversion 13

14 Interpolation With Precomputation In some occasions polynomial interpolations have to be computed many times in succession. 14

15 Algorithm3 Interpolation after Precomputiation 15

16 Compare Algo2 and Algo3 Device: Intel XEON 2.66GHz. Using gcrypt library. 16 Algorithm2 Algorithm3

17 Within/Without Precomputation 17

18 Interleaved IHME These fields may become rather large, e.g.. IHME’s running time is still,so it will be very slow. 18

19 Interleaved IHME For instance, an IHME setting with and Could split all messages into 8 chunks Each of length We get new field The gain in efficiency might be superlinear. 19

20 V-fold IHME => is a prime, is a nature number. index space message space 20

21 Comparison v-fold/IHME by Algo2, *14=1120

22 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 22

23 Group Initialization Phase Performance in this phase is not very important, because it is only executing once. They improve on storage size of group parameters. 23

24 Group Initialization Phase A safe prime is a prime number such that,where is a prime as well. 24

25 Implementing CreateGroup 25

26 User Registration Phase By altering the generation of user credentials to: cred = with 26

27 Implementing Adduser 27

28 Multi-Group Handshake Protocol Users have a set at least; in first-round messages are encoded over a much small field of elements 28

29 Multi-Group Handshake Protocol In second-round, the per-group key confirmation messages are of length Where bits would suffice. It mades the field size to be elements. 29

30 Multi-Group Handshake Protocol Part1 30

31 Multi-Group Handshake Protocol Part2 31

32 Multi-Group Handshake Protocol Part3 32

33 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 33

34 Analysis 34 Symmetric Key Size Asymmetric Key Size Is it possible < ?

35 Outline Introduction Initial Technique Polynomial Interpolation Optimized Multi-Group AH Protocol Analysis Conclusion 35

36 Conclusion They heavily modified the group management and handshake algorihms to achieve considerably better performance. It showed that AH authentication in the multi- group setting, and provided appropriate performance measurements. 36


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