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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

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

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

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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

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

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

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

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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.

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

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

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Algorithm1 Polynomial Interpolation 11

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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

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Algorithm2 Interpolation with Deferred Inversion 13

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

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Algorithm3 Interpolation after Precomputiation 15

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

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Within/Without Precomputation 17

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

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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

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

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

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

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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

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

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Implementing CreateGroup 25

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

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Implementing Adduser 27

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

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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

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Multi-Group Handshake Protocol Part1 30

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Multi-Group Handshake Protocol Part2 31

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Multi-Group Handshake Protocol Part3 32

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

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

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

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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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