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Threshold and Proactive Pseudo-Random Permutations

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Aleksandr Yampolskiy
Aleksandr Yampolskiy
Technology
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Threshold and Proactive Pseudo-Random Permutations Joint work with Yevgeniy Dodis and Moti Yung Aleksandr Yampolskiy (Yale) TCC 2006
Talk Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]
What Is a Pseudo-Random Permutation? x E SK ( x ) SK …  x  ( x ) ¼ ,[object Object],[object Object]
Distributed Block Ciphers ,[object Object],[object Object]
Efficiency ,[object Object],[object Object],[object Object]
Original Luby-Rackoff Construction ,[object Object],[object Object],[object Object],L R S T R T V F SK 1 F SK 2 F SK 3 h 1/(R+SK 1 ) h 1/(S+SK 2 ) h 1/(T+SK 3 ) S
Our Results ,[object Object],[object Object],[object Object],[object Object]
Oblivious Distributed PRF ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Perform crypto ops. piecewise using shares of x and SK .
Naor-Reingold PRF ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],k=6, x=011011 a 1 a 2 a 3 a 4 a 5 a 6 g g a 2 g a 2 a 3 g a 2 a 3 a 5 g a 2 a 3 g a 2 a 3 a 5 a 6 g NR(011011)
Distributing NR-PRF ,[object Object],[object Object],[object Object],[object Object],[object Object]
Dodis-Yampolskiy PRF ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Extending the input length ,[object Object],[object Object],[object Object],[object Object],k bits a ¼ k 1/3 bits log P bits k bits
Distributing DY-PRF ,[object Object],[object Object],[object Object],[object Object],[object Object]
Distributing DY PRF Protocol for server P j : Input: shares of input’s bits [x 1 ],…,[x m ] and of the secret key ([i], [SK]) ,[object Object],[object Object],[object Object],[object Object],[object Object],Running time is dominated by bit conversion protocol, using O((mn+mlog m) ¢ B) bit ops.
Let’s Recap! ,[object Object],[object Object],[object Object]
Distributing Feistel Permutation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proof of Security ,[object Object],[object Object]
Secure threshold PRP if Pr[b=b’]  ½ virtual environment B A
Proactive Security ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X X X X X X X X window
Practical Application : Distributed Authenticated Encryption ,[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Thank You! Any Questions?

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Threshold and Proactive Pseudo-Random Permutations

  • 1. Threshold and Proactive Pseudo-Random Permutations Joint work with Yevgeniy Dodis and Moti Yung Aleksandr Yampolskiy (Yale) TCC 2006
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  • 19. Secure threshold PRP if Pr[b=b’]  ½ virtual environment B A
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  • 23. Thank You! Any Questions?