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A Verifiable Random Function With Short Proofs and Keys Yevgeniy Dodis Aleksandr Yampolskiy (NYU) (Yale)
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]
Non-interactive lottery [MR02] ,[object Object],[object Object],Organizer F SK ( . ) x 1  = 3 x 2  = 8 x 3  = 5
Non-interactive lottery (cont.) ,[object Object],[object Object],F SK ( . ) F SK (3) = 10 F SK (8) = 11 F SK (5) = 15 Organizer
Non-interactive lottery (cont.) ,[object Object],[object Object],[object Object]
Verifiable Random Function ,[object Object],[object Object],[object Object],[object Object]
Previous work  ,[object Object],[object Object],[object Object],
Previous work (cont.) ,[object Object],[object Object],[object Object]
Previous work (cont.) ,[object Object],[object Object],[object Object],[object Object]
Previous work (cont.) ,[object Object],[object Object],[object Object],[object Object]
Our work ,[object Object],[object Object],[object Object],
Bilinear groups ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Compexity assumptions ,[object Object],[object Object],[object Object],[object Object]
Our VUF ,[object Object],[object Object],[object Object],[object Object],{
Our VUF (cont.) ,[object Object],[object Object],adversary challenger (PK, SK) PK x 1 x 2 x k … y 1 y 2 y k … adversary challenger (PK, SK) PK x i y i
Our VUF (cont.) ,[object Object],[object Object]
Our VUF (cont.) ,[object Object],[object Object]
Our VRF  ,[object Object],[object Object],[object Object],[object Object],{ our VUF
Proof of security : big picture ,[object Object],[object Object],[object Object]
Proof of security : big picture B A ,[object Object],(g, g  , …, g (  q ) ,   ) Is   = e(g,g) 1/   Challenger VRF game …
Proof of security : sketch ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proof of security : sketch B A (g, g  , …, g (  q ) ,   ) Challenger ,[object Object],(PK, SK) PK      is not  e(g,g) 1/  not random x *
Extending the input size ,[object Object],[object Object],[object Object],[object Object]
Extending the input size (cont.) ,[object Object],0 a-1 y=F(0 a ) z=F(0 a-1 1) F(z0) F(z1) F(y0) F(y1) F(F(y1)1) F(F(y1)0) 0 1 0 1 0 1 0 1 VRF value for  x = 011
Efficiency ,[object Object],[object Object],Group size Length of proofs and keys 160  bits, elliptic group >3,200  bytes [Dod03], [Lys02] 14,383  bits, Z n * 280,000  bytes [MRV99] 1,000  bits,  elliptic group 125  bytes Our VRF
Compact e-cash [CHL05] ,[object Object],[object Object],[object Object],[object Object]
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object]
 

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A verifiable random function with short proofs and keys

  • 1. A Verifiable Random Function With Short Proofs and Keys Yevgeniy Dodis Aleksandr Yampolskiy (NYU) (Yale)
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