A verifiable random function with short proofs and keys

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]

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 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]

A verifiable random function with short proofs and keys

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