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Spreading Rumors Quietly and the Subgroup Escape Problem

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Aleksandr Yampolskiy
Aleksandr Yampolskiy
Tecnologia
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Spreading Rumors Quietly and the Subgroup Escape Problem Aleksandr Yampolskiy Joint work with James Aspnes, Zoë Diamadi, Kristian Gjøsteen, and René Peralta
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Our model ,[object Object],[object Object],The British are coming!
Our model (cont.) ,[object Object],[object Object],The British are coming! The British are coming! The British are coming! The British are coming!
The adversary… ,[object Object],[object Object],You started a rumor!
The goal ,[object Object],[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Blind coupon mechanism ,[object Object],[object Object],[object Object],[object Object]
Blind coupon mechanism (cont.) ,[object Object],[object Object],[object Object]
Blind coupon mechanism (cont.) ,[object Object],[object Object],[object Object],[object Object],¼ ,[object Object],¼ ,[object Object],¼ 0 1 1 ,[object Object],0 0 0 c 0 1 1 c , 1 0 , 1 1
Simple inefficient construction ,[object Object],[object Object],[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Abstract group structure (U, G, D) ,[object Object],[object Object],[object Object],U G D invalid dummy signal
Hardness assumptions ,[object Object],[object Object],G D G ??? ¼
Hardness assumptions (cont.) ,[object Object],[object Object],G G ¼ ??? D
Generic security of subgroup escape problem ,[object Object],[object Object],[object Object],[object Object],negligible if |G|/|U| is small
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The BCM on abstract group structure (U, G, D) ,[object Object],[object Object],[object Object],[object Object],[object Object],{
The BCM on abstract group structure (U, G, D) (cont.) ,[object Object]
The BCM on abstract group structure (U, G, D) (cont.) ,[object Object],[object Object],[object Object],[object Object]
Elliptic Curves over Z n ,[object Object],[object Object],[object Object],[object Object],P 1 P 2 P 1 + P 2
Elliptic Curves over Z n (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Elliptic Curves over Z n (cont.) ,[object Object],[object Object],[object Object],[object Object],U G D invalid signal dummy
Elliptic Curves over Z n (cont.) ,[object Object],[object Object],[object Object]
Bilinear groups ,[object Object],[object Object],[object Object],U G D invalid signal dummy
Bilinear groups (cont.) ,[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Yay! Almost there!
Spreading rumors with the BCM ,[object Object],[object Object],1 0 0 0
Spreading rumors with the BCM ,[object Object],$#!@ 1 1 0 0 0 1
Spreading rumors with the BCM ,[object Object],[object Object],$#!@ ,[object Object],[object Object],[object Object],1 0 0 0 1 1
Spreading rumors with the BCM (cont.) ,[object Object],[object Object]
Spreading rumors with the BCM (cont.) ,[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object]
Open problems ,[object Object],[object Object],?
 

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  • 1. Spreading Rumors Quietly and the Subgroup Escape Problem Aleksandr Yampolskiy Joint work with James Aspnes, Zoë Diamadi, Kristian Gjøsteen, and René Peralta
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