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2006
IEEE

Explicit Exclusive Set Systems with Applications to Broadcast Encryption

11 years 6 months ago
Explicit Exclusive Set Systems with Applications to Broadcast Encryption
A family of subsets C of [n] def = {1, . . . , n} is (r, t)exclusive if for every S ⊂ [n] of size at least n − r, there exist S1, . . . , St ∈ C with S = S1∪S2∪· · · ∪St. These families, also known as complement-cover families, have cryptographic applications, and form the basis of informationtheoretic broadcast encryption and multi-certificate revocation. We give the first explicit construction of such families with size poly(r, t)nr/t , essentially matching a basic lower bound. Our techniques are algebraic in nature. When r = O(t), as is natural for many applications, we can improve our bound to poly(r, t) n r 1/t . Further, when r, t are small, our construction is tight up to a factor of r. We also provide a poly(r, t, log n) algorithm for finding S1, . . . , St, which is crucial for efficient use in applications. Previous constructions either had much larger size, were randomized and took super-polynomial time to find S1, . . . , St, or did not work for arbitra...
Craig Gentry, Zulfikar Ramzan, David P. Woodruff
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors Craig Gentry, Zulfikar Ramzan, David P. Woodruff
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