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- Craig Gentry, Alice Silverberg
- ASIACRYPT
- 2002

We present hierarchical identity-based encryption schemes and signature schemes that have total collusion resistance on an arbitrary number of levels and that have chosen ciphertext security in the random oracle model assuming the difficulty of the Bilinear Diffie-Hellman problem.

- Dan Boneh, Alice Silverberg
- IACR Cryptology ePrint Archive
- 2002

We study the problem of finding efficiently computable non-degenerate multilinear maps from G1 to G2, where G1 and G2 are groups of the same prime order, and where computing discrete logarithms in G1 is hard. We present several applications to cryptography, explore directions for building such maps, and give some reasons to believe that finding examples… (More)

- Karl Rubin, Alice Silverberg
- IACR Cryptology ePrint Archive
- 2003

We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Like those systems, we obtain small key sizes. While Lucas-based systems and XTR are essentially restricted to exponentiation, we are able to perform multiplication as… (More)

- Alice Silverberg, Jessica Staddon, Judy L. Walker
- IEEE Trans. Information Theory
- 2003

We apply results from algebraic coding theory to solve problems in cryptography, by using recent results on list decoding of error-correcting codes to efficiently find traitors who collude to create pirates. We produce schemes for which the TA (traceability) traitor tracing algorithm is very fast. We compare the TA and IPP (identifiable parent property)… (More)

- Alice Silverberg, Jessica Staddon, Judy L. Walker
- IACR Cryptology ePrint Archive
- 2001

We apply powerful, recently discovered techniques for the list decoding of error-correcting codes to the problem of efficiently tracing traitors. Much work has focused on methods for constructing such traceability schemes, but the complexity of the traitor tracing algorithms has received little attention. A widely used traitor tracing algorithm, the TA… (More)

- Karl Rubin, Alice Silverberg
- Journal of Cryptology
- 2008

We show that supersingular Abelian varieties can be used to obtain higher MOV security per bit, in all characteristics, than supersingular elliptic curves. We give a point compression/decompression algorithm for primitive subgroups associated with elliptic curves that gives shorter signatures, ciphertexts, or keys for the same security while using the… (More)

- Karl Rubin, Alice Silverberg
- CRYPTO
- 2002

For certain security applications, including identity based encryption and short signature schemes, it is useful to have abelian varieties with security parameters that are neither too small nor too large. Supersingular abelian varieties are natural candidates for these applications. This paper determines exactly which values can occur as the security… (More)

- B Mazur, K Rubin, A Silverberg
- 2008

If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases… (More)

- Dan Boneh, Karl Rubin, Alice Silverberg
- IACR Cryptology ePrint Archive
- 2009

We apply the Cocks-Pinch method to obtain pairing-friendly composite order groups with prescribed embedding degree associated to ordinary elliptic curves, and we show that new security issues arise in the composite order setting.

- Karl Rubin, Alice Silverberg
- Math. Comput.
- 2007

We give easy ways to distinguish between the twists of an ordinary elliptic curve E over Fp in order to identify one with p+ 1− 2U points, when p = U2 + dV 2 with 2U, 2V ∈ Z and E is constructed using the CM method. This is useful for finding elliptic curves with a prescribed number of points, and is a new, faster, and easier way to implement the last step… (More)