dc.contributor.author |
Escala, Alex |
dc.contributor.author |
Herold, Gottfried |
dc.contributor.author |
Kiltz, Eike |
dc.contributor.author |
Ràfols, Carla |
dc.contributor.author |
Villar, Jorge |
dc.date |
2013 |
dc.identifier.citation |
Escala A, Herold G, Kiltz E, Ràfols C, Villar J. An Algebraic Framework for Diffie-Hellman Assumptions. In: Caretti R, Garay JA, editors.
Advances in Cryptology – CRYPTO 2013. 33rd Annual Cryptology Conference Proceedings, Part II; 2013 Aug 18-22; Santa Barbara, CA, USA. Berling: Springer; 2013. p. 129-47. (LNCS; no. 8043). DOI: 10.1007/978-3-642-40084-1_8 |
dc.identifier.citation |
https://dx.doi.org/10.1007/978-3-642-40084-1_8 |
dc.identifier.uri |
http://hdl.handle.net/10230/42257 |
dc.format |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Springer |
dc.relation |
Caretti R, Garay JA, editors.
Advances in Cryptology – CRYPTO 2013. 33rd Annual Cryptology Conference Proceedings, Part II; 2013 Aug 18-22; Santa Barbara, CA, USA. Berling: Springer; 2013. p. 129-47. (LNCS; no. 8043). |
dc.rights |
© International Association for Cryptologic Research 2013
The final publication is available at Springer via
https://doi.org/10.1007/978-3-642-40084-1_8 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Diffie-Hellman assumption |
dc.subject |
Generic hardness |
dc.subject |
Groth-Sahai proofs |
dc.subject |
Hash proof systems |
dc.subject |
Public-key encryption |
dc.title |
An algebraic framework for Diffie-Hellman assumptions |
dc.type |
info:eu-repo/semantics/conferenceObject |
dc.type |
info:eu-repo/semantics/acceptedVersion |
dc.description.abstract |
Comunicació presentada a: CRYPTO 2013 The 33rd Annual Cryptology Conference, celebrada del 18 al 22 d'agost de 2013 a Santa Bàrbara, Califòrnia, Estats Units d'Amèrica. |
dc.description.abstract |
We put forward a new algebraic framework to generalize and analyze Di_e-Hellman like Decisional
Assumptions which allows us to argue about security and applications by considering only algebraic
properties. Our D`;k-MDDH assumption states that it is hard to decide whether a vector in G` is
linearly dependent of the columns of some matrix in G`_k sampled according to distribution D`;k. It
covers known assumptions such as DDH, 2-Lin (linear assumption), and k-Lin (the k-linear assumption).
Using our algebraic viewpoint, we can relate the generic hardness of our assumptions in m-linear groups
to the irreducibility of certain polynomials which describe the output of D`;k. We use the hardness results
to _nd new distributions for which the D`;k-MDDH-Assumption holds generically in m-linear groups. In
particular, our new assumption 2-SCasc is generically hard in bilinear groups and, compared to 2-Lin, has
shorter description size, which is a relevant parameter for e_ciency in many applications. These results
support using our new assumption as a natural replacement for the 2-Lin Assumption which was already
used in a large number of applications.
To illustrate the conceptual advantages of our algebraic framework, we construct several fundamental
primitives based on any MDDH-Assumption. In particular, we can give many instantiations of a primitive
in a compact way, including public-key encryption, hash-proof systems, pseudo-random functions, and
Groth-Sahai NIZK and NIWI proofs. As an independent contribution we give more e_cient NIZK proofs
for membership in a subgroup of G`, for validity of ciphertexts and for equality of plaintexts. The results
imply very signi_cant e_ciency improvements for a large number of schemes, most notably Naor-Yung
type of constructions. |
dc.description.abstract |
_ |
dc.description.abstract |
Funded by a Sofja Kovalevskaja Award of the Alexander von Humboldt Foundation and the German Federal Ministry for Education and Research.
Partially supported by the Spanish Government through projects MTM2009-07694 and Consolider Ingenio 2010 CDS2007-00004 ARES. |