Paper 2015/390

Dual System Encryption Framework in Prime-Order Groups

Nuttapong Attrapadung

Abstract

We propose a new generic framework for achieving fully secure attribute based encryption (ABE) in prime-order bilinear groups. It is generic in the sense that it can be applied to ABE for arbitrary predicate. All previously available frameworks that are generic in this sense are given only in composite-order bilinear groups. These consist of the frameworks proposed by Wee (TCC'14) and Attrapadung (Eurocrypt'14). Both frameworks provide abstractions of dual-system encryption techniques introduced by Waters (Crypto'09). Our framework can be considered as a prime-order version of Attrapadung's framework and works in a similar manner: it relies on a main component called pair encodings, and it generically compiles any secure pair encoding scheme for a predicate in consideration to a fully secure ABE scheme for that predicate. One feature of our new compiler is that although the resulting ABE schemes will be newly defined in prime-order groups, we require essentially the same security notions of pair encodings as before. Beside the security of pair encodings, our framework assumes only the Matrix Diffie-Hellman assumption, introduced by Escala et al. (Crypto'13), which is a weak assumption that includes the Decisional Linear assumption as a special case. As for its applications, we can plug in available pair encoding schemes and automatically obtain the first fully secure ABE realizations in prime-order groups for predicates of which only fully secure schemes in composite-order groups were known. These include ABE for regular languages, ABE for monotone span programs (and hence Boolean formulae) with short ciphertexts or keys, and completely unbounded ABE for monotone span programs. As a side result, we establish the first generic implication from ABE for monotone span programs to ABE for branching programs. Consequently, we obtain fully-secure ABE for branching programs in some new variants, namely, unbounded, short-ciphertext, and short-key variants. Previous ABE schemes for branching programs are bounded and require linear-size ciphertexts and keys.

Note: Add Table 3,4 for comparisons.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Attribute-based encryptionDual system encryptionPrime-order bilinear groupsFull securityGeneric framework.
Contact author(s)
n attrapadung @ aist go jp
History
2015-06-15: revised
2015-04-29: received
See all versions
Short URL
https://ia.cr/2015/390
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/390,
      author = {Nuttapong Attrapadung},
      title = {Dual System Encryption Framework in Prime-Order Groups},
      howpublished = {Cryptology ePrint Archive, Paper 2015/390},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/390}},
      url = {https://eprint.iacr.org/2015/390}
}
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