Paper 2017/563
Weak is Better: Tightly Secure Short Signatures from Weak PRFs
Jacob Alperin-Sheriff and Daniel Apon
Abstract
The Boyen-Li signature scheme [Asiacrypt'16] is a major theoretical breakthrough. Via a clever homomorphic evaluation of a pseudorandom function over their verification key, they achieve a reduction loss in security linear in the underlying security parameter and entirely independent of the number of message queries made, while still maintaining short signatures (consisting of a single short lattice vector). All previous schemes with such an independent reduction loss in security required a linear number of such lattice vectors, and even in the classical world, the only schemes achieving short signatures relied on non-standard assumptions. We improve on their result, providing a verification key smaller by a linear factor, a significantly tighter reduction with only a constant loss, and signing and verification algorithms that could plausibly run in about 1 second. Our main idea is to change the scheme in a manner that allows us to replace the pseudorandom function evaluation with an evaluation of a much more efficient weak pseudorandom function. As a matter of independent interest, we give an improved method of randomized inversion of the G gadget matrix [MP12], which reduces the noise growth rate in homomorphic evaluations performed in a large number of lattice-based cryptographic schemes, without incurring the high cost of sampling discrete Gaussians.
Metadata
- Available format(s)
- Publication info
- Preprint. MINOR revision.
- Keywords
- weak pseudorandom functionssignatureslattice-based cryptography
- Contact author(s)
- jacobmas @ gmail com
- History
- 2017-06-14: received
- Short URL
- https://ia.cr/2017/563
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/563, author = {Jacob Alperin-Sheriff and Daniel Apon}, title = {Weak is Better: Tightly Secure Short Signatures from Weak {PRFs}}, howpublished = {Cryptology {ePrint} Archive, Paper 2017/563}, year = {2017}, url = {https://eprint.iacr.org/2017/563} }