Abstract
We present a lattice-based stateless signature scheme provably secure in the standard model. Our scheme has a constant number of matrices in the public key and a single lattice vector (plus a tag) in the signatures. The best previous lattice-based encryption schemes were the scheme of Ducas and Micciancio (CRYPTO 2014), which required a logarithmic number of matrices in the public key and that of Bohl et. al (J. of Cryptology 2014), which required a logarithmic number of lattice vectors in the signature. Our main technique involves using fully homomorphic computation to compute a degree \(d\) polynomial over the tags hidden in the matrices in the public key. In the scheme of Ducas and Micciancio, only functions linear over the tags in the public key matrices were used, which necessitated having \(d\) matrices in the public key.
As a matter of independent interest, we extend Wichs’ (eprint 2014) recent construction of homomorphic trapdoor functions into a primitive we call puncturable homomorphic trapdoor functions (PHTDFs). This primitive abstracts out most of the properties required in many different lattice-based cryptographic constructions. We then show how to combine a PHTDF along with a function satisfying certain properties (to be evaluated homomorphically) to give an eu-scma signature scheme.
J. Alperin-Sheriff—This material is based upon work supported by DARPA under agreement number FA8750-11-C-0096. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of DARPA or U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
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Alperin-Sheriff, J. (2015). Short Signatures with Short Public Keys from Homomorphic Trapdoor Functions. In: Katz, J. (eds) Public-Key Cryptography -- PKC 2015. PKC 2015. Lecture Notes in Computer Science(), vol 9020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46447-2_11
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DOI: https://doi.org/10.1007/978-3-662-46447-2_11
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