Symbolic Methods in Computational Cryptography Proofs
Gilles Barthe, Benjamin Grégoire, Charlie Jacomme, Steve Kremer, and Pierre-Yves Strub. Symbolic Methods in Computational Cryptography Proofs. In Proceedings of the 32nd IEEE Computer Security Foundations Symposium (CSF'19), pp. 136–151, IEEE Computer Society Press, Hoboken, NJ, USA, June 2019.
doi:10.1109/CSF.2019.00017
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Abstract
Code-based game-playing is a popular methodology for proving security of cryptographic constructions and side-channel countermeasures. This methodology relies on treating cryptographic proofs as an instance of relational program verification (between probabilistic programs), and decomposing the latter into a series of elementary relational program verification steps. In this paper, we develop principled methods for proving such elementary steps for probabilistic programs that operate over finite fields and related algebraic structures. We focus on three essential properties: program equivalence, information flow, and uniformity. We give characterizations of these properties based on deducibility and other notions from symbolic cryptography. We use (sometimes improve) tools from symbolic cryptography to obtain decision procedures or sound proof methods for program equivalence, information flow, and uniformity. Finally, we evaluate our approach using examples drawn from provable security and from side-channel analysis - for the latter, we focus on the masking countermeasure against differential power analysis. A partial implementation of our approach is integrated in EasyCrypt, a proof assistant for provable security, and in MaskVerif, a fully automated prover for masked implementations.
BibTeX
@inproceedings{BGJKS-csf19,
abstract = {Code-based game-playing is a popular methodology for
proving security of cryptographic constructions and
side-channel countermeasures. This methodology
relies on treating cryptographic proofs as an
instance of relational program verification (between
probabilistic programs), and decomposing the latter
into a series of elementary relational program
verification steps. In this paper, we develop
principled methods for proving such elementary steps
for probabilistic programs that operate over finite
fields and related algebraic structures. We focus on
three essential properties: program equivalence,
information flow, and uniformity. We give
characterizations of these properties based on
deducibility and other notions from symbolic
cryptography. We use (sometimes improve) tools from
symbolic cryptography to obtain decision procedures
or sound proof methods for program equivalence,
information flow, and uniformity. Finally, we
evaluate our approach using examples drawn from
provable security and from side-channel analysis -
for the latter, we focus on the masking
countermeasure against differential power
analysis. A partial implementation of our approach
is integrated in EasyCrypt, a proof assistant for
provable security, and in MaskVerif, a fully
automated prover for masked implementations. },
address = {Hoboken, NJ, USA},
author = {Barthe, Gilles and Gr{\'e}goire, Benjamin and
Jacomme, Charlie and Kremer, Steve and Strub,
Pierre-Yves },
booktitle = {{P}roceedings of the 32nd IEEE Computer Security
Foundations Symposium (CSF'19)},
month = jun,
pages = {136--151},
publisher = {{IEEE} Computer Society Press},
title = {Symbolic Methods in Computational Cryptography
Proofs},
year = 2019,
acronym = {{CSF}'19},
nmonth = 6,
doi = {10.1109/CSF.2019.00017},
url = {https://ieeexplore.ieee.org/document/8823706},
{https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8823706},
}