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Towards Sound Fresh Re-keying with Hard (Physical) Learning Problems

  • Stefan Dziembowski
  • Sebastian FaustEmail author
  • Gottfried Herold
  • Anthony Journault
  • Daniel Masny
  • François-Xavier Standaert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9815)

Abstract

Most leakage-resilient cryptographic constructions aim at limiting the information adversaries can obtain about secret keys. In the case of asymmetric algorithms, this is usually obtained by secret sharing (aka masking) the key, which is made easy by their algebraic properties. In the case of symmetric algorithms, it is rather key evolution that is exploited. While more efficient, the scope of this second solution is limited to stateful primitives that easily allow for key evolution such as stream ciphers. Unfortunately, it seems generally hard to avoid the need of (at least one) execution of a stateless primitive, both for encryption and authentication protocols. As a result, fresh re-keying has emerged as an alternative solution, in which a block cipher that is hard to protect against side-channel attacks is re-keyed with a stateless function that is easy to mask. While previous proposals in this direction were all based on heuristic arguments, we propose two new constructions that, for the first time, allow a more formal treatment of fresh re-keying. More precisely, we reduce the security of our re-keying schemes to two building blocks that can be of independent interest. The first one is an assumption of Learning Parity with Leakage, which leverages the noise that is available in side-channel measurements. The second one is based on the Learning With Rounding assumption, which can be seen as an alternative solution for low-noise implementations. Both constructions are efficient and easy to mask, since they are key homomorphic or almost key homomorphic.

Keywords

Security Level Block Cipher Random Oracle Linear Feedback Shift Register Pseudo Random Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Stefan Dziembowski is supported by the Foundation for Polish Science WELCOME/2010-4/2 grant founded within the framework of the EU Innovative Economy Operational Programme. Sebastian Faust is funded by the Emmy Noether Program FA 1320/1-1 of the German Research Foundation (DFG). Gottfried Herold is funded by the ERC grant 307952 (acronym FSC). Anthony Journault is funded by the INNOVIRIS project SCAUT. Daniel Masny is supported by the DFG Research Training Group GRK 1817/1. François-Xavier Standaert is a research associate of the Belgian Fund for Scientific Research (FNRS-F.R.S.). His work was funded in parts by the ERC project 280141 (acronym CRASH) and the ARC project NANOSEC.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Stefan Dziembowski
    • 1
  • Sebastian Faust
    • 2
    Email author
  • Gottfried Herold
    • 2
  • Anthony Journault
    • 3
  • Daniel Masny
    • 2
  • François-Xavier Standaert
    • 3
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland
  2. 2.Fakultät für MathematikUniversity of BochumBochumGermany
  3. 3.ICTEAM – Crypto GroupUniversité catholique de LouvainLouvain-la-NeuveBelgium

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