Verified Proofs of Higher-Order Masking
- 2.6k Downloads
In this paper, we study the problem of automatically verifying higher-order masking countermeasures. This problem is important in practice, since weaknesses have been discovered in schemes that were thought secure, but is inherently exponential: for \(t\)-order masking, it involves proving that every subset of \(t\) intermediate variables is distributed independently of the secrets. Some tools have been proposed to help cryptographers check their proofs, but are often limited in scope.
We propose a new method, based on program verification techniques, to check the independence of sets of intermediate variables from some secrets. Our new language-based characterization of the problem also allows us to design and implement several algorithms that greatly reduce the number of sets of variables that need to be considered to prove this independence property on all valid adversary observations. The result of these algorithms is either a proof of security or a set of observations on which the independence property cannot be proved. We focus on AES implementations to check the validity of our algorithms. We also confirm the tool’s ability to give useful information when proofs fail, by rediscovering existing attacks and discovering new ones.
KeywordsHigher-order masking Automatic tools EasyCrypt
- 1.Akinyele, J., Barthe, G., Grégoire, B., Schmidt, B., Strub, P.-Y.: Certified synthesis of efficient batch verifiers. In: 27th IEEE Computer Security Foundations Symposium, CSF 2014. IEEE Computer Society (2014) (to appear)Google Scholar
- 2.Balasch, J., Gierlichs, B., Grosso, V., Reparaz, O., Standaert, F.-X.: On the cost of lazy engineering for masked software implementations. Cryptology ePrint Archive, Report 2014/413 (2014). http://eprint.iacr.org/2014/413
- 3.Barthe, G., Belaïd, S., Dupressoir, F., Fouque, P.-A., Grégoire, B., Strub, P.-Y.: Verified proofs of higher-order masking. Cryptology ePrint Archive, Report 2015/060 (2015). http://eprint.iacr.org/
- 4.Barthe, G., Crespo, J.M., Gulwani, S., Kunz, C., Marron, M.: From relational verification to SIMD loop synthesis. In: Nicolau, A., Shen, X., Amarasinghe, S.P., Vuduc, R.W. (eds.) Principles and Practice of Parallel Programming (PPoPP), pp. 123–134. ACM (2013)Google Scholar
- 8.Barthe, G., Grégoire, B., Zanella-Béguelin, S.: Formal certification of code-based cryptographic proofs. In: 36th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2009, pp. 90–101. ACM (2009)Google Scholar
- 17.Eldib, H., Wang, C., Taha, M.M.I., Schaumont, P.: QMS: evaluating the side-channel resistance of masked software from source code. In: The 51st Annual Design Automation Conference 2014, DAC 2014, San Francisco, CA, USA, June 1–5, pp. 1–6. ACM (2014)Google Scholar
- 19.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)Google Scholar
- 20.Gomes, C.P., Sabharwal, A., Selman, B.: Model counting. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 633–654. IOS Press (2009)Google Scholar
- 23.Mangard, S., Oswald, E., Popp, T.: Power analysis attacks - revealing the secrets of smart cards. Springer (2007)Google Scholar
- 29.Pettai, M., Laud, P.: Automatic proofs of privacy of secure multi-party computation protocols against active adversaries. Cryptology ePrint Archive, Report 2014/240 (2014). http://eprint.iacr.org/2014/240