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Probabilistic relational verification for cryptographic implementations,” Unpublished manuscript
, 2013
"... Relational program logics have been used for mechanizing for-mal proofs of various cryptographic constructions. With an eye to-wards scaling these successes towards end-to-end security proofs for implementations of distributed systems, we present RF⋆, a rela-tional extension of F⋆, a general-purpose ..."
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Relational program logics have been used for mechanizing for-mal proofs of various cryptographic constructions. With an eye to-wards scaling these successes towards end-to-end security proofs for implementations of distributed systems, we present RF⋆, a rela-tional extension of F⋆, a general-purpose higher-order stateful pro-gramming language with a verification system based on refinement types. The distinguishing feature of RF ⋆ is a relational Hoare logic for a higher-order, stateful, probabilistic language. Through care-ful language design, we adapt the F ⋆ typechecker to generate both classic and relational verification conditions, and to automatically discharge their proofs using an SMT solver. Thus, we are able to benefit from the existing features of F⋆, including its abstraction facilities for modular reasoning about program fragments. We eval-uate RF ⋆ experimentally by programming a series of cryptographic constructions and protocols, and by verifying their security proper-ties, ranging from information flow to unlinkability, integrity, and privacy. Moreover, we validate the design of RF ⋆ by formalizing in Coq a core probabilistic λ-calculus and a relational refinement type system and proving the soundness of the latter against a deno-tational semantics of the probabilistic λ-calculus.
Fully Automated Analysis of Padding-Based Encryption in the Computational Model
, 2013
"... Computer-aided verification provides effective means of analyzing the security of cryptographic primitives. However, it has remained a challenge to achieve fully automated analyses yielding guarantees that hold against computational (rather than symbolic) attacks. This paper meets this challenge for ..."
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Computer-aided verification provides effective means of analyzing the security of cryptographic primitives. However, it has remained a challenge to achieve fully automated analyses yielding guarantees that hold against computational (rather than symbolic) attacks. This paper meets this challenge for public-key encryption schemes built from trapdoor permutations and hash functions. Using a novel combination of techniques from computational and symbolic cryptography, we present proof systems for analyzing the chosen-plaintext and chosen-ciphertext security of such schemes in the random oracle model. Building on these proof systems, we develop a toolset that bundles together fully automated proof and attack finding algorithms. We use this toolset to build a comprehensive database of encryption
Automated analysis of cryptographic assumptions in generic group models
- In Advances in Cryptology – CRYPTO 2014, LNCS
, 2014
"... Abstract. We initiate the study of principled, automated, methods for analyzing hardness assumptions in generic group models, following the approach of symbolic cryptography. We start by defining a broad class of generic and symbolic group models for different settings—symmetric or asymmetric (level ..."
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Abstract. We initiate the study of principled, automated, methods for analyzing hardness assumptions in generic group models, following the approach of symbolic cryptography. We start by defining a broad class of generic and symbolic group models for different settings—symmetric or asymmetric (leveled) k-linear groups—and by proving “computational soundness ” theorems for the symbolic models. Based on this result, we formulate a very general master theorem that formally relates the hard-ness of a (possibly interactive) assumption in these models to solving problems in polynomial algebra. Then, we systematically analyze these problems. We identify different classes of assumptions and obtain de-cidability and undecidability results. Then, we develop and implement automated procedures for verifying the conditions of master theorems, and thus the validity of hardness assumptions in generic group models. The concrete outcome of this work is an automated tool which takes as input the statement of an assumption, and outputs either a proof of its generic hardness or shows an algebraic attack against the assumption. 1
On Robustness of Trust Systems
"... Abstract. Trust systems assist in dealing with users who may betray one another. Cunning users (attackers) may attempt to hide the fact that they betray others, deceiving the system. Trust systems that are difficult to deceive are considered more robust. To formally reason about robustness, we forma ..."
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Abstract. Trust systems assist in dealing with users who may betray one another. Cunning users (attackers) may attempt to hide the fact that they betray others, deceiving the system. Trust systems that are difficult to deceive are considered more robust. To formally reason about robustness, we formally model the abilities of an attacker. We prove that the attacker model is maximal, i.e. 1) the attacker can perform any feasible attack and 2) if a single attacker cannot perform an attack, then a group of attackers cannot perform that attack. Therefore, we can formulate robustness analogous to security. 1
Symbolic Probabilistic Analysis of Off-line Guessing
"... Abstract. We introduce a probabilistic framework for the automated analysis of security protocols. Our framework provides a general method for expressing properties of cryptographic primitives, modeling an attacker who is more powerful than conventional Dolev-Yao attackers. Within our framework, we ..."
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Abstract. We introduce a probabilistic framework for the automated analysis of security protocols. Our framework provides a general method for expressing properties of cryptographic primitives, modeling an attacker who is more powerful than conventional Dolev-Yao attackers. Within our framework, we can model equational properties of cryptographic primitives as well as property statements about their weaknesses, e.g. primitives leaking partial information about messages or the use of weak algorithms for random number generation. Moreover, we can use these properties to find attacks and estimate their success probability. Existing symbolic methods can neither model such properties nor find such attacks. We show that the probability estimates we obtain are negligibly different from those yielded by a generalized random oracle model based on sampling (the random variables associated to symbolic) terms into bitstrings, while respecting the stipulated properties of cryptographic primitives. As case studies, we use a prototype implementation of our framework to model non-trivial properties of RSA encryption and automatically estimate the probability of off-line guessing attacks on the EKE protocol.
Certified computer-aided cryptography: efficient provably secure machine code from high-level implementations
"... We present a computer-aided framework for proving concrete security bounds for cryptographic machine code implementations. The front-end of the framework is an interactive verification tool that extends the EasyCrypt framework to reason about relational properties of C-like programs extended with id ..."
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We present a computer-aided framework for proving concrete security bounds for cryptographic machine code implementations. The front-end of the framework is an interactive verification tool that extends the EasyCrypt framework to reason about relational properties of C-like programs extended with idealised probabilistic operations in the style of code-based security proofs. The framework also incorporates an extension of the CompCert certified compiler to support trusted libraries providing complex arithmetic calculations or instantiating idealised components such as sampling operations. This certified compiler allows us to carry to executable code the security guarantees established at the high-level, and is also instrumented to detect when compilation may interfere with side-channel countermeasures deployed in source code. We demonstrate the applicability of the framework with the RSA-OAEP encryption scheme, as standardized in PKCS#1 v2.1. The outcome is a rigorous analysis of the advantage of an adversary to break the security of assembly implementations of the algorithms specified by the standard. The example also provides two contributions of independent interest: it is the first application of computer-aided cryptographic tools to real-world security, and the first application of CompCert to cryptographic software. 1.
Universidad de Buenos Aires
"... Abstract. Many prior trust management frameworks provide authorization logics for specifying policies based on distributed trust. However, to implement a security protocol using these frameworks, one usually resorts to a general-purpose programming language. To reason about the security of the entir ..."
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Abstract. Many prior trust management frameworks provide authorization logics for specifying policies based on distributed trust. However, to implement a security protocol using these frameworks, one usually resorts to a general-purpose programming language. To reason about the security of the entire system, one must study not only policies in the authorization logic, but also hard-to-analyze implementation code. This paper proposes DKAL ⋆ , a language for constructing executable specifications of authorization protocols. Protocol and policy designers can use DKAL ⋆ ’s authorization logic for expressing distributed trust relationships, and its small rule-based programming language to describe the message sequence of a protocol. Importantly, many low-level details of the protocol (e.g., marshaling formats or management of state consistency) are left abstract in DKAL ⋆ , but sufficient details must be provided in order for the protocol to be executable. We formalize the semantics of DKAL ⋆ , giving it an operational semantics and a type system. We prove various properties of DKAL ⋆ , including type soundness and a decidability property for its underlying logic. We also present an interpreter for DKAL ⋆ , mechanically verified for correctness and security. We evaluate our work experimentally on several examples. 1
Automated Analysis and Synthesis of Padding-Based Encryption Schemes
, 2012
"... Verifiable security is an emerging approach in cryptography that advocates the use of principled tools for building machine-checked security proofs of cryptographic constructions. Existing tools following this approach, such as EasyCrypt or CryptoVerif, fall short of finding proofs automatically for ..."
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Verifiable security is an emerging approach in cryptography that advocates the use of principled tools for building machine-checked security proofs of cryptographic constructions. Existing tools following this approach, such as EasyCrypt or CryptoVerif, fall short of finding proofs automatically for many interesting constructions. In fact, devising automated methods for analyzing the security of large classes of cryptographic constructions is a long-standing problem which precludes a systematic exploration of the space of possible designs. This paper addresses this issue for padding-based encryption schemes, a class of public-key encryption schemes built from hash functions and trapdoor permutations, which includes widely used constructions such as RSA-OAEP. Firstly, we provide algorithms to search for proofs of security against chosen-plaintext and chosenciphertext attacks in the random oracle model. These algorithms are based on domain-specific logics with a computational interpretation and yield quantitative security guarantees; for proofs of chosen-plaintext security, we output machine-checked proofs in EasyCrypt. Secondly, we provide a crawler for exhaustively exploring the space of padding-based encryption schemes under user-specified restrictions (e.g. on the size of their description), using filters to prune the search space. Lastly, we provide a
Automatically Checking Commitment Protocols in ProVerif without False Attacks
"... Abstract. ProVerif over-approximates the attacker’s power to enable verification of processes under replication. Unfortunately, this results in ProVerif finding false attacks. This problem is particularly common in protocols whereby a participant commits to a particular value and later reveals their ..."
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Abstract. ProVerif over-approximates the attacker’s power to enable verification of processes under replication. Unfortunately, this results in ProVerif finding false attacks. This problem is particularly common in protocols whereby a participant commits to a particular value and later reveals their value. We introduce a method to reduce false attacks when analysing secrecy. First, we show how inserting phases into non-replicated processes enables a more accurate translation to Horn clauses which avoids some false attacks. Secondly, we generalise our methodology to processes under replication. Finally, we demonstrate the applicability of our technique by analysing BlueTooth Simple Pairing. Moreover, we propose a simplification of this protocol that achieves the same security goal. 1
