Certified Reasoning with Infinity

Sharma, Asankhaya; Wang, Shengyi; Costea, Andreea; Hobor, Aquinas; Chin, Wei-Ngan

doi:10.1007/978-3-319-19249-9_31

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…Another static analysis based approach by Moy et al (Moy et al, 2009) uses the Z3 solver to do integer overflow checking as part of the PREFIX tool (Bush et al, 2000). A certified prover for presburger arithmetic extended with positive and negative infinities has been described in (Sharma, 2015;Sharma et al, 2015).…”

Section: Related Workmentioning

confidence: 99%

Automated Verification of Integer Overflow

Sharma

2019

Preprint

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Integer overflow accounts for one of the major source of bugs in software. Verification systems typically assume a well defined underlying semantics for various integer operations and do not explicitly check for integer overflow in programs. In this paper we present a specification mechanism for expressing integer overflow. We develop an automated procedure for integer overflow checking during program verification. We have implemented a prototype integer overflow checker and tested it on a benchmark consisting of already verified programs (over 14k LOC). We have found 43 bugs in these programs due to integer overflow.

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Section: Related Workmentioning

confidence: 99%

Automated Verification of Integer Overflow

Sharma

2019

Preprint

Self Cite

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“…Our implementation brings several contributions of independent interest, including an improvement of the memory restriction system of EasyCrypt, and a library and automation support to reason about extended integers that are used for reasoning about cost. For the latter we follow [31] and reduce formulae about extended integers to integer formulae that can be sent to SMT solvers. Another key step is to embed our Hoare logic for cost into the ambient higher-order logic-similar to what is done for the other program logics of EasyCrypt.…”

Section: Introductionmentioning

confidence: 99%

Mechanized Proofs of Adversarial Complexity and Application to Universal Composability

Barbosa

Barthe

Grégoire

et al. 2023

ACM Trans. Priv. Secur.

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In this paper we enhance the EasyCrypt proof assistant to reason about computational complexity of adversaries. The key technical tool is a Hoare logic for reasoning about computational complexity (execution time and oracle calls) of adversarial computations. Our Hoare logic is built on top of the module system used by EasyCrypt for modeling adversaries. We prove that our logic is sound w.r.t. the semantics of EasyCrypt programs — we also provide full semantics for the EasyCrypt module system, which was previously lacking. We showcase (for the first time in EasyCrypt and in other computer-aided cryptographic tools) how our approach can express precise relationships between the probability of adversarial success and their execution time. In particular, we can quantify existentially over adversaries in a complexity class, and express general composition statements in simulation-based frameworks. Moreover, such statements can be composed to derive standard concrete security bounds for cryptographic constructions whose security is proved in a modular way. As a main benefit of our approach, we revisit security proofs of some well-known cryptographic constructions and we present a new formalization of Universal Composability (UC).

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Mechanized Proofs of Adversarial Complexity and Application to Universal Composability

Barbosa

Barthe

Grégoire

et al. 2021

Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security

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In this paper we enhance the EasyCrypt proof assistant to reason about computational complexity of adversaries. The key technical tool is a Hoare logic for reasoning about computational complexity (execution time and oracle calls) of adversarial computations. Our Hoare logic is built on top of the module system used by EasyCrypt for modeling adversaries. We prove that our logic is sound w.r.t. the semantics of EasyCrypt programs -we also provide full semantics for the EasyCrypt module system, which was previously lacking.We showcase (for the first time in EasyCrypt and in other computer-aided cryptographic tools) how our approach can express precise relationships between the probability of adversarial success and their execution time. In particular, we can quantify existentially over adversaries in a complexity class, and express general composition statements in simulation-based frameworks. Moreover, such statements can be composed to derive standard concrete security bounds for cryptographic constructions whose security is proved in a modular way. As a main benefit of our approach, we revisit security proofs of some well-known cryptographic constructions and we present a new formalization of Universal Composability (UC).

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Certified Reasoning with Infinity

Cited by 4 publications

References 19 publications

Automated Verification of Integer Overflow

Automated Verification of Integer Overflow

Mechanized Proofs of Adversarial Complexity and Application to Universal Composability

Mechanized Proofs of Adversarial Complexity and Application to Universal Composability

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