Formal Verification of Arithmetic Circuits by Function Extraction

Yu, Cunxi; Brown, W. E.; Liu, Duo; Rossi, André; Ciesielski, Maciej

doi:10.1109/tcad.2016.2547898

Cited by 50 publications

(72 citation statements)

References 29 publications

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“…In our implementation, the high-level gate instantiation oracle produces optimized gates, tailored for multiparty computation applications similar to those used by CBMC-GC, and which we assume to be correct down to extensive testing. Formally verifying the implementations of these gates can be done, e.g., by using the approach in [58]. We leave this for future work.…”

Section: Back-end Compiler Passesmentioning

confidence: 99%

A Fast and Verified Software Stack for Secure Function Evaluation

Almeida

Barbosa

Barthe

et al. 2017

Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security

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We present a high-assurance software stack for secure function evaluation (SFE). Our stack consists of three components: i. a verified compiler (CircGen) that translates C programs into Boolean circuits; ii. a verified implementation of Yao's SFE protocol based on garbled circuits and oblivious transfer; and iii. transparent application integration and communications via FRESCO, an open-source framework for secure multiparty computation (MPC). CircGen is a general purpose tool that builds on CompCert, a verified optimizing compiler for C. It can be used in arbitrary Boolean circuit-based cryptography deployments. The security of our SFE protocol implementation is formally verified using EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, and it leverages a new formalization of garbled circuits based on the framework of Bellare, Hoang, and Rogaway (CCS 2012). We conduct a practical evaluation of our approach, and conclude that it is competitive with state-of-the-art (unverified) approaches. Our work provides concrete evidence of the feasibility of building efficient, verified, implementations of higher-level cryptographic systems. All our development is publicly available.

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Section: Back-end Compiler Passesmentioning

confidence: 99%

A Fast and Verified Software Stack for Secure Function Evaluation

Almeida

Barbosa

Barthe

et al. 2017

Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security

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“…Several state-of-theart SAT and SMT solvers have been applied to those problems, including MiniSAT [23], Lingeling [1], Boolector [16], and others. However, the complexity of ACEC for large arithmetic circuits has been shown to be extremely high [18] [25]. Alternatively, the problem can be modeled as equivalence checking against an arithmetic specification given by a bit-vector formula, but the complexity of this method is the same as the ACEC method [25].…”

Section: Background 21 Formal Verification Of Arithmetic Circuitsmentioning

confidence: 99%

“…Computer algebra methods are considered to be best suited to solve arithmetic verification problems [25] [19]. Using these methods, the verification problem is formulated as a proof obligation, stating that the implementation satisfies the specification [5, 17-19, 21, 25?…”

Section: Computer Algebra Approachmentioning

confidence: 99%

“…A comprehensive review of the state-of-the-art computer algebra methods for arithmetic circuit verification can be found in [19]. The authors formally prove soundness and completeness of the two complementary approaches: the polynomial rewriting method of [25] [21] and the ideal membership testing of [17]. The difficulties of verifying bit-optimized and technology mapped multipliers have been discussed as well.…”

Section: Computer Algebra Approachmentioning

confidence: 99%

“…There has been a considerable progress in formal verification of arithmetic designs in the last decade. In particular, computer algebra techniques that use polynomial representation of a gate-level arithmetic circuit, show significant advantages in analyzing arithmetic circuits [17][5] [25] [18][21] [19]. This is in contrast to other formal methods, such as BDDs or SAT, that rely on a strictly Boolean circuit representation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral approach to verifying non-linear arithmetic circuits

Yu¹,

Su²,

Yasin³

et al. 2019

Proceedings of the 24th Asia and South Pacific Design Automation Conference

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This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of polynomial expression; it uses the distribution of coefficients of the monomials to determine the type of arithmetic function under verification. In contrast to previous works, the proof of functional correctness is achieved by computing an algebraic spectrum combined with local rewriting of word-level polynomials. The speedup is achieved by propagating coefficients through the circuit using And-Inverter Graph (AIG) datastructure. The effectiveness of the method is demonstrated with experiments including standard and Booth multipliers, and other synthesized non-linear arithmetic circuits up to 1024 bits containing over 12 million gates.

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