Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

Smart contracts are computer programs that can be correctly executed by a network of mutually distrusting nodes, without the need of an external trusted authority. Since smart contracts handle and transfer assets of considerable value, besides their correct execution it is also crucial that their implementation is secure against attacks which aim at stealing or tampering the assets. We study this problem in Ethereum, the most well-known and used framework for smart contracts so far. We analyse the security vulnerabilities of Ethereum smart contracts, providing a taxonomy of common programming pitfalls which may lead to vulnerabilities. We show a series of attacks which exploit these vulnerabilities, allowing an adversary to steal money or cause other damage.

A Survey of Attacks on Ethereum Smart Contracts SoK

/pdf/a-survey-of-attacks-on-ethereum-smart-contracts-43l3b2jez9.pdf

A survey of attacks on Ethereum smart contracts.

Permissionless blockchains allow the execution of arbitrary programs (called smart contracts), enabling mutually untrusted entities to interact without relying on trusted third parties. Despite their potential, repeated security concerns have shaken the trust in handling billions of USD by smart contracts. To address this problem, we present Securify, a security analyzer for Ethereum smart contracts that is scalable, fully automated, and able to prove contract behaviors as safe/unsafe with respect to a given property. Securify's analysis consists of two steps. First, it symbolically analyzes the contract's dependency graph to extract precise semantic information from the code. Then, it checks compliance and violation patterns that capture sufficient conditions for proving if a property holds or not. To enable extensibility, all patterns are specified in a designated domain-specific language. Securify is publicly released, it has analyzed >18K contracts submitted by its users, and is regularly used to conduct security audits by experts. We present an extensive evaluation of Securify over real-world Ethereum smart contracts and demonstrate that it can effectively prove the correctness of smart contracts and discover critical violations.

/pdf/securify-practical-security-analysis-of-smart-contracts-3m9isitgew.pdf

Securify: Practical Security Analysis of Smart Contracts

A privacy preserving association rule mining algorithm was introducedThis algorithm preserved privacy of individual values by computing scalar productMeanwhile the algorithm of computing scalar product was given and the security was analyzed

Privacy preserving association rule mining in vertically partitioned data

EasyCrypt is a tool-assisted framework for reasoning about probabilistic computations in the presence of adversarial code, whose main application has been the verification of security properties of cryptographic constructions in the computational model. We report on a significantly enhanced version of EasyCrypt that accommodates a richer, user-extensible language of probabilistic expressions and, more fundamentally, supports reasoning about approximate forms of program equivalence. This enhanced framework allows us to express a broader range of security properties, that notably include approximate and computational differential privacy. We illustrate the use of the framework by verifying two protocols: a two-party protocol for computing the Hamming distance between bit-vectors, yielding two-sided privacy guarantees; and a novel, efficient, and privacy-friendly distributed protocol to aggregate smart meter readings into statistics and bills.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/easypriv.pdf

Verified Computational Differential Privacy with Applications to Smart Metering

The TLS Internet Standard features a mixed bag of cryptographic algorithms and constructions, letting clients and servers negotiate their use for each run of the handshake. Although many ciphersuites are now well-understood in isolation, their composition remains problematic, and yet it is critical to obtain practical security guarantees for TLS, as all mainstream implementations support multiple related runs of the handshake and share keys between algorithms.

/pdf/proving-the-tls-handshake-secure-as-it-is-1o6codj8yk.pdf

Proving the TLS Handshake Secure (As It Is)

We design and prototype protocols for processing smart-meter readings while preserving user privacy We provide support for computing non-linear functions on encrypted readings, implemented by adapting to our setting efficient secret-sharing-based secure multi-party computation techniques Meter readings are jointly processed by a (public) storage service and a few independent authorities, each owning an additive share of the readings For non-linear processing, these parties consume pre-shared materials, produced by an off-line trusted third party This party never processes private readings; it may be implemented using trusted hardware or somewhat homomorphic encryption The protocol involves minimal, off-line support from the meters---a few keyed hash computations and no communication overhead

/pdf/smart-meter-aggregation-via-secret-sharing-4nj5y5dgah.pdf

Smart meter aggregation via secret-sharing

We present Low*, a language for low-level programming and verification, and its application to high-assurance optimized cryptographic libraries. Low* is a shallow embedding of a small, sequential, well-behaved subset of C in F*, a dependently-typed variant of ML aimed at program verification. Departing from ML, Low* does not involve any garbage collection or implicit heap allocation; instead, it has a structured memory model a la CompCert, and it provides the control required for writing efficient low-level security-critical code. 
By virtue of typing, any Low* program is memory safe. In addition, the programmer can make full use of the verification power of F* to write high-level specifications and verify the functional correctness of Low* code using a combination of SMT automation and sophisticated manual proofs. At extraction time, specifications and proofs are erased, and the remaining code enjoys a predictable translation to C. We prove that this translation preserves semantics and side-channel resistance. 
We provide a new compiler back-end from Low* to C and, to evaluate our approach, we implement and verify various cryptographic algorithms, constructions, and tools for a total of about 28,000 lines of code, specification and proof. We show that our Low* code delivers performance competitive with existing (unverified) C cryptographic libraries, suggesting our approach may be applicable to larger-scale low-level software.

Verified Low-Level Programming Embedded in F*

The record layer is the main bridge between TLS applications and internal sub-protocols. Its core functionality is an elaborate form of authenticated encryption: streams of messages for each sub-protocol (handshake, alert, and application data) are fragmented, multiplexed, and encrypted with optional padding to hide their lengths. Conversely, the sub-protocols may provide fresh keys or signal stream termination to the record layer. Compared to prior versions, TLS 1.3 discards obsolete schemes in favor of a common construction for Authenticated Encryption with Associated Data (AEAD), instantiated with algorithms such as AES-GCM and ChaCha20-Poly1305. It differs from TLS 1.2 in its use of padding, associated data and nonces. It also encrypts the content-type used to multiplex between sub-protocols. New protocol features such as early application data (0-RTT and 0.5-RTT) and late handshake messages require additional keys and a more general model of stateful encryption. We build and verify a reference implementation of the TLS record layer and its cryptographic algorithms in F*, a dependently typed language where security and functional guarantees can be specified as pre-and post-conditions. We reduce the high-level security of the record layer to cryptographic assumptions on its ciphers. Each step in the reduction is verified by typing an F* module, for each step that involves a cryptographic assumption, this module precisely captures the corresponding game. We first verify the functional correctness and injectivity properties of our implementations of one-time MAC algorithms (Poly1305 and GHASH) and provide a generic proof of their security given these two properties. We show the security of a generic AEAD construction built from any secure one-time MAC and PRF. We extend AEAD, first to stream encryption, then to length-hiding, multiplexed encryption. Finally, we build a security model of the record layer against an adversary that controls the TLS sub-protocols. We compute concrete security bounds for the AES_128_GCM, AES_256_GCM, and CHACHA20_POLY1305 ciphersuites, and derive recommended limits on sent data before re-keying. We plug our implementation of the record layer into the miTLS library, confirm that they interoperate with Chrome and Firefox, and report initial performance results. Combining our functional correctness, security, and experimental results, we conclude that the new TLS record layer (as described in RFCs and cryptographic standards) is provably secure, and we provide its first verified implementation.

/pdf/implementing-and-proving-the-tls-1-3-record-layer-2cy0nyvuvy.pdf

Santiago Zanella-Béguelin

Papers

Verified Computational Differential Privacy with Applications to Smart Metering

Proving the TLS Handshake Secure (As It Is)

Smart meter aggregation via secret-sharing

Verified Low-Level Programming Embedded in F*

Implementing and Proving the TLS 1.3 Record Layer