Computer-Aided Cryptographic Proofs

International audienceProvable security [6] is at the heart of modern cryptography. It advocates a mathematical approach in which the security of new cryptographic constructions is defined rigorously, and provably reduced to one or several assumptions, such as the hardness of a computational problem, or the existence of an ideal functionality. A typical provable security statement is of the form: for all adversary against the cryptographic construction TeX , there exists an adversary TeX against a security assumption TeX , such that if TeX has a high probability of breaking the scheme TeX in time t, then TeX has a high probability of breaking the assumption TeX in time t′ (defined as a function of t)

Denial-of-Service Resistance in Key Establishment

Denial of Service (DoS) attacks are an increasing problem for network connected systems. Key establishment protocols are applications that are particularly vulnerable to DoS attack as they are typically required to perform computationally expensive cryptographic operations in order to authenticate the protocol initiator and to generate the cryptographic keying material that will subsequently be used to secure the communications between initiator and responder. The goal of DoS resistance in key establishment protocols is to ensure that attackers cannot prevent a legitimate initiator and responder deriving cryptographic keys without expending resources beyond a responder-determined threshold. In this work we review the strategies and techniques used to improve resistance to DoS attacks. Three key establishment protocols implementing DoS resistance techniques are critically reviewed and the impact of misapplication of the techniques on DoS resistance is discussed. Recommendations on effectively applying resistance techniques to key establishment protocols are made

Automated Cryptographic Analysis of the Pedersen Commitment Scheme

Aiming for strong security assurance, recently there has been an increasing interest in formal verification of cryptographic constructions. This paper presents a mechanised formal verification of the popular Pedersen commitment protocol, proving its security properties of correctness, perfect hiding, and computational binding. To formally verify the protocol, we extended the theory of EasyCrypt, a framework which allows for reasoning in the computational model, to support the discrete logarithm and an abstraction of commitment protocols. Commitments are building blocks of many cryptographic constructions, for example, verifiable secret sharing, zero-knowledge proofs, and e-voting. Our work paves the way for the verification of those more complex constructions.Comment: 12 pages, conference MMM-ACNS 201

On the Cryptographic Hardness of Local Search

We show new hardness results for the class of Polynomial Local Search problems (PLS): - Hardness of PLS based on a falsifiable assumption on bilinear groups introduced by Kalai, Paneth, and Yang (STOC 2019), and the Exponential Time Hypothesis for randomized algorithms. Previous standard model constructions relied on non-falsifiable and non-standard assumptions. - Hardness of PLS relative to random oracles. The construction is essentially different than previous constructions, and in particular is unconditionally secure. The construction also demonstrates the hardness of parallelizing local search. The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property

Computer-aided proofs for multiparty computation with active security

Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas such as auctioning, email filtering, and secure teleconference. Given its importance, it is crucial that the protocols are specified and implemented correctly. In the programming language community it has become good practice to use computer proof assistants to verify correctness proofs. In the field of cryptography, EasyCrypt is the state of the art proof assistant. It provides an embedded language for probabilistic programming, together with a specialized logic, embedded into an ambient general purpose higher-order logic. It allows us to conveniently express cryptographic properties. EasyCrypt has been used successfully on many applications, including public-key encryption, signatures, garbled circuits and differential privacy. Here we show for the first time that it can also be used to prove security of MPC against a malicious adversary. We formalize additive and replicated secret sharing schemes and apply them to Maurer's MPC protocol for secure addition and multiplication. Our method extends to general polynomial functions. We follow the insights from EasyCrypt that security proofs can be often be reduced to proofs about program equivalence, a topic that is well understood in the verification of programming languages. In particular, we show that in the passive case the non-interference-based definition is equivalent to a standard game-based security definition. For the active case we provide a new NI definition, which we call input independence

Verifying privacy by little interaction and no process equivalence

While machine-assisted verification of classical security goals such as confidentiality and authentication is well-established, it is less mature for recent ones. Electronic voting protocols claim properties such as voter privacy. The most common modelling involves indistinguishability, and is specified via trace equivalence in cryptographic extensions of process calculi. However, it has shown restrictions. We describe a novel model, based on unlinkability between two pieces of information. Specifying it as an extension to the Inductive Method allows us to establish voter privacy without the need for approximation or session bounding. The two models and their latest specifications are contrasted

On formal verification of arithmetic-based cryptographic primitives

Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to computationally hard problems. Those reductions can be subtle and tedious, and thus not easily checkable. On top of the proof assistant Coq, we had implemented in previous work a toolbox for writing and checking game-based security proofs of cryptographic primitives. In this paper we describe its extension with number-theoretic capabilities so that it is now possible to write and check arithmetic-based cryptographic primitives in our toolbox. We illustrate our work by machine checking the game-based proofs of unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and semantic security of the public-key cryptographic scheme of Goldwasser and Micali.Comment: 13 page

Towards mechanized correctness proofs for cryptographic algorithms: Axiomatization of a probabilistic Hoare style logic

In [Corin, den Hartog in ICALP 2006] we build a formal verification technique for game based correctness proofs of cryptograhic algorithms based on a probabilistic Hoare style logic [den Hartog, de Vink in IJFCS 13(3), 2002]. An important step towards enabling mechanized verification within this technique is an axiomatization of implication between predicates which is purely semantically defined in [den Hartog, de Vink in IJFCS 13(3), 2002]. In this paper we provide an axiomatization and illustrate its place in the formal verification technique of [Corin, den Hartog in ICALP 2006]