A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc. Errors in the CPs can lead to great financial and social damage, therefore it is necessary to use mathematical methods to justify the correctness and safety of the CPs. In this paper, a new mathematical model of a CP is introduced, which allows one to describe both the CPs and their properties. It is shown how, on the base of this model, it is possible to solve the problems of verification of CPs.
Cryptographic protocols with single blind copying were defined and modeled by Comon and Cortier using the new class $\mathcal C$ of first order clauses. They showed its satisfiability problem to be in 3-DEXPTIME. We improve this result by showing that satisfiability for this class is NEXPTIME-complete, using new resolution techniques. We show satisfiability to be DEXPTIME-complete if clauses are Horn, which is what is required for modeling cryptographic protocols. While translation to Horn clauses only gives a DEXPTIME upper bound for the secrecy problem for these protocols, we further show th…
Informal arguments that cryptographic protocols are secure can be made rigorous using inductive definitions. The approach is based on ordinary predicate calculus and copes with infinite-state systems. Proofs are generated using Isabelle/HOL. The human effort required to analyze a protocol can be as little as a week or two, yielding a proof script that takes a few minutes to run. Protocols are inductively defined as sets of traces. A trace is a list of communication events, perhaps comprising many interleaved protocol runs. Protocol descriptions incorporate attacks and accidental losses. The mo…
Consider the problem of verifying security properties of a cryptographic protocol coded in C. We propose an automatic solution that needs neither a pre-existing protocol description nor manual annotation of source code. First, symbolically execute the C program to obtain symbolic descriptions for the network messages sent by the protocol. Second, apply algebraic rewriting to obtain a process calculus description. Third, run an existing protocol analyser (ProVerif) to prove security properties or find attacks. We formalise our algorithm and appeal to existing results for ProVerif to establish c…
Analysis of cryptographic protocols in a symbolic model is relative to a deduction system that models the possible actions of an attacker regarding an execution of this protocol. We present in this paper a transformation algorithm for such deduction systems provided the equational theory has the finite variant property. the termination of this transformation entails the decidability of the ground reachability problems. We prove that it is necessary to add one other condition to obtain the decidability of non-ground problems, and provide one new such criterion.
Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing, etc. Errors in CPs can bring to great financial and social damage, therefore it is necessary to use mathematical methods to substantiate the correctness and safety of CPs. In this paper, a distributed process model of CPs is presented, which allows one to formally describe CPs and their properties. It is shown how to solve the problems of verification of CP…
Internet of Things (IoT) is a system that consists of a large number of smart devices connected through a network. The number of these devices is increasing rapidly, which creates a massive and complex network with a vast amount of data communicated over that network. One way to protect this data in transit, i.e., to achieve data confidentiality, is to use lightweight encryption algorithms for IoT protocols. However, the design and implementation of such protocols is an error-prone task; flaws in the implementation can lead to devastating security vulnerabilities. These vulnerabilities can be …
Type-flaw attacks and multi-protocol attacks on security protocols have been frequently reported in the literature. Heather et al. and Guttman et al. have proven that these could be prevented by tagging encrypted components with distinct constants in a standard protocol model with free message algebra and perfect encryption. However, most "real-world" protocols such as SSL 3.0 are designed with the Exclusive-OR (XOR) operator that possesses algebraic properties, breaking the free algebra assumption. These algebraic properties induce equational theories that need to be considered when analyzing…
We present a formal logic for quantitative reasoning about security properties of network protocols. The system allows us to derive concrete security bounds that can be used to choose key lengths and other security parameters. We provide axioms for reasoning about digital signatures and random nonces, with security properties based on the concrete security of signature schemes and pseudorandom number generators (PRG). The formal logic supports first-order reasoning and reasoning about protocol invariants, taking concrete security bounds into account. Proofs constructed in our logic also provid…
We introduce what --if some kind of group action exists-- is a truly (information theoretically) safe cryptographic communication system: a protocol which provides \emph{zero} information to any passive adversary having full access to the channel.
This work initiates an analysis of several cryptographic protocols from a rational point of view using a game-theoretical approach, which allows us to represent not only the protocols but also possible misbehaviours of parties. Concretely, several concepts of two-person games and of two-party cryptographic protocols are here combined in order to model the latters as the formers. One of the main advantages of analysing a cryptographic protocol in the game-theory setting is the possibility of describing improved and stronger cryptographic solutions because possible adversarial behaviours may be …
Current formal approaches have been successfully used to find design flaws in many security protocols. However, it is still challenging to automatically analyze protocols due to their large or infinite state spaces. In this paper, we propose a novel framework that can automatically verifying security protocols without any human intervention. Experimental results show that SmartVerif automatically verifies security protocols that cannot be automatically verified by existing approaches. The case study also validates the effectiveness of our dynamic strategy.
In this paper we propose a general definition of secrecy for cryptographic protocols in the Dolev-Yao model. We give a sufficient condition ensuring secrecy for protocols where rules have encryption depth at most two, that is satisfied by almost all practical protocols. The only allowed primitives in the class of protocols we consider are pairing and encryption with atomic keys. Moreover, we describe an algorithm of practical interest which transforms a cryptographic protocol into a secure one from the point of view of secrecy, without changing its original goal with respect to secrecy of nonc…
In this paper, we show a new tagging scheme for cryptographic protocol messages. Under this tagging, equational theories of operators such as exclusive-or, binary addition etc. are effectively disabled, when terms are unified. We believe that this result has a significant impact on protocol analysis and security, since unification is at the heart of symbolic protocol analysis. Hence, disabling equational theories in unification implies disabling them altogether in protocol analysis for most operators and theories.
Several of the basic cryptographic constructs have associated algebraic structures. Formal models proposed by Dolev and Yao to study the (unconditional) security of public key protocols form a group. The security of some types of protocols can be neatly formulated in this algebraic setting. We investigate classes of two-party protocols. We then consider extension of the formal algebraic framework to private-key protocols. We also discuss concrete realization of the formal models. In this case, we propose a definition in terms of pseudo-free groups.
This thesis presents an automated method for verifying security properties of protocol implementations written in the C language. We assume that each successful run of a protocol follows the same path through the C code, justified by the fact that typical security protocols have linear structure. We then perform symbolic execution of that path to extract a model expressed in a process calculus similar to the one used by the CryptoVerif tool. The symbolic execution uses a novel algorithm that allows symbolic variables to represent bitstrings of potentially unknown length to model incoming proto…
Encryption has increasingly been used in all applications for various purposes, but it also brings big challenges to network security. In this paper, we take first steps towards addressing some of these chal- lenges by introducing a novel system to identify key exchange protocols, which are usually required if encryption keys are not pre-shared. We ob- served that key exchange protocols yield certain patterns of high-entropy data blocks, e.g. as found in key material. We propose a multi-resolution approach of accurately detecting high-entropy data blocks and a method of generating scalable fin…
There is a large amount of work dedicated to the formal verification of security protocols. In this paper, we revisit and extend the NP-complete decision procedure for a bounded number of sessions. We use a, now standard, deducibility constraints formalism for modeling security protocols. Our first contribution is to give a simple set of constraint simplification rules, that allows to reduce any deducibility constraint system to a set of solved forms, representing all solutions (within the bound on sessions). As a consequence, we prove that deciding the existence of key cycles is NP-complete f…
We develop a theory of decidable inductive invariants for an infinite-state variant of the Applied pi-calculus, with applications to automatic verification of stateful cryptographic protocols with unbounded sessions/nonces. Since the problem is undecidable in general, we introduce depth-bounded protocols, a strict generalisation of a class from the literature, for which our decidable analysis is sound and complete. Our core contribution is a procedure to check that an invariant is inductive, which implies that every reachable configuration satisfies it. Our invariants can capture security prop…
In this paper, we show how practical the little theorem of witness functions is in detecting security flaws in some category of cryptographic protocols. We convey a formal analysis of the Needham-Schroeder symmetric-key protocol in the theory of witness functions. We show how it helps to teach about a security vulnerability in a given step of this protocol where the value of security of a particular sensitive ticket in a sent message unexpectedly plummets compared with its value when received. This vulnerability may be exploited by an intruder to mount a replay attack as described by Denning a…
In this paper, we present a new semi-decidable procedure to analyze cryptographic protocols for secrecy based on a new class of functions that we call: the Witness-Functions. A Witness-Function is a reliable function that guarantees the secrecy in any protocol proved increasing once analyzed by it. Hence, the problem of correctness becomes a problem of protocol growth. A Witness-Function operates on derivative messages in a role-based specification and introduces new derivation techniques. We give here the technical aspects of the Witness-Functions and we show how to use them in a semi-decidab…
In several critical military missions, more than one decision level are involved. These decision levels are often independent and distributed, and sensitive pieces of information making up the military mission must be kept hidden from one level to another even if all of the decision levels cooperate to accomplish the same task. Usually, a mission is negotiated through insecure networks such as the Internet using cryptographic protocols. In such protocols, few security properties have to be ensured. However, designing a secure cryptographic protocol that ensures several properties at once is a …
Proving that a cryptographic protocol is correct for secrecy is a hard task. One of the strongest strategies to reach this goal is to show that it is increasing, which means that the security level of every single atomic message exchanged in the protocol, safely evaluated, never deceases. Recently, two families of functions have been proposed to measure the security level of atomic messages. The first one is the family of interpretation-functions. The second is the family of witness-functions. In this paper, we show that the witness-functions are more efficient than interpretation-functions. W…
Much of the literature on rational cryptography focuses on analyzing the strategic properties of cryptographic protocols. However, due to the presence of computationally-bounded players and the asymptotic nature of cryptographic security, a definition of sequential rationality for this setting has thus far eluded researchers. We propose a new framework for overcoming these obstacles, and provide the first definitions of computational solution concepts that guarantee sequential rationality. We argue that natural computational variants of subgame perfection are too strong for cryptographic proto…
Numerous exploits of client-server protocols and applications involve modifying clients to behave in ways that untampered clients would not, such as crafting malicious packets. In this paper, we demonstrate practical verification of a cryptographic protocol client's messaging behavior as being consistent with the client program it is believed to be running. Moreover, we accomplish this without modifying the client in any way, and without knowing all of the client-side inputs driving its behavior. Our toolchain for verifying a client's messages explores multiple candidate execution paths in the…
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 co…
We describe how to verify security properties of C code for cryptographic protocols by using a general-purpose verifier. We prove security theorems in the symbolic model of cryptography. Our techniques include: use of ghost state to attach formal algebraic terms to concrete byte arrays and to detect collisions when two distinct terms map to the same byte array; decoration of a crypto API with contracts based on symbolic terms; and expression of the attacker model in terms of C programs. We rely on the general-purpose verifier VCC; we guide VCC to prove security simply by writing suitable heade…
The realm of this thesis is cryptographic protocol theory in the quantum world. We study the security of quantum and classical protocols against adversaries that are assumed to exploit quantum effects to their advantage. Security in the quantum world means that quantum computation does not jeopardize the assumption, underlying the protocol construction. But moreover, we encounter additional setbacks in the security proofs, which are mostly due to the fact that some well-known classical proof techniques are forbidden by certain properties of a quantum environment. Interestingly, we can exploit …
Key substitution vulnerable signature schemes are signature schemes that permit an intruder, given a public verification key and a signed message, to compute a pair of signature and verification keys such that the message appears to be signed with the new signature key. A digital signature scheme is said to be vulnerable to destructive exclusive ownership property (DEO) If it is computationaly feasible for an intruder, given a public verification key and a pair of message and its valid signature relatively to the given public key, to compute a pair of signature and verification keys and a new …
Several quantum process algebras have been proposed and successfully applied in verification of quantum cryptographic protocols. All of the bisimulations proposed so far for quantum processes in these process algebras are state-based, implying that they only compare individual quantum states, but not a combination of them. This paper remedies this problem by introducing a novel notion of distribution-based bisimulation for quantum processes. We further propose an approximate version of this bisimulation that enables us to prove more sophisticated security properties of quantum protocols which …
Online services commonly attempt to verify the legitimacy of users with CAPTCHAs. However, CAPTCHAs are annoying for users, often difficult for users to solve, and can be defeated using cheap labor or, increasingly, with improved algorithms. We propose a new protocol for clients to prove their legitimacy, allowing the client's devices to vouch for the client. The client's devices, and those in close proximity, provide a one-time passcode that is verified by the device manufacturer. This verification proves that the client has physical access to expensive and trusted devices, vouching for the c…
This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n-1 where n is the number of players, which is the minimum.
Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasona…
We present SCADE and Lustre models of the Message Authenticator Algorithm (MAA), which is one of the first cryptographic functions for computing a message authentication code. The MAA was adopted between 1987 and 2001, in international standards (ISO 8730 and ISO 8731-2), to ensure the authenticity and integrity of banking transactions. This paper discusses the choices and the challenges of our MAA implementations. Our SCADE and Lustre models validate 201 official test vectors for the MAA.
The technique considers a message as binary string on which a Efficient Cryptographic Protocol using Recursive Bitwise amd pairs of Bits of operation (RBPBO) is performed. A block of n bits is taken as an input stream, where n varies from 4 to 256, from a continuous stream of bits and the technique operates on it to generate the intermediate encrypted stream. This technique directly involves all the bits of blocks in a boolean operation and a session key. The same operation is performed repeatedly for different block sizes as per the specification of a session key to generate the final encrypt…
We introduce knowledge flow analysis, a simple and flexible formalism for checking cryptographic protocols. Knowledge flows provide a uniform language for expressing the actions of principals, assump- tions about intruders, and the properties of cryptographic primitives. Our approach enables a generalized two-phase analysis: we extend the two-phase theory by identifying the necessary and sufficient proper- ties of a broad class of cryptographic primitives for which the theory holds. We also contribute a library of standard primitives and show that they satisfy our criteria.
Security of cryptographic protocols can be analysed by creating a model in a formal language and verifying the model in a tool. All such tools focus on the last part of the analysis, verification, and the interpretation of the specification is only explained in papers. Rather, we focus on the interpretation and modelling part by presenting a tool to aid the cryptographer throughout the process and automatically generating code in a target language. We adopt a data-centric approach where the protocol design is stored in a structured way rather than as textual specifications. Previous work shows…
In this paper a secret message/image transmission technique has been proposed through (2, 2) visual cryptographic share which is non-interpretable in general. A binary image is taken as cover image and authenticating message/image has been fabricated into it through a hash function where two bits in each pixel within four bits from LSB of the pixel is embedded and as a result it converts the binary image to gray scale one. (2,2) visual cryptographic shares are generated from this converted gray scale image. During decoding shares are combined to regenerate the authenticated image from where th…
We propose MetaCP, a Meta Cryptography Protocol verification tool, as an automated tool simplifying the design of security protocols through a graphical interface. The graphical interface can be seen as a modern editor of a non-relational database whose data are protocols. The information of protocols are stored in XML, enjoying a fixed format and syntax aiming to contain all required information to specify any kind of protocol. This XML can be seen as an almost semanticless language, where different plugins confer strict semantics modelling the protocol into a variety of back-end verification…
Understanding the Usability of Cryptographic Verification Tools
Samsung R&D Institute Bangladesh（三星孟加拉研发中心）；Bangladesh University of Engineering and Technology（孟加拉国工程与技术大学）；Towson University（陶森大学）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）
Cryptographic protocols aim at securing communications over insecure networks such as the Internet, where dishonest users may listen to communications and interfere with them. A secure communication has a different meaning depending on the underlying application. It ranges from the confidentiality of a data to e.g. verifiability in electronic voting systems. Another example of a security notion is privacy. Formal symbolic models have proved their usefulness for analysing the security of protocols. Until quite recently, most results focused on trace properties like confidentiality or authentica…
This work is intended as an introduction to cryptographic security and a motivation for the widely used Quantum Key Distribution (QKD) security definition. We review the notion of security necessary for a protocol to be usable in a larger cryptographic context, i.e., for it to remain secure when composed with other secure protocols. We then derive the corresponding security criterion for QKD. We provide several examples of QKD composed in sequence and parallel with different cryptographic schemes to illustrate how the error of a composed protocol is the sum of the errors of the individual prot…
The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication. As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur. CONTENTS P3. Cryptographic systems before quantum cryptography P7. Preamble to quantum cryptography P10. The BB84 quantum cryptographic protocol without noise P16. The BB84 quantum cryptographic protocol with noise P19..The B92…
The level of trust accorded to certification authorities has been decreasing over the last few years as several cases of misbehavior and compromise have been observed. Log-based approaches, such as Certificate Transparency, ensure that fraudulent TLS certificates become publicly visible. However, a key element that log-based approaches still lack is a way for clients to verify that the log behaves in a consistent and honest manner. This task is challenging due to privacy, efficiency, and deployability reasons. In this paper, we propose the first (to the best of our knowledge) gossip protocols …
The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed.
Attacks on classical cryptographic protocols are usually modeled by allowing an adversary to ask queries from an oracle. Security is then defined by requiring that as long as the queries satisfy some constraint, there is some problem the adversary cannot solve, such as compute a certain piece of information. In this paper, we introduce a fundamentally new model of quantum attacks on classical cryptographic protocols, where the adversary is allowed to ask several classical queries in quantum superposition. This is a strictly stronger attack than the standard one, and we consider the security of…
