Symbolically Analyzing Security Protocols Using Tamarin

During the last three decades, there has been considerable research devoted to the symbolic analysis of security protocols and existing tools have had considerable success both in detecting attacks on protocols and showing their absence. Nevertheless, there is still a large discrepancy between the symbolic models that one specifies on paper and the models that can be effectively analyzed by tools. In this paper, we present the Tamarin prover for the symbolic analysis of security protocols. Tamarin takes as input a security protocol model, specifying the actions taken by the agents running the protocol in different roles (e.g., the protocol initiator, the responder, and the trusted key server), a specification of the adversary, and a specification of the protocol’s desired properties. Tamarin can then be used to automatically construct a proof that the protocol fulfills its specified properties, even when arbitrarily many instances of the protocol’s roles are interleaved in parallel, together with the actions of the adversary

Automated Analysis in Generic Groups

This thesis studies automated methods for analyzing hardness assumptions in generic group models, following ideas of symbolic cryptography. We define a broad class of generic and symbolic group models for different settings---symmetric or asymmetric (leveled) k-linear groups - and prove \u27\u27computational soundness\u27\u27 theorems for the symbolic models. Based on this result, we formulate a master theorem that relates the hardness of an assumption to solving problems in polynomial algebra. We systematically analyze these problems identifying different classes of assumptions and obtain decidability and undecidability results. Then, we develop automated procedures for verifying the conditions of our master theorems, and thus the validity of hardness assumptions in generic group models. The concrete outcome is an automated tool, the Generic Group Analyzer, which takes as input the statement of an assumption, and outputs either a proof of its generic hardness or shows an algebraic attack against the assumption. Structure-preserving signatures are signature schemes defined over bilinear groups in which messages, public keys and signatures are group elements, and the verification algorithm consists of evaluating \u27\u27pairing-product equations\u27\u27. Recent work on structure-preserving signatures studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While the size of keys and signatures is crucial for many applications, another aspect of performance is the time it takes to verify a signature. The most expensive operation during verification is the computation of pairings. However, the concrete number of pairings is not captured by the number of pairing-product equations considered in earlier work. We consider the question of what is the minimal number of pairing computations needed to verify structure-preserving signatures. We build an automated tool to search for structure-preserving signatures matching a template. Through exhaustive search we conjecture lower bounds for the number of pairings required in the Type~II setting and prove our conjecture to be true. Finally, our tool exhibits examples of structure-preserving signatures matching the lower bounds, which proves tightness of our bounds, as well as improves on previously known structure-preserving signature schemes

Verification of Stateful Cryptographic Protocols with Exclusive OR

International audienceIn cryptographic protocols, in particular RFID protocols, exclusive-or (XOR) operations are common. Due to the inherent complexity of faithful models of XOR, there is only limited tool support for the verification of cryptographic protocols using XOR. In this paper, we improve the TAMARIN prover and its underlying theory to deal with an equational theory modeling XOR operations. The XOR theory can be combined with all equational theories previously supported, including user-defined equational theories. This makes TAMARIN the first verification tool for cryptographic protocols in the symbolic model to support simultaneously this large set of equational theories, protocols with global mutable state, an unbounded number of sessions, and complex security properties including observational equivalence. We demonstrate the effectiveness of our approach by analyzing several protocols that rely on XOR, in particular multiple RFID-protocols, where we can identify attacks as well as provide proofs

Cryptographic Pairings: Efficiency and DLP security

This thesis studies two important aspects of the use of pairings in cryptography, efficient algorithms and security. Pairings are very useful tools in cryptography, originally used for the cryptanalysis of elliptic curve cryptography, they are now used in key exchange protocols, signature schemes and Identity-based cryptography. This thesis comprises of two parts: Security and Efficient Algorithms. In Part I: Security, the security of pairing-based protocols is considered, with a thorough examination of the Discrete Logarithm Problem (DLP) as it occurs in PBC. Results on the relationship between the two instances of the DLP will be presented along with a discussion about the appropriate selection of parameters to ensure particular security level. In Part II: Efficient Algorithms, some of the computational issues which arise when using pairings in cryptography are addressed. Pairings can be computationally expensive, so the Pairing-Based Cryptography (PBC) research community is constantly striving to find computational improvements for all aspects of protocols using pairings. The improvements given in this section contribute towards more efficient methods for the computation of pairings, and increase the efficiency of operations necessary in some pairing-based protocol

Automated Unbounded Verification of Stateful Cryptographic Protocols with Exclusive OR

International audienceExclusive-or (XOR) operations are common in cryptographic protocols, in particular in RFID protocols and electronic payment protocols. Although there are numerous applications , due to the inherent complexity of faithful models of XOR, there is only limited tool support for the verification of cryptographic protocols using XOR.The TAMARIN prover is a state-of-the-art verification tool for cryptographic protocols in the symbolic model. In this paper, we improve the underlying theory and the tool to deal with an equational theory modeling XOR operations. The XOR theory can be freely combined with all equational theories previously supported, including user-defined equational theories. This makes TAMARIN the first tool to support simultaneously this large set of equational theories, protocols with global mutable state, an unbounded number of sessions, and complex security properties including observational equivalence. We demonstrate the effectiveness of our approach by analyzing several protocols that rely on XOR, in particular multiple RFID-protocols, where we can identify attacks as well as provide proofs

Function-specific schemes for verifiable computation

An integral component of modern computing is the ability to outsource data and computation to powerful remote servers, for instance, in the context of cloud computing or remote file storage. While participants can benefit from this interaction, a fundamental security issue that arises is that of integrity of computation: How can the end-user be certain that the result of a computation over the outsourced data has not been tampered with (not even by a compromised or adversarial server)? Cryptographic schemes for verifiable computation address this problem by accompanying each result with a proof that can be used to check the correctness of the performed computation. Recent advances in the field have led to the first implementations of schemes that can verify arbitrary computations. However, in practice the overhead of these general-purpose constructions remains prohibitive for most applications, with proof computation times (at the server) in the order of minutes or even hours for real-world problem instances. A different approach for designing such schemes targets specific types of computation and builds custom-made protocols, sacrificing generality for efficiency. An important representative of this function-specific approach is an authenticated data structure (ADS), where a specialized protocol is designed that supports query types associated with a particular outsourced dataset. This thesis presents three novel ADS constructions for the important query types of set operations, multi-dimensional range search, and pattern matching, and proves their security under cryptographic assumptions over bilinear groups. The scheme for set operations can support nested queries (e.g., two unions followed by an intersection of the results), extending previous works that only accommodate a single operation. The range search ADS provides an exponential (in the number of attributes in the dataset) asymptotic improvement from previous schemes for storage and computation costs. Finally, the pattern matching ADS supports text pattern and XML path queries with minimal cost, e.g., the overhead at the server is less than 4% compared to simply computing the result, for all our tested settings. The experimental evaluation of all three constructions shows significant improvements in proof-computation time over general-purpose schemes

Pairing computation on hyperelliptic curves of genus 2

Bilinear pairings have been recently used to construct cryptographic schemes with new and novel properties, the most celebrated example being the Identity Based Encryption scheme of Boneh and Franklin. As pairing computation is generally the most computationally intensive part of any painng-based cryptosystem, it is essential to investigate new ways in which to compute pairings efficiently. The vast majority of the literature on pairing computation focuscs solely on using elliptic curves. In this thesis we investigate pairing computation on supersingular hyperelliptic curves of genus 2 Our aim is to provide a practical alternative to using elliptic curves for pairing based cryptography. Specifically, we illustrate how to implement pairings efficiently using genus 2 curves, and how to attain performance comparable to using elliptic curves. We show that pairing computation on genus 2 curves over F2m can outperform elliptic curves by using a new variant of the Tate pairing, called the r¡j pairing, to compute the fastest pairing implementation in the literature to date We also show for the first time how the final exponentiation required to compute the Tate pairing can be avoided for certain hyperelliptic curves. We investigate pairing computation using genus 2 curves over large prime fields, and detail various techniques that lead to an efficient implementation, thus showing that these curves are a viable candidate for practical use

Geppetto: Versatile Verifiable Computation

Cloud computing sparked interest in Verifiable Computation protocols, which allow a weak client to securely outsource computations to remote parties. Recent work has dramatically reduced the client’s cost to verify the correctness of results, but the overhead to produce proofs largely remains impractical. Geppetto introduces complementary techniques for reducing prover overhead and increasing prover flexibility. With Multi-QAPs, Geppetto reduces the cost of sharing state between computations (e.g., for MapReduce) or within a single computation by up to two orders of magnitude. Via a careful instantiation of cryptographic primitives, Geppetto also brings down the cost of verifying outsourced cryptographic computations (e.g., verifiably computing on signed data); together with Geppetto’s notion of bounded proof bootstrapping, Geppetto improves on prior bootstrapped systems by five orders of magnitude, albeit at some cost in universality. Geppetto also supports qualitatively new properties like verifying the correct execution of proprietary (i.e., secret) algorithms. Finally, Geppetto’s use of energy-saving circuits brings the prover’s costs more in line with the program’s actual (rather than worst-case) execution time. Geppetto is implemented in a full-fledged, scalable compiler that consumes LLVM code generated from a variety of apps, as well as a large cryptographic library

Developing an Automatic Generation Tool for Cryptographic Pairing Functions

Pairing-Based Cryptography is receiving steadily more attention from industry, mainly because of the increasing interest in Identity-Based protocols. Although there are plenty of applications, efficiently implementing the pairing functions is often difficult as it requires more knowledge than previous cryptographic primitives. The author presents a tool for automatically generating optimized code for the pairing functions which can be used in the construction of such cryptographic protocols. In the following pages I present my work done on the construction of pairing function code, its optimizations and how their construction can be automated to ease the work of the protocol implementer. Based on the user requirements and the security level, the created cryptographic compiler chooses and constructs the appropriate elliptic curve. It identifies the supported pairing function: the Tate, ate, R-ate or pairing lattice/optimal pairing, and its optimized parameters. Using artificial intelligence algorithms, it generates optimized code for the final exponentiation and for hashing a point to the required group using the parametrisation of the chosen family of curves. Support for several multi-precision libraries has been incorporated: Magma, MIRACL and RELIC are already included, but more are possible