Private Multi-party Matrix Multiplication and Trust Computations

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose a protocol with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using ProVerif, a cryptographic protocol verification tool, we are able to check the security of the protocol and provide a countermeasure for each attack found by the tool. We also give a randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.Comment: Pierangela Samarati. SECRYPT 2016 : 13th International Conference on Security and Cryptography, Lisbonne, Portugal, 26--28 Juillet 2016. 201

Generating S-Boxes from Semi-fields Pseudo-extensions

Block ciphers, such as the AES, correspond to a very important family of secret-key cryptosystems. The security of such systems partly relies on what is called the S-box. This is a vectorial Boolean function f : F n 2 ֒→ F n 2 , where n is the size of the blocks. It is often the only non linear opera-tion in the algorithm. The most well-known attacks against block ciphers algorithms are the known-plaintext attacks called differential cryptanal-ysis [4, 10] and linear cryptanalysis [11]. To protect such cryptosystems against linear and differential attacks, S-boxes are designed to fulfill some cryptographic criteria (balancedness, high nonlinearity, high algebraic de-gree, avalanche, or transparency [2, 12]) and are usually defined on finite fields, like F2n [7, 3]. Unfortunately, it seems difficult to find good S-Boxes, at least for bijective ones: random generation does not work [8, 9] and the one used in the AES or Camellia are actually variations around a single function, the inverse function in F2n . Would the latter function have an unforeseen weakness (for instance if more practical algebraic attacks are developped), it would be desirable to have some replacement candidates. For that matter, we propose to weaken a little bit the algebraic part of the design of S-Boxes and use finite semi-fields instead of finite fields to build such S-Boxes. Finite semi-fields relax the associativity and com-mutativity of the multiplication law. While semi-fields of a given order are unique up to isomorphism, on the contrary semi-fields of a given order can be numerous: nowadays, on the one hand, it is for instance easy to generate all the 36 semi-fields of order 2 4 , but, on the other hand, it is not even known how many semi-fields are there of order 2 8 . Therefore, we propose to build S-Boxes via semi-fields pseudo extensions of the form S 2 2 4 , where S 2 4 is any semi-field of order 2 4 , and mimic in this structure the use of the inverse function in a finite field. We report here the construction of 10827 S-Boxes, 7052 non CCZ-equivalent, with maximal nonlinearity, differential invariants, degrees and bit interdependency. Among the latter 2963 had fix points, and among the ones without fix points, 3846 had the avalanche level of AES and 243 1 the better avalanche level of Camellia. Among the latter 232 have a better transparency level than the inverse function on a finite field

Trivial Transciphering With Trivium and TFHE

We examine the use of Trivium and Kreyvium as transciphering mechanisms for use with the TFHE FHE scheme. Originally these two ciphers were investigated for FHE transciphering only in the context of the BGV/BFV FHE schemes; this is despite Trivium and Kreyvium being particarly suited to TFHE. Recent work by Dobraunig et al. gave some initial experimental results using TFHE. We show that these two symmetric ciphers have excellent performance when homomorphically evaluated using TFHE. Indeed we improve upon the results of Dobraunig et al. by at least two orders of magnitude in terms of latency. This shows that, for TFHE at least, one can transcipher using a standardized symmetric cipher (Trivium), without the need for special FHE-friendly ciphers being employed. For applications wanting extra security, but without the benefit of relying on a standardized cipher, our work shows that Kreyvium is a good candidate

CONCRETE: Concrete Operates oN Ciphertexts Rapidly by Extending TfhE

International audienceFully homomorphic encryption (FHE) extends traditional encryption schemes. It allows one to directly compute on encrypted data without requiring access to the decryption key. This paper introduces CONCRETE, an open-source library developed in Rust that builds on the state-of-art TFHE cryptosystem. It provides a userfriendly interface making FHE easy to integrate. The library deals with inputs of arbitrary format and comes with an extensive set of operations to play with ciphertexts, including a programmable bootstrapping. CONCRETE is available on GitHub at URL https:// github.com/zama-ai/concrete and on https://crates.io

Faster Secret Keys for (T)FHE

GLWE secret keys come with some associated public information, like their size or the distribution probability of their coefficients. Those information have an impact on the FHE algorithms, their computational cost, their noise growth, and the overall security level. In this paper, we identify two limitations with (T)FHE: there is no fine-grained control over the size of a GLWE secret key, and there is a minimal noise variance which leads to an unnecessary increment of the level of security with large GLWE secret keys. We introduce two (non exclusive) new types of secret keys for GLWE-based cryptosystems, that are designed to overcome the aforementioned limitations. We explain why these are as secure as the traditional ones, and detail all the improvements that they brought to the FHE algorithms. We provide many comparisons with state-of-the-art TFHE techniques, and benchmarks showing computational speed-ups between $1.3$ and $2.4$ while keeping the same level of security and failure probability. Furthermore, the size of the public material (i.e., key switching and bootstrapping keys) is also reduced by factors from $1.5$ and $2.7$

Parameter Optimization & Larger Precision for (T)FHE

In theory, Fully Homomorphic Encryption schemes allow users to compute any operation over encrypted data. However in practice, one of the major difficulties lies into determining secure cryptographic parameters that minimize the computational cost of evaluating a circuit. In this paper, we propose a solution to solve this open problem. Even though it mainly focuses on TFHE, the method is generic enough to be adapted to all the current FHE schemes. TFHE is particularly suited, for small precision messages, from Boolean to 5-bit integers. It is possible to instantiate bigger integers with this scheme, however the computational cost quickly becomes unpractical. By studying the parameter optimization problem for TFHE, we observed that if one wants to evaluate operations on larger integers, the best way to do it is by encrypting the message into several ciphertexts, instead of considering bigger parameters for a single ciphertext. In the literature, one can find some constructions going in that direction, which are mainly based on radix and CRT representations of the message. However, they still present some limitations, such as inefficient algorithms to evaluate generic homomorphic lookup tables and no solution to work with arbitrary modulus for the message space. We overcome these limitations by proposing two new ways to evaluate homomorphic modular reductions for any modulo in the radix approach, by introducing on the one hand a new hybrid representation, and on the other hand by exploiting a new efficient algorithm to evaluate generic lookup tables on several ciphertexts. The latter is not only a programmable bootstrapping but does not require any padding bit, as needed in the original TFHE bootstrapping. We additionally provide benchmarks to support our results in practice. Finally, we formalize the parameter selection as an optimization problem, and we introduce a framework based on it enabling easy and efficient translation of an arithmetic circuit into an FHE graph of operation along with its optimal set of cryptographic parameters. This framework offers a plethora of features: fair comparisons between FHE operators, study of contexts that are favorable to a given FHE strategy/algorithm, failure probability selection for the entire use case, and so on

Security Architecture for Point-to-Point Splitting Protocols

International audienceThe security of industrial supervisory control and data acquisition systems (SCADA) has become a major concern since the Stuxnet worm in 2010. As these systems are connected to the physical world, this makes them possibly hazardous if a malicious attacker is able to take over their control. SCADA can live up to 40 years, are particularly hard to patch, and quite often have no security feature at all. Thus, rather than securing them, network segregation is often used to prevent attackers from entering the industrial system. In this paper, we propose a generic solution: embed a point-to-point splitting protocol within a physical device, thus able to physically isolate networks, perform deep packet inspection and also provide encryption if necessary. We obtain a kind of next generation firewall, encompassing at least both diode and firewall features, for which conformity to security policies can be ensured. Then we define a set of associated security properties for such devices and the requirements for such a device's security architecture and filtering rules. Finally, we propose a secure hardware implementation

Evaluation de la confiance dans les architectures de sécurité

In a increasingly connected world, trust in information systems is essential. Thus, many questions about their security arise. Topics of these questions include individual data confidentiality as well as protection of Industrial Critical Systems(ICS). For instance, ICS are deployed in sectors including energy or transportation where security is of high importance. In this thesis, we address three problems related to the security architecture of information systems. We first propose an architecture for a protocol splitting device. This provides protection against networkattacks by isolating and filtering data exchanges. We show that this new security equipment is well suited for ICS. Then, we focus on end-user security. We define a user-centric Public Key Infrastructure (PKI) called LocalPKI. By using self-signed certificates, this infrastructure combines the user-friendliness of PGP-based PKI and the security of hierarchical PKI. Finally, we improve the trust anchormechanism. It is employed by Certification Authorities (CA) and especially used in PKIX or LocalPKI. In that respect, we first define multi-party protocols to securely compute dot and matrix products. Then, we explain how to apply them on trust aggregations and thus on the reputation of certification authorities.Dans un monde de plus en plus connecté, la question de la confiance dans les sys-tèmes d’information qui nous entourent devient primordiale, et amène naturellement à des interrogations quant à leur sécurité. Les enjeux de cette dernière concernent autant la confidentialité des données individuelles que la protection des architectures critiques, notamment déployées dans le domaine de l’énergie et du transport. Dans cette thèse, nous abordons trois problématiques liées aux architectures de sécurité des systèmes d’information. Tout d’abord, nous proposons une architecture pour un module de rupture protocolaire, fournissant une protection face aux attaques utilisant le réseau comme vecteur. Grâce à l’isolation et le filtrage des échanges qu’il réalise, nous montrons que ce nouvel équipement est particulièrement adapté à la sécurisation des systèmes de contrôle-commandes. Nous abordons ensuite le thème de la sécurité des utilisateurs finaux ou objets connectés, par la définition d’une Infrastructure de Gestion de Clefs (IGC) centrée sur ces derniers, dénommée LocalPKI. Elle repose sur l’utilisation de certificats auto-signés, et son objectif est d’allier la simplicité des IGC pair-à-pair avec la sécurité des IGC hiérarchiques.Enfin, nous nous intéressons à l’amélioration du mécanisme des ancres de confiance pour les autorités de certification, utilisé par exemple dans PKIX et LocalPKI. A cet égard, nous commençons par définir des protocoles multi-parties permettant de calculer des produits scalaires et matriciels, préservant la confidentialité des données. Nous montrons finalement comment les appliquer dans le cadre de l’agrégation de confiance, et par conséquent à la réputation des autorités de certificatio

Trust evaluation in security architectures

Dans un monde de plus en plus connecté, la question de la confiance dans les sys-tèmes d’information qui nous entourent devient primordiale, et amène naturellement à des interrogations quant à leur sécurité. Les enjeux de cette dernière concernent autant la confidentialité des données individuelles que la protection des architectures critiques, notamment déployées dans le domaine de l’énergie et du transport. Dans cette thèse, nous abordons trois problématiques liées aux architectures de sécurité des systèmes d’information. Tout d’abord, nous proposons une architecture pour un module de rupture protocolaire, fournissant une protection face aux attaques utilisant le réseau comme vecteur. Grâce à l’isolation et le filtrage des échanges qu’il réalise, nous montrons que ce nouvel équipement est particulièrement adapté à la sécurisation des systèmes de contrôle-commandes. Nous abordons ensuite le thème de la sécurité des utilisateurs finaux ou objets connectés, par la définition d’une Infrastructure de Gestion de Clefs (IGC) centrée sur ces derniers, dénommée LocalPKI. Elle repose sur l’utilisation de certificats auto-signés, et son objectif est d’allier la simplicité des IGC pair-à-pair avec la sécurité des IGC hiérarchiques.Enfin, nous nous intéressons à l’amélioration du mécanisme des ancres de confiance pour les autorités de certification, utilisé par exemple dans PKIX et LocalPKI. A cet égard, nous commençons par définir des protocoles multi-parties permettant de calculer des produits scalaires et matriciels, préservant la confidentialité des données. Nous montrons finalement comment les appliquer dans le cadre de l’agrégation de confiance, et par conséquent à la réputation des autorités de certificationIn a increasingly connected world, trust in information systems is essential. Thus, many questions about their security arise. Topics of these questions include individual data confidentiality as well as protection of Industrial Critical Systems(ICS). For instance, ICS are deployed in sectors including energy or transportation where security is of high importance. In this thesis, we address three problems related to the security architecture of information systems. We first propose an architecture for a protocol splitting device. This provides protection against networkattacks by isolating and filtering data exchanges. We show that this new security equipment is well suited for ICS. Then, we focus on end-user security. We define a user-centric Public Key Infrastructure (PKI) called LocalPKI. By using self-signed certificates, this infrastructure combines the user-friendliness of PGP-based PKI and the security of hierarchical PKI. Finally, we improve the trust anchormechanism. It is employed by Certification Authorities (CA) and especially used in PKIX or LocalPKI. In that respect, we first define multi-party protocols to securely compute dot and matrix products. Then, we explain how to apply them on trust aggregations and thus on the reputation of certification authorities

Dual Protocols for Private Multi-party Matrix Multiplication and Trust Computations

International audienceThis paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose two dual protocols with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using cryptographic protocol verification tools, we are able to check the security of both protocols and provide a countermeasure for each attack found by the tools. We also give a generic randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes