In this paper, we extend Inner-Product Functional Encryption (IPFE), where there is just a vector in the key and a vector in the single sender's ciphertext, to two-client ciphertexts. More precisely, in our two-client functional encryption scheme, there are two Data Providers who can independently encrypt vectors x and y for a data consumer who can, from a functional decryption key associated to a vector α, compute ∑αi xiyi = x ⋅ Diag(α) ⋅ yT. Ciphertexts are linear in the dimension of the vectors, whereas the functional decryption keys are of constant size. We study two interesting particular cases:

Abstract We propose AriaNN, a low-interaction privacy-preserving framework for private neural network training and inference on sensitive data. Our semi-honest 2-party computation protocol (with a trusted dealer) leverages function secret sharing, a recent lightweight cryptographic protocol that allows us to achieve an efficient online phase. We design optimized primitives for the building blocks of neural networks such as ReLU, MaxPool and BatchNorm. For instance, we perform private comparison for ReLU operations with a single message of the size of the input during the online phase, and with preprocessing keys close to 4× smaller than previous work. Last, we propose an extension to support n-party private federated learning. We implement our framework as an extensible system on top of PyTorch that leverages CPU and GPU hardware acceleration for cryptographic and machine learning operations. We evaluate our end-to-end system for private inference between distant servers on standard neural networks such as AlexNet, VGG16 or ResNet18, and for private training on smaller networks like LeNet. We show that computation rather than communication is the main bottleneck and that using GPUs together with reduced key size is a promising solution to overcome this barrier.

Decision forests are classical models to efficiently make decision on complex inputs with multiple features. While the global structure of the trees or forests is public, sensitive information have to be protected during the evaluation of some client inputs with respect to some server model. Indeed, the comparison thresholds on the server side may have economical value while the client inputs might be critical personal data. In addition, soundness is also important for the receiver. In our case, we will consider the server to be interested in the outcome of the model evaluation so that the client should not be able to bias it. In this paper, we propose a new offline/online protocol between a client and a server with a constant number of rounds in the online phase, with both privacy and soundness against malicious clients.

This note is a corrigendum for the paper ‘Public‐key encryption indistinguishable under plaintext‐checkable attacks’, IET Information Security (2016), 10(6): 288, http://doi.org/10.1049/iet‐ifs.2015.0500 .

Machine learning on encrypted data has received a lot of attention thanks to recent breakthroughs in homomorphic encryption and secure multi-party computation. It allows outsourcing computation to untrusted servers without sacrificing privacy of sensitive data. We propose a practical framework to perform partially encrypted and privacy-preserving predictions which combines adversarial training and functional encryption. We first present a new functional encryption scheme to efficiently compute quadratic functions so that the data owner controls what can be computed but is not involved in the calculation: it provides a decryption key which allows one to learn a specific function evaluation of some encrypted data. We then show how to use it in machine learning to partially encrypt neural networks with quadratic activation functions at evaluation time and we provide a thorough analysis of the information leaks based on indistinguishability of data items of the same label. Last, since several encryption schemes cannot deal with the last thresholding operation used for classification, we propose a training method to prevent selected sensitive features from leaking which adversarially optimizes the network against an adversary trying to identify these features. This is of great interest for several existing works using partially encrypted machine learning as it comes with almost no cost on the model's accuracy and significantly improves data privacy.

Functional encryption is a nice tool that bridges the gap between usability and privacy when providing access to huge databases: while being encrypted, aggregated information is available with a fine-tuned control by the owner of the database who can specify the functions he allows users to compute on the data. Unfortunately, giving access to several functions might leak too much information on the database, since once the decryption capability is given for a specific function, this is for an unlimited number of ciphertexts. In the particular case of the inner-product, if rows or records of the database contain l fields on which one got l independent inner-product capabilities, one can extract all the individual fields. On the other hand, the major applications that make use of inner-products, such as machine-learning, need to compute many of them.

PAKE protocols, for Password-Authenticated Key Exchange, enable two parties to establish a shared cryptographically strong key over an insecure network using a short common secret as authentication means. After the seminal work by Bellovin and Merritt, with the famous EKE, for Encrypted Key Exchange, various settings and security notions have been defined, and many protocols have been proposed.

We propose the first user authentication and key exchange protocols that can tolerate strong corruptions on the client-side. If a user happens to log in to a server from a terminal that has been fully compromised, then the other past and future user's sessions initiated from honest terminals stay secure. We define the security model for Human Authenticated Key Exchange HAKE) protocols and first propose two generic protocols based on human-compatible (HC) function family, password-authenticated key exchange (PAKE), commitment, and authenticated encryption. We prove our HAKE protocols secure under reasonable assumptions and discuss efficient instantiations. We thereafter propose a variant where the human gets help from a small device such as RSA SecurID. This permits to implement an HC function family with stronger security and thus allows to weaken required assumptions on the PAKE. This leads to the very efficient HAKE which is still secure in case of strong corruptions. We believe that our work will promote further developments in the area of human-oriented cryptography.

Indistinguishability under chosen‐ciphertext attack (IND‐CCA) is now considered the de facto security notion for public‐key encryption. However, this sometimes offers a stronger security guarantee than what is needed. In this study, the authors consider a weaker security notion, termed as indistinguishability under plaintext‐checking attacks (IND‐PCA), in which the adversary has only access to an oracle indicating whether or not a given ciphertext encrypts a given message. After formalising this notion, the authors design a new public‐key encryption scheme satisfying it. The new scheme is a variant of the Cramer–Shoup encryption scheme with shorter ciphertexts. Its security is also based on the plain decisional Diffie–Hellman (DDH) assumption. Additionally, the algebraic properties of the new scheme allow proving plaintext knowledge using Groth–Sahai non‐interactive zero‐knowledge proofs or smooth projective hash functions. Finally, as a concrete application, the authors show that, for many password‐based authenticated key exchange (PAKE) schemes in the Bellare–Pointcheval–Rogaway security model, they can safely replace the underlying IND‐CCA encryption schemes with their new IND‐PCA one. By doing so, they reduce the overall communication complexity of these protocols and obtain the most efficient PAKE schemes to date based on plain DDH.

Divisible e‐cash systems allow users to withdraw a unique coin of value 2 n units from a bank, but then to spend it in several times to distinct merchants. In such a system, whereas users want anonymity of their transactions, the bank wants to prevent, or at least detect, double‐spending, and trace defrauders. While this primitive was introduced two decades ago, quite a few (really) anonymous constructions have been proposed. In addition, all but one were just proven secure in the random oracle model, but still with either weak security models or quite complex settings and thus costly constructions. The unique proposal, secure in the standard model, appeared recently and is unpractical. As evidence, the authors left the construction of an efficient scheme secure in this model as an open problem. In this study, the authors answer it with the first efficient divisible e‐cash system secure in the standard model. It is based on a new way of building the coins, with a unique and public global tree structure for all the coins. Actually, they propose two constructions which offer a tradeoff between efficiency and security. They both achieve constant time for withdrawing and spending amounts of 2 ℓ units, while allowing the bank to quickly detect double‐spendings by a simple comparison of the serial numbers of deposited coins to the ones of previously spent coins.

A pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. A formal security model for PRNGs with input was proposed in 2005 by Barak and Halevi (BH). This model involves an internal state that is refreshed with a (potentially biased) external random source, and a cryptographic function that outputs random numbers from the continually internal state. In this work we extend the BH model to also include a new security property capturing how it should accumulate the entropy of the input data into the internal state after state compromise. This property states that a good PRNG should be able to eventually recover from compromise even if the entropy is injected into the system at a very slow pace, and expresses the real-life expected behavior of existing PRNG designs. Unfortunately, we show that neither the model nor the specific PRNG construction proposed by BH meet this new property, despite meeting a weaker robustness notion introduced by BH. From a practical side, we give a precise assessment of the Linux PRNGs, /dev/random and /dev/urandom. In particular, we show attacks proving that these PRNGs are not robust according to our definition, due to vulnerabilities in their entropy estimator and their internal mixing function. Finally, we propose a simple PRNG construction that is provably robust in our new and stronger adversarial model and we show that it is more efficient than the Linux PRNGs. We therefore recommend to use this construction whenever a PRNG with input is used for cryptography.

Broadcast encryption aims at sending a content to a large arbitrary group of users at once. Currently, the most efficient schemes provide constant-size headers, that encapsulate ephemeral session keys under which the payload is encrypted. However, in practice, and namely for pay-TV, providers have to send various contents to different groups of users. Headers are thus specific to each group, one for each channel: as a consequence, the global overhead is linear in the number of channels. Furthermore, when one wants to zap to and watch another channel, one has to get the new header and decrypt it to learn the new session key: either the headers are sent quite frequently or one has to store all the headers, even if one watches one channel only. Otherwise, the zapping time becomes unacceptably long.

Blind signatures allow users to obtain signatures on messages hidden from the signer; moreover, the signer cannot link the resulting message/signature pair to the signing session. This paper presents blind signature schemes, in which the number of interactions between the user and the signer is min imal and whose blind signatures are short. Our schemes are defined over bilinear groups and are proved secure in the common-reference-string model without random oracles and under standard assumptions: CDH and the decision-linear assumption. (We also give variants over asymmetric groups based on similar assumptions.) The blind signatures are Waters signatures, which consist of 2 group elements. Moreover, we instantiate partially blind signatures, where the message consists of a part hidden from the signer and a commonly known public part, and schemes achieving perfect blindness. We propose new variants of blind signatures, such as signer-friendly partially blind signatures, where the public part can be chosen by the signer without prior agreement, 3-party blind signatures, as well as blind signatures on multiple aggregated messages provided by independent sources. We also extend Waters signatures to non-binary alphabets by proving a new result on the underlying hash function.

Verified security provides a firm foundation for cryptographic proofs by means of rigorous programming language techniques and verification methods. EasyCrypt is a framework that realizes the verified security paradigm and supports the machine-checked construction and verification of cryptographic proofs using state-of-the-art SMT solvers, automated theorem provers and interactive proof assistants. Previous experiments have shown that EasyCrypt is effective for a posteriori validation of cryptographic systems. In this paper, we report on the first application of verified security to a novel cryptographic construction, with strong security properties and interesting practical features. Specifically, we use EasyCrypt to prove in the Random Oracle Model the IND-CCA security of a redundancy-free public-key encryption scheme based on trapdoor one-way permutations. Somewhat surprisingly, we show that even with a zero-length redundancy, Boneh's SAEP scheme (an OAEP-like construction with a single-round Feistel network rather than two) converts a trapdoor one-way permutation into an IND-CCA-secure scheme, provided the permutation satisfies two additional properties. We then prove that the Rabin function and RSA with short exponent enjoy these properties, and thus can be used to instantiate the construction we propose to obtain efficient encryption schemes. The reduction that justifies the security of our construction is tight enough to achieve practical security with reasonable key sizes.

In this paper, we study the security of a practical randomness extractor and its application in the TLS standard. Randomness extraction is the first stage of key derivation functions since the secret shared between the entities does not always come from a uniformly distributed source. More precisely, we wonder if the Hmac function, used in many standards, can be considered as a randomness extractor? We show that when the shared secret is put in the key space of the Hmac function, there are two cases to consider depending on whether the key is larger than the block-length of the hash function or not. In both cases, we provide a formal proof that the output is pseudo-random, but under different assumptions. Nevertheless, all the assumptions are related to the fact that the compression function of the underlying hash function behaves like a pseudo-random function. This analysis allows us to prove the TLS randomness extractor for Diffie-Hellman and RSA key exchange. Of independent interest, we study a computational analog to the leftover hash lemma for computational almost universal hash function families: any pseudo-random function family matches the latter definition.

Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.

In this paper, we show how to design an efficient, provably secure password-based authenticated key exchange mechanism specifically for the TLS (Transport Layer Security) protocol. The goal is to provide a technique that allows users to employ (short) passwords to securely identify themselves to servers. As our main contribution, we describe a new password-based technique for user authentication in TLS, called Simple Open Key Exchange (SOKE). Loosely speaking, the SOKE ciphersuites are unauthenticated Diffie-Hellman ciphersuites in which the client's Diffie-Hellman ephemeral public value is encrypted using a simple mask generation function. The mask is simply a constant value raised to the power of (a hash of) the password.The SOKE ciphersuites, in advantage over previous password-based authentication ciphersuites for TLS, combine the following features. First, SOKE has formal security arguments; the proof of security based on the computational Diffie-Hellman assumption is in the random oracle model, and holds for concurrent executions and for arbitrarily large password dictionaries. Second, SOKE is computationally efficient; in particular, it only needs operations in a sufficiently large prime-order subgroup for its Diffie-Hellman computations (no safe primes). Third, SOKE provides good protocol flexibility because the user identity and password are only required once a SOKE ciphersuite has actually been negotiated, and after the server has sent a server identity.

Password-based key exchange schemes are designed to provide entities communicating over a public network, and sharing a (short) password only, with a session key (e.g, the key is used for data integrity and/or confidentiality). The focus of the present paper is on the analysis of very efficient schemes that have been proposed to the IEEE P1363 Standard working group on password-based authenticated key-exchange methods, but which actual security was an open problem. We analyze the AuthA key exchange scheme and give a complete proof of its security. Our analysis shows that the AuthA protocol and its multiple modes of operations are provably secure under the computational Diffie-Hellman intractability assumption, in both the random-oracle and the ideal-ciphers models.

Group Diffie-Hellman protocols for Authenticated Key Exchange (AKE) are designed to provide a pool of players with a shared secret key which may later be used, for example, to achieve multicast message integrity. Over the years, several schemes have been offered. However, no formal treatment for this cryptographic problem has ever been suggested. In this paper, we present a security model for this problem and use it to precisely define AKE (with "implicit" authentication) as the fundamental goal, and the entity-authentication goal as well. We then define in this model the execution of an authenticated group Diffie-Hellman scheme and prove its security.

This paper introduces a simple alternative to the hash-and-sign paradigm, from the security point of view but for signing short messages, called twinning. A twin signature is obtained by signing twice a short message by a signature scheme. Analysis of the concept in different settings yields the following results:

The aim of electronic voting schemes is to provide a set of protocols that allow voters to cast ballots while a group of authorities collect the votes and output the final tally. In this paper we describe a practical multi-candidate election scheme that guarantees privacy of voters, public verifiability, and robustness against a coalition of malicious authorities. Furthermore, we address the problem of receipt-freeness and incoercibility of voters. Our new scheme is based on the Paillier cryptosystem and on some related zero-knowledge proof techniques. The voting schemes are very practical and can be efficiently implemented in a real system.

In this paper, we present new blind signature schemes based on the factorization problem.They are the first blind signat,ure schemes proved secure relatively to factorization.By security, we mean that no "one-more forgery" is possible even under a parallel attack.In other terms, a user that receives k electronic coins cannot manufacture K + 1.Those security definitions have been introduced by Pointcheval and Stern [lS] for use in electronic cash.In fact, blind signatures were defined with this aim and it is still their most important application, together with anonymous voting.In the following, we will present an efficient reduction of an attack to a factorization algorithm in the random oracle model [l].