International Association
for Cryptologic Research

We explore large-scale fault-tolerant multiparty computation on a minimal communication graph. Our goal is to be able to privately aggregate data from thousands of users - for example, in order to obtain usage statistics from users' phones. To reflect typical phone deployments, we limit communication to the star graph (so that all users only talk to a single central server). To provide fault-tolerance, we require the computation to complete even if some users drop out mid-computation, which is inevitable if the computing devices are personally owned smartphones. Variants of this setting have been considered for the problem of secure aggregation by Chan et al. (Financial Cryptography 2012) and Bonawitz et al. (CCS 2017). We call this setting Large-scale One-server Vanishing-participants Efficient MPC (LOVE MPC).

We show that LOVE MPC requires at least three message flows, and that a three-message protocol requires some setup (such as a PKI). We then build LOVE MPC with optimal round- and communication- complexity (assuming semi-honest participants and a deployed PKI), using homomorphic ad hoc threshold encryption (HATE). We build the first HATE scheme with constant-size ciphertexts (although the public key length is linear in the number of users). Unfortunately, this construction is merely a feasibility result, because it relies on differing-inputs obfuscation.

We also construct more practical three- and five- message LOVE MPC in the PKI model for addition or multiplication. Unlike in the obfuscation-based construction, the per user message length in these protocols is linear in the number of users. However, the five-message protocol still has constant amortized message length, because only the first two messages are long, but they need to be exchanged only once (i.e., are input-independent and reusable) and thus can be viewed as setup.

We present here Wave the first ``hash-and-sign'' code-based signature scheme which strictly follows the GPV strategy [GPV08]. It uses the family of ternary generalized $(U,U+V)$ codes. We prove that Wave achieves {\em existential unforgeability under adaptive chosen message attacks} (EUF-CMA) in the random oracle model (ROM) with a tight reduction to two assumptions from coding theory: one is a distinguishing problem that is related to the trapdoor we insert in our scheme, the other one is DOOM, a multiple target version of syndrome decoding. The algorithm produces uniformly distributed signatures through a suitable rejection sampling. Our scheme enjoys efficient signature and verification algorithms. For 128 bits of classical security, signature are $8$ thousand bits long and the public key size is slightly smaller than one megabyte. Furthermore, with our current choice of parameters, the rejection rate is limited to one rejection every 3 or 4 signatures.

The Number Theoretic Transform (NTT) provides efficient algorithm for multiplying large degree polynomials. It is commonly used in cryptographic schemes that are based on the hardness of the Ring Learning With Errors problem (RLWE), which is a popular basis for post-quantum key exchange, encryption and digital signature. To apply NTT, modulus q should satisfy that q ≡ 1 mod 2n, RLWE- based schemes have to choose an oversized modulus, which leads to excessive bandwidth. In this work, we present “Preprocess-then-NTT (Pt-NTT)” technique which weakens the limitation of modulus q, i.e., we only require q ≡ 1 mod n or q ≡ 1 mod n/2. Based on this technique, we provide new parameter settings for KYBER and NEWHOPE (two NIST candidates). In these new schemes, we can reduce public key size and ciphertext size at a cost of very little efficiency loss.

Message franking enables a receiver to report a potential abuse in a secure messaging system which employs an end to end encryption. Such mechanism is crucial for accountability and is already widely adopted in real world product such as Facebook messenger. Grubs et al initiated a systematic study of such a new primitive, and Dodis et al gave a more efficient construction.

We observe that in all existing message franking schemes, the receiver has to reveal the whole communication for a session in order to report one abuse. This is highly undesirable in many settings where revealing other non-abusive part of the communication leaks too much information; what is worse, a foxy adversary may intentionally mixing private information of the receiver with the abusive message so that the receiver will be reluctant to report. This essentially renders the abuse reporting mechanism ineffective.

To tackle this problem, we propose a new primitive called targeted opening compactly committing AEAD (TOCE for short). In a TOCE, the receiver can select arbitrary subset of bits from the plaintext to reveal during opening, while keep all the rest still secure as in an authenticated encryption. We gave a careful formulation and give a generic construction. The generic construction allowing a bit level opening may require a substantial number of passes of symmetric key ciphers when encrypting a large message such as a picture. We thus further set forth and give a more efficient non-black-box construction allowing a block-level (e.g., 256 bit) opening. We also propose a privacy-efficiency trade off if we can relax the security of non-opened messages to be one way secure (they are still semantically secure if no opening).

Multi-user (mu) security considers large-scale attackers (e.g., state actors) that given access to a number of sessions, attempt to compromise {\em at least} one of them. Mu security of authenticated encryption (AE) was explicitly considered in the development of TLS 1.3.

This paper revisits the mu security of GCM, which remains to date the most widely used dedicated AE mode. We provide new concrete security bounds which improve upon previous work by adopting a refined parameterization of adversarial resources that highlights the impact on security of (1) nonce re-use across users and of (2) re-keying.

As one of the main applications, we give tight security bounds for the nonce-randomization mechanism adopted in the record protocol of TLS 1.3 as a mitigation of large-scale multi-user attacks. We provide tight security bounds that yield the first validation of this method. In particular, we solve the main open question of Bellare and Tackmann (CRYPTO '16), who only considered restricted attackers which do not attempt to violate integrity, and only gave non-tight bounds.

Transaction throughput, confirmation latency and confirmation reliability are fundamental performance measures of any blockchain system in addition to its security. In a decentralized setting, these measures are limited by two underlying physical network attributes: communication capacity and speed-of-light propagation delay. Existing systems operate far away from these physical limits. In this work we introduce Prism, a new proof-of-work blockchain protocol, which can achieve 1) security against up to 50% adversarial hashing power; 2) optimal throughput up to the capacity C of the network; 3) confirmation latency for honest transactions proportional to the propagation delay D, with confirmation error probability exponentially small in CD ; 4) eventual total ordering of all transactions. Our approach to the design of this protocol is based on deconstructing the blockchain into its basic functionalities and systematically scaling up these functionalities to approach their physical limits.

Authenticated Encryption ($\mathsf{AE}$) achieves confidentiality and authenticity, the two most fundamental goals of cryptography, in a single scheme. A common strategy to obtain $\mathsf{AE}$ is to combine a Message Authentication Code $(\mathsf{MAC})$ and an encryption scheme, either nonce-based or $\mathsf{iv}$-based. Out of the 180 possible combinations, Namprempre et al.~[25] proved that 12 were secure, 164 insecure and 4 were left unresolved: A10, A11 and A12 which use an $\iv$-based encryption scheme and N4 which uses a nonce-based one. The question of the security of these composition modes is particularly intriguing as N4, A11, and A12 are more efficient than the 12 composition modes that are known to be provably secure.\\ We prove that: $(i)$ N4 is not secure in general, $(ii)$ A10, A11 and A12 have equivalent security, $(iii)$ A10, A11, A12 and N4 are secure if the underlying encryption scheme is either misuse-resistant or ``message malleable'', a property that is satisfied by many classical encryption modes, $(iv)$ A10, A11 and A12 are insecure if the underlying encryption scheme is stateful or untidy.\\ All the results are quantitative.

Despite their usage of pseudonyms rather than persistent identifiers, most existing cryptocurrencies do not provide users with any meaningful levels of privacy. This has prompted the creation of privacy-enhanced cryptocurrencies such as Monero and Zcash, which are specifically designed to counteract the tracking analysis possible in currencies like Bitcoin. These cryptocurrencies, however, also suffer from some drawbacks: in both Monero and Zcash, the set of potential unspent coins is always growing, which means users cannot store a concise representation of the blockchain. In Zcash, furthermore, users cannot deny their participation in anonymous transactions.

In this paper, we address both of these limitations. By combining a technique we call updatable keys with efficient zero-knowledge arguments, we propose a new cryptocurrency, QuisQuis, that achieves provably secure notions of anonymity while still allowing users to deny participation and store a relatively small amount of data.

NIST is considering the standardization of threshold schemes for cryptographic primitives. Your feedback and participation is welcome. Below are some useful links and dates:

• Draft NIST report (NISTIR 8214) on threshold schemes for cryptographic primitives --- public comments period till October 22, 2018.
• NIST Threshold Cryptography Workshop will take place March 11-12, 2019. The submission deadline is December 17, 2018.
• Project webpage: https://csrc.nist.gov/projects/threshold-cryptography
• Mailing list (public forum): https://csrc.nist.gov/Projects/Threshold-Cryptography/Collaboration

For questions or comments, contact threshold-crypto (at) nist.gov

Context. Methods of known kleptography implementations are being investigated. The article focuses mostly on SETUP design of subliminal data leakage channels.

Aim. Suggest approaches to develop SETUP resistant cryptosystems.

Methods. The necessary conditions for SETUP implementation are building in entropy source (otherwise generated secret will be predictable). In this article, it's considered subscriber whose protocol implementation is suspected to be modified by Developer (the malicious actor who is able to influence on cryptosystem implementation) to create subliminal leakage channel. The possible countermeasure is to prohibit usage own random sources for subscribers, enforce generate random values from public counters. %them to use external Trusted Random Number Generation service.

Results. The formal model for basic SETUP scheme has been suggested. Approach to develop SETUP resistant protocols has been described. Two basic SETUP-resistance protocols (nonce generation protocol and Diffie-Hellman key agreement protocol) have been proposed.

We give a simple proof that the decisional Learning With Errors (LWE) problem with binary secrets (and an arbitrary polynomial number of samples) is at least as hard as the standard LWE problem (with unrestricted, uniformly random secrets, and a bounded, quasi-linear number of samples). This proves that the binary-secret LWE distribution is pseudorandom, under standard worst-case complexity assumptions on lattice problems. Our results are similar to those proved by (Brakerski, Langlois, Peikert, Regev and Stehle, STOC 2013), but provide a shorter, more direct proof, and a small improvement in the noise growth of the reduction.

ECDSA is a standardized signing algorithm that is widely used in TLS, code signing, cryptocurrency and more. Due to its importance, the problem of securely computing ECDSA in a distributed manner (known as threshold signing) has received considerable interest. However, despite this interest, there is still no full threshold solution for more than 2 parties (meaning that any $t$-out-of-$n$ parties can sign, security is preserved for any $t-1$ or fewer corrupted parties, and $t\leq n$ can be any value thus supporting an honest minority) that has practical key distribution. This is due to the fact that all previous solutions for this utilize Paillier homomorphic encryption, and efficient distributed Paillier key generation for more than two parties is not known.

In this paper, we present the first truly practical full threshold ECDSA signing protocol that has both fast signing and fast key distribution. This solves a years-old open problem, and opens the door to practical uses of threshold ECDSA signing that are in demand today. One of these applications is the construction of secure cryptocurrency wallets (where key shares are spread over multiple devices and so are hard to steal) and cryptocurrency custody solutions (where large sums of invested cryptocurrency are strongly protected by splitting the key between a bank/financial institution, the customer who owns the currency, and possibly a third-party trustee, in multiple shares at each). There is growing practical interest in such solutions, but prior to our work these could not be deployed today due to the need for distributed key generation.

A software watermarking scheme enables one to embed a "mark" (i.e., a message) within a program while preserving the program's functionality. Moreover, there is an extraction algorithm that recovers an embedded message from a program. The main security goal is that it should be difficult to remove the watermark without destroying the functionality of the program. Existing constructions of watermarking focus on watermarking cryptographic functions like pseudorandom functions (PRFs); even in this setting, realizing watermarking from standard assumptions remains difficult. The first lattice-based construction of secret-key watermarking due to Kim and Wu (CRYPTO 2017) only ensures mark-unremovability against an adversary who does not have access to the mark-extraction oracle. The construction of Quach et al. (TCC 2018) achieves the stronger notion of mark-unremovability even if the adversary can make extraction queries, but has the drawback that the watermarking authority (who holds the watermarking secret key) can break pseudorandomness of all PRF keys in the family (including unmarked keys).

In this work, we construct new lattice-based secret-key watermarking schemes for PRFs that both provide unremovability against adversaries that have access to the mark-extraction oracle and offer a strong and meaningful notion of pseudorandomness even against the watermarking authority (i.e., the outputs of unmarked keys are pseudorandom almost everywhere). Moreover, security of several of our schemes can be based on the hardness of computing quasi-polynomial approximations to worst-case lattice problems. This is a qualitatively weaker assumption than that needed for existing lattice-based constructions of watermarking (that support message-embedding), all of which require sub-exponential approximation factors. Our constructions rely on a new cryptographic primitive called an extractable PRF, which is of independent interest.

Efficient scalar multiplication algorithms require a single finite field inversion at the end to convert from projective to affine coordinates. This inversion consumes a significant proportion of the total time. The present work makes a comprehensive study of inversion over Mersenne and pseudo-Mersenne prime order fields. Inversion algorithms for such primes are based on exponentiation which in turn requires efficient algorithms for multiplication, squaring and modulo reduction. From a theoretical point of view, we present a number of algorithms for multiplication/squaring and reduction leading to a number of different inversion algorithms which are appropriate for different settings. Our algorithms collect together and generalise ideas which are scattered across various papers and codes. At the same time, they also introduce new ideas to improve upon existing works. A key theoretical feature of our work, which is not present in previous works, is that we provide formal statements and detailed proofs of correctness of the different reduction algorithms that we describe. On the implementation aspect, a total of twenty primes are considered, covering all previously proposed cryptographically relevant (pseudo-)Mersenne prime order fields at various security levels. For each of these fields, we provide 64-bit assembly implementations of all the relevant inversion algorithms for a wide range of Intel processors. We were able to find previous 64-bit implementations of inversion for six of the twenty primes considered in this work. On the Haswell, Skylake and Kabylake processors of Intel, for all the six primes where previous implementations are available, our implementations outperform such previous implementations. The assembly codes that we have developed are publicly available and can be used as a plug-in to replace the inversion routines in existing softwares for scalar multiplication.

The recent progress in key derivation (Barak at al. CRYPTO'11, Dodis Yu TCC'2013) introduced the concept of constrained profiles for attackers advantage, recognizing that security bounds can be significantly improved (alternatively: lots of randomness can be saved) when the advantage, as the function of the key, is bounded in mean or variance. This paper studies \emph{minimal requirements for keys} to achieve security under such restricted attackers.

We frame the problem as characterizing \emph{pseudorandomness against constrained distinguishers} and show that minimal assumptions are respectively (a) high smooth min-entropy and (b) high smooth collision entropy. This matches the (folklore extension of) assumptions of previous works.

Besides providing lower bounds, we offer more insights into this key derivation problem and elegant proof techniques of geometric flavor.

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.

Constrained pseudorandom functions (CPRFs) allow learning `constrained' PRF keys that can evaluate the PRF on a subset of the input space, or based on some sort of predicate. First introduced by Boneh and Waters [AC'13], Kiayias et al. [CCS'13] and Boyle et al. [PKC'14], they have been shown to be a useful cryptographic primitive with many applications. The full security definition of CPRFs requires the adversary to learn multiple constrained keys, a requirement for all of these applications. Unfortunately, existing constructions of CPRFs satisfying this security notion are only known from exceptionally strong cryptographic assumptions, such as indistinguishability obfuscation (IO) and the existence of multilinear maps, even for very weak predicates. CPRFs from more standard assumptions only satisfy security for a single constrained key query.

In this work, we give the first construction of a CPRF that can issue a constant number of constrained keys for bit-fixing predicates, only requiring the existence of one-way functions (OWFs). This is a much weaker assumption compared with all previous constructions. In addition, we prove that the new scheme satisfies \(1\)-key privacy (otherwise known as constraint-hiding), and that it also achieves fully adaptive security. This is the only construction to achieve adaptive security outside of the random oracle model, and without sub-exponential security losses. Our technique represents a noted departure from existing CPRF constructions. We hope that it may lead to future constructions that can expose a greater number of keys, or consider more expressive predicates (such as bounded-depth circuit constraints).

Classical-style BFT protocols use two or more rounds of voting to confirm each block, e.g., in PBFT, they are called the “prepare” round and the “commit” round respectively. Recently, an elegant pipelining idea came out of the cryptocurrency community, i.e., if each block required two rounds of voting, why not piggyback the second round on the next block’s voting? We refer to this idea as the pipelined-BFT paradigm. We describe a simple partially synchronous blockchain protocol called PaLa that is inspired by the pipelined-BFT paradigm. In PaLa, a proposer proposes a block extending the freshest notarized chain seen so far. Consensus nodes vote on the proposal if certain conditions are met. When a block gains at least 2n 3 votes it becomes notarized. A block becomes finalized if the next immediate block becomes notarized too. We propose a conceptually simple and provably secure committee rotation algorithm for PaLa. We also describe a generalization called “doubly-pipelined PaLa” that is geared towards settings that require high throughput.

We describe PiLi, an extremely simple synchronous blockchain that tolerates minority corruptions. The protocol description is the extremely natural and intuitive. Informally, every epoch, an eligible proposer proposes a block (tagged with the current epoch) extending the freshest notarized chain observed so far. Nodes vote on all valid proposals from eligible proposers as long as 1) the proposed block extends from a parent chain has been notarized in the node’s view; and 2) this parent is “not too stale”. When a block gains votes from the majority of nodes, it is considered notarized but not necessarily final. If a node observes a notarized chain ending with 6 blocks of consecutive epochs and no other notarized blocks of these 6 epochs have been seen, then this notarized chain except the trailing 5 blocks are considered final.

Lightweight block ciphers are today of paramount importance to provide security services in constrained environments. Recent studies have questioned the security properties of PRESENT, which makes it evident the need to study alternative ciphers. In this work we provide hardware architectures for Midori and GIFT, and compare them against implementations for PRESENT and GIMLI under fair conditions. The hardware description for our designs is made publicly available.