International Association
for Cryptologic Research

The rapid growth of the globalized integrated circuit (IC) supply chain has drawn the attention of numerous malicious actors that try to exploit it for profit. One of the most prominent targets of such parties is the third-party intellectual property (3PIP) vendors and their circuit designs. With the increasing number of transactions between vendors and system integrators, the threat of IP reuse and piracy has become a significant consideration for the IC industry. What is more, the correctness of 3PIP designs should be verified before integration, imposing another challenge for 3PIP vendors since they have to prove the functionality of their designs to system integrators while protecting the privacy of the circuit implementations. To eliminate this deadlock, we utilize the cryptographic technique of 'zero-knowledge proofs' to enable 3PIP vendors to convince system integrators about various functional properties of a circuit (e.g., area, power, frequency) without disclosing its netlist (i.e., in zero-knowledge). Our approach comprises a circuit compiler that transforms arbitrary netlists into a zero knowledge-friendly format and a library of modules that provide cryptographic guarantees for various properties of the netlist while hiding the actual gates. We evaluate our method using combinational and sequential circuits from the ISCAS and ITC benchmark suites.

Machine learning algorithms crucially depend on non-linear mathematical functions such as division (for normalization), exponentiation (for softmax and sigmoid), tanh (as an activation function), logarithm (for cross-entropy loss), and square root (for back-propagation of normalization layers). However, when machine learning is performed over secure computation, these protocols incur a large communication overhead and high round complexity. In this work, we propose new multi-party computation (MPC) protocols for such functions. Our protocols achieve constant round complexity (3 for semi-honest, 4 for malicious), an order of magnitude lower communication (54-121x lower than prior art), and high concrete efficiency (2-1163x faster runtime). We rely on recent advances in function secret sharing (FSS) to construct these protocols. Our contributions can be summarized as follows:

(1) A constant round protocol to securely evaluate non-linear functions such as division, exponentiation, logarithm, and tanh (in comparison to prior art which uses round complexity proportional to the rounds of iterative methods/required precision) with high accuracy. This construction largely follows prior work in look-up style secure computation. (2) Our main contribution is the extension of the above protocol to be secure in the presence of malicious adversaries in the honest majority setting. We provide a malicious sketching protocol for FSS schemes that works over rings and in order to prove its security, we extend (and prove) a corresponding form of Schwartz-Zippel lemma over rings. This is the first such extension of the lemma and it can be of independent interest in other domains of secure computation. (3) We implement our protocol and showcase order of magnitude improvements in runtime and communication. Given the low round complexity and substantially lower communication, our protocols achieve even better performance over network constrained environments such as WAN. Finally, we showcase how such functions can lead to scalability in machine learning.

Note that techniques presented are applicable beyond the application of machine learning as the protocols effectively present an efficient 1-out-of-N oblivious transfer or an efficient private information retrieval protocol.

As cloud computing becomes increasingly ubiquitous, protecting the confidentiality of data outsourced to third parties becomes a priority. While encryption is a natural solution to this problem, traditional algorithms may only protect data at rest and in transit, but do not support encrypted processing. In this work we introduce Romeo, which enables easy-to-use privacy-preserving processing of data in the cloud using homomorphic encryption. Romeo automatically converts arbitrary programs expressed in Verilog HDL into equivalent homomorphic circuits that are evaluated using encrypted inputs. For our experiments, we employ cryptographic circuits, such as AES, and benchmarks from the ISCAS'85 and ISCAS'89 suites.

In this work, we present the first fault injection analysis of the Number Theoretic Transform (NTT). The NTT is an integral computation unit, widely used for polynomial multiplication in several structured lattice-based key encapsulation mechanisms (KEMs) and digital signature schemes. We identify a critical single fault vulnerability in the NTT, which severely reduces the entropy of its output. This in turn enables us to perform a wide-range of attacks applicable to lattice-based KEMs as well as signature schemes. In particular, we demonstrate novel key recovery and message recovery attacks targeting the key generation and encryption procedure of Kyber KEM. We also propose novel existential forgery attacks targeting deterministic and probabilistic signing procedure of Dilithium, followed by a novel verification bypass attack targeting its verification procedure. All proposed exploits are demonstrated with high success rate using electromagnetic fault injection on state-of-the-art implementations of Kyber and Dilithium, from the open-source pqm4 library on the ARM Cortex-M4 microcontroller.

Byzantine agreement (BA) is a fundamental primitive in distributed systems and has received huge interest as an important building block for blockchain systems. Classical byzantine agreement considers a setting where $n$ parties with fixed, known identities want to agree on an output in the presence of an adversary. Motivated by blockchain systems, the assumption of fixed identities is weakened by using a \emph{resource-based model}. In such models, parties do not have fixed known identities but instead have to invest some expensive resources to participate in the protocol. Prominent examples for such resources are computation (measured by, e.g., proofs-of-work) or money (measured by proofs-of-stake). Unlike in the classical setting where BA without trusted setup (e.g., a PKI or an unpredictable beacon) is impossible for $t \geq n/3$ corruptions, in such resource-based models, BA can be constructed for the optimal threshold of $t
Positive Result: We present the first protocol for BA with expected constant round complexity and termination under adaptive corruption, honest majority and without a PKI. Earlier work achieved round complexity $O(n\kappa^2)$ (CRYPTO'15) or $O(\kappa)$ (PKC'18), where $\kappa$ is the security parameter.

Negative Result: We give the first lower bound on the communication complexity of BA in a model where parties have restricted computational resources. Concretely, we show that a multicast complexity of $O(\sqrt{n})$ is necessary even if the parties have access to a VDF oracle.

CCA-like game-based security definitions capture confidentiality by asking an adversary to distinguish between honestly computed encryptions of chosen plaintexts. In the context of voting systems, such guarantees have been shown to be sufficient to prove ballot privacy (Asiacrypt'12).

In this paper, we observe that they fall short when one seeks to obtain receipt-freeness, that is, when corrupted voters who submit chosen ciphertexts encrypting their vote must be prevented from proving how they voted to a third party.

Since no known encryption security notion can lead to a receipt-free ballot submission process, we address this challenge by proposing a novel publicly verifiable encryption primitive coined Traceable Receipt-free Encryption (TREnc) and a new notion of traceable CCA security filling the definitional gap underlined above.

We propose two TREnc instances, one generic achieving stronger guarantees for the purpose of relating it to existing building blocks, and a dedicated one based on SXDH. Both support the encryption of group elements in the standard model, while previously proposed encryption schemes aiming at offering receipt-freeness only support a polynomial-size message space, or security in the generic group model.

Eventually, we demonstrate how a TREnc can be used to build receipt-free voting protocols, by following a standard blueprint.

In this work, we generalize threshold Schnorr signatures, ElGamal encryption, and a wide variety of other functionalities, using a novel formalism of group reconstruction circuits (GRC)s. We construct a UC secure MPC protocol for computing these circuits on secret shared inputs, even in the presence of malicious parties. Applied to concrete circuits, our protocol yields threshold signature and encryption schemes with similar round complexity and concrete efficiency to functionality-specific protocols. Our formalism also generalizes to other functionalities, such as polynomial commitments and openings.

We construct a public-coin 3-round zero-knowledge argument for NP assuming (i) the sub-exponential hardness of the learning with errors (LWE) problem and (ii) the existence of keyless multi-collision-resistant hash functions against slightly super-polynomial-time adversaries. These assumptions are almost identical to those that were used recently to obtain a private-coin 3-round zero-knowledge argument [Bitansky et al., STOC 2018]. (The difference is that we assume sub-exponential hardness instead of quasi-polynomial hardness for the LWE problem.)

Zero-knowledge proof systems are usually designed to support computations for circuits over $\mathbb{F}_2$ or $\mathbb{F}_p$ for large $p$, but not for computations over $\mathbb{Z}_{2^k}$, which all modern CPUs operate on. Although $\mathbb{Z}_{2^k}$-arithmetic can be emulated using prime moduli, this comes with an unavoidable overhead. Recently, Baum et al. (CCS 2021) suggested a candidate construction for a designated-verifier zero-knowledge proof system that natively runs over $\mathbb{Z}_{2^k}$. Unfortunately, their construction requires preprocessed random vector oblivious linear evaluation (VOLE) to be instantiated over $\mathbb{Z}_{2^k}$. Currently, it is not known how to efficiently generate such random VOLE in large quantities.

In this work, we present a maliciously secure, VOLE extension protocol that can turn a short seed-VOLE over $\mathbb{Z}_{2^k}$ into a much longer, pseudorandom VOLE over the same ring. Our construction borrows ideas from recent protocols over finite fields, which we non-trivially adapt to work over $\mathbb{Z}_{2^k}$. Moreover, we show that the approach taken by the QuickSilver zero-knowledge proof system (Yang et al. CCS 2021) can be generalized to support computations over $\mathbb{Z}_{2^k}$. This new VOLE-based proof system, which we call QuarkSilver, yields better efficiency than the previous zero-knowledge protocols suggested by Baum et al. Furthermore, we implement both our VOLE extension and our zero-knowledge proof system, and show that they can generate 13-50 million VOLEs per second for 64 to 256 bit rings, and evaluate 1.3 million 64 bit multiplications per second in zero-knowledge.

This paper provides the first analysis of reflection ciphers such as PRINCE from a provable security viewpoint.

As a first contribution, we initiate the study of key-alternating reflection ciphers in the ideal permutation model. Specifically, we prove the security of the two-round case and give matching attacks. The resulting security bound takes form \(O(qp^2/2^{2n}+q^2/2^n)\), where \(q\) is the number of construction evaluations and \(p\) is the number of direct adversarial queries to the underlying permutation. Since the two-round construction already achieves an interesting security lower bound, this result can also be of interest for the construction of reflection ciphers based on a single public permutation.

Our second contribution is a generic key-length extension method for reflection ciphers. It provides an attractive alternative to the $FX$ construction, which is used by PRINCE and other concrete key-alternating reflection ciphers. We show that our construction leads to better security with minimal changes to existing designs. The security proof is in the ideal cipher model and relies on a reduction to the two-round Even-Mansour cipher with a single round key. In order to obtain the desired result, we sharpen the bad-transcript analysis and consequently improve the best-known bounds for the single-key Even-Mansour cipher with two rounds. This improvement is enabled by a new sum-capture theorem that is of independent interest.

We introduce a new security notion that lies right in between pseudorandom permutations (PRPs) and strong pseudorandom permutations (SPRPs). We call this new security notion and any (tweakable) cipher that satisfies it a $\textit{rugged pseudorandom permutation}$ (RPRP). Rugged pseudorandom permutations lend themselves to some interesting applications, have practical benefits, and lead to novel cryptographic constructions. Our focus is on variable-length tweakable RPRPs, and analogous to the encode-then-encipher paradigm of Bellare and Rogaway, we can generically transform any such cipher into different AEAD schemes with varying security properties. However, the benefit of RPRPs is that they can be constructed more efficiently as they are weaker primitives than SPRPs (the notion traditionally required by the encode-then-encipher paradigm). We can construct RPRPs using only two layers of processing, whereas SPRPs typically require three layers of processing over the input data. We also identify a new transformation that yields RUP-secure AEAD schemes with more compact ciphertexts than previously known. Further extending this approach, we arrive at a new generalized notion of authenticated encryption and a matching construction, which we refer to as $\textit{nonce-set AEAD}$. Nonce-set AEAD is particularly well-suited in the context of secure channels, like QUIC and DTLS, that operate over unreliable transports and employ a window mechanism at the receiver's end of the channel. We conclude by presenting a generic construction for transforming a nonce-set AEAD scheme into an order-resilient secure channel. Our channel construction sheds new light on order-resilient channels and additionally leads to more compact ciphertexts when instantiated from RPRPs.

Recent work of Li and Micciancio (Eurocrypt 2021) has shown that the traditional formulation of indistinguishability under chosen plaintext attack (INDCPA) is not adequate to capture the security of approximate homomorphic encryption against passive adversaries, and identified a stronger INDCPA^D security definition (INDCPA with decryption oracles) as the appropriate security target for approximate encryption schemes.

We show how to any approximate homomorphic encryption scheme achieving the weak INDCPA security definition, into one which is provably INDCPA^D secure, offering strong guarantees against realistic passive attacks. The method works by post-processing the output of the decryption function with a mechanism satisfying an appropriate notion of differential privacy (DP), adding an amount of noise tailored to the worst-case error growth of the homomorphic computation.

We apply these results to the approximate homomorphic encryption scheme of Cheon, Kim, Kim, and Song (CKKS, Asiacrypt 2017), proving that adding Gaussian noise to the output of CKKS decryption suffices to achieve INDCPA^D security. We precisely quantify how much Gaussian noise must be added by proving nearly matching upper and lower bounds, showing that one cannot hope to significantly reduce the amount of noise added in this post-processing step. As an additional contribution, we present and use a finer-grained definition of bit security that distinguishes between a computational security parameter (c) and a statistical one (s). Based on our upper and lower bounds, we propose parameters for the counter-measures recently adopted by open-source libraries implementing CKKS.

Lastly, we investigate the plausible claim that smaller DP noise parameters might suffice to achieve INDCPA^D-security for schemes supporting more accurate (dynamic, key dependent) estimates of ciphertext noise during decryption. Perhaps surprisingly, we show that this claim is false, and that DP mechanisms with noise parameters tailored to the error present in a given ciphertext, rather than worst-case error, are vulnerable to INDCPA^D attacks.

In this work we present a novel actively secure multiparty computation protocol in the dishonest majority setting, where the computation domain is a ring of the type $\mathbb{Z}_{2^k}$. Instead of considering an ``extension ring'' of the form $\mathbb{Z}_{2^{k+\kappa}}$ as in SPD$\mathbb{Z}_{2^k}$ (Cramer et al, CRYPTO 2018) and its derivatives, we make use of an actual ring extension, or more precisely, a Galois ring extension $\mathbb{Z}_{p^k}[\mathtt{X}]/(h(\mathtt{X}))$ of large enough degree, in order to ensure that the adversary cannot cheat except with negligible probability. These techniques have been used already in the context of honest majority MPC over $\mathbb{Z}_{p^k}$, and to the best of our knowledge, our work constitutes the first study of the benefits of these tools in the dishonest majority setting.

Making use of Galois ring extensions requires great care in order to avoid paying an extra overhead due to the use of larger rings. To address this, reverse multiplication-friendly embeddings (RMFEs) have been used in the honest majority setting (e.g.~Cascudo et al, CRYPTO 2018), and more recently in the dishonest majority setting for computation over $\mathbb{Z}_2$ (Cascudo and Gundersen, TCC 2020). We make use of the recent RMFEs over $\mathbb{Z}_{p^k}$ from (Cramer et al, CRYPTO 2021), together with adaptations of some RMFE optimizations introduced in (Abspoel et al, ASIACRYPT 2021) in the honest majority setting, to achieve an efficient protocol that only requires in its online phase $12.4k(n-1)$ bits of amortized communication complexity and one round of communication for each multiplication gate. We also instantiate the necessary offline phase using Oblivious Linear Evaluation (OLE) by generalizing the approach based on Oblivious Transfer (OT) proposed in MASCOT (Keller et al, CCS 2016). To this end, and as an additional contribution of potential independent interest, we present a novel technique using Multiplication-Friendly Embeddings (MFEs) to achieve OLE over Galois ring extensions using black-box access to an OLE protocol over the base ring $\mathbb{Z}_{p^k}$ without paying a quadratic cost in terms of the extension degree. This generalizes the approach in MASCOT based on Correlated OT Extension. Finally, along the way we also identify a bug in a central proof in MASCOT, and we implicitly present a fix in our generalized proof.

As the Bitcoin mining landscape becomes more competitive, analyzing potential attacks under the assumption of rational miners becomes increasingly relevant. In the rational setting, blockchain users can bribe miners to reap an unfair benefit. Established protocols such as Duplex Micropayment Channels and Lightning Channels are susceptible to bribery, which upends their financial guarantees. Indeed, we prove that in a two-party contract in which the honest party can spend an output right away, whereas the malicious can only spend the same output after a timelock, the latter party can promise a high fee to the miners, who then intentionally ignore the transaction of the honest party in anticipation of the higher fee. This effectively prevents a valid transaction from ever entering the blockchain, resulting in potentially severe financial losses for the honest and considerable gains for the malicious party.

We expand previous results on timelock bribes to more realistic blockchains, proving that a general class of contracts are susceptible. We then apply our results to Duplex Micropayment Channels and Lightning Channels, providing exact bounds on their safe operating region. Furthermore, we enhance the Bitcoin Script of Duplex Micropayment Channels so that the coins of a party that attempts to bribe are given to the miners as fees, therefore effectively disincentivizing bribes. Our solution, named Suborn channels, is implemented as a proof-of-concept. We also propose a small change to Lightning Channels that achieves a similar effect. Moreover, we formally express the exact circumstances under which our two proposals ensure alignment of miner incentives with the prescribed protocol outcome.

Multiparty randomized encodings (Applebaum, Brakerski, and Tsabary, SICOMP 2021) reduce the task of securely computing a complicated multiparty functionality $f$ to the task of securely computing a simpler functionality $g$. The reduction is non-interactive and preserves information-theoretic security against a passive (semi-honest) adversary, also referred to as privacy. The special case of a degree-2 encoding $g$ (2MPRE) has recently found several applications to secure multiparty computation (MPC) with either information-theoretic security or making black-box access to cryptographic primitives. Unfortunately, as all known constructions are based on information-theoretic MPC protocols in the plain model, they can only be private with an honest majority.

In this paper, we break the honest-majority barrier and present the first construction of general 2MPRE that remains secure in the presence of a dishonest majority. Our construction encodes every $n$-party functionality $f$ by a 2MPRE that tolerates at most $t=\lfloor 2n/3\rfloor$ passive corruptions.

We derive several applications including: (1) The first non-interactive client-server MPC protocol with perfect privacy against any coalition of a minority of the servers and up to $t$ of the $n$ clients; (2) Completeness of 3-party functionalities under non-interactive $t$-private reductions; and (3) A single-round $t$-private reduction from general-MPC to an ideal oblivious transfer (OT). These positive results partially resolve open questions that were posed in several previous works. We also show that $t$-private 2MPREs are necessary for solving (2) and (3), thus establishing new equivalence theorems between these three notions.

Finally, we present a new approach for constructing fully-private 2MPREs based on multi-round protocols in the OT-hybrid model that achieve \emph{perfect privacy} against active attacks. Moreover, by slightly restricting the power of the active adversary, we derive an equivalence between these notions. This forms a surprising, and quite unique, connection between a non-interactive passively-private primitive to an interactive actively-private primitive.

We propose a new AEAD mode of operation for an efficient countermeasure against side-channel attacks. Our mode achieves the smallest memory with high-order masking, by minimizing the states that are duplicated in masking. An $s$-bit key-dependent state is necessary for achieving $s$-bit security, and the conventional schemes always protect the entire $s$ bits with masking. We reduce the protected state size by introducing an unprotected state in the key-dependent state: we protect only a half and give another half to a side-channel adversary. Ensuring independence between the unprotected and protected states is the key technical challenge since mixing these states reveals the protected state to the adversary. We propose a new mode $\mathsf{HOMA}$ that achieves $s$-bit security using a tweakable block cipher with the $s/2$-bit block size. We also propose a new primitive for instantiating $\mathsf{HOMA}$ with $s=128$ by extending the SKINNY tweakable block cipher to a 64-bit plaintext block, a 128-bit key, and a $(256+3)$-bit tweak. We make hardware performance evaluation by implementing $\mathsf{HOMA}$ with high-order masking for $d \le 5$. For any $d > 0$, $\mathsf{HOMA}$ outperforms the current state-of-the-art $\mathsf{PFB\_Plus}$ by reducing the circuit area larger than that of the entire S-box.

Recent work has produced interactive Zero Knowledge (ZK) proof systems that can express proofs as arbitrary C programs (Heath et al., 2021, henceforth referred to as ZEE); these programs can be executed by a simulated ZK processor that runs in the 10KHz range.

In this work, we demonstrate that such proof systems are amenable to high degrees of parallelism. Our epoch parallelism-based approach allows the prover and verifier to divide the ZK proof into pieces such that each piece can be executed on a different machine. These proof snippets can then be glued together, and the glued parallel proofs are equivalent to the original sequential proof.

We implemented and we experimentally evaluate an epoch parallel version of the ZEE proof system. By running the prover and verifier each across 31 2-core machines, we achieve a ZK processor that runs at up to 394KHz. This allowed us to run a benchmark involving the Linux program bzip2, which would have required at least 11 days with the former ZEE system, in only 8.5 hours.

We build a complete and efficient ZK toolchain that handles proof statements encoded as arbitrary ANSI C programs.

Zero-Knowledge (ZK) proofs are foundational in cryptography. Recent ZK research has focused intensely on non-interactive proofs of small statements, useful in blockchain scenarios. We instead target large statements that are useful, e.g., in proving properties of programs.

Recent work (Heath and Kolesnikov, CCS 2020 [HK20a]) designed a proof-of-concept ZK machine (ZKM). Their machine executes arbitrary programs over a minimal instruction set, authenticating in ZK the program execution. In this work, we significantly extend this research thrust, both in terms of efficiency and generality. Our contributions include: • A rich and performance-oriented architecture for representing arbitrary ZK proofs as programs. • A complete compiler toolchain providing full support for ANSI C95 programs. We ran off-the-shelf buggy versions of sed and gzip, proving in ZK that each program has a bug. To our knowledge, this is the first ZK system capable of executing standard Linux programs. • Improved ZK RAM. [HK20a] introduced an efficient ZK-specific RAM BubbleRAM that consumes $O(\log^2 n)$ communication per access. We extend BubbleRAM with multi-level caching, decreasing communication to $O(\log n)$ per access. This introduces the possibility of a cache miss, which we handle cheaply. Our experiments show that cache misses are rare; in isolation, i.e., ignoring other processor costs, BubbleCache improves communication over BubbleRAM by more than $8\times$. Using BubbleCache improves our processor’s total communication (including costs of cache misses) by $\approx 25-30$%. • Numerous low-level optimizations, resulting in a CPU that is both more expressive and $\approx 5.5\times$ faster than [HK20a]’s. • Attention to user experience. Our engineer-facing ZK instrumentation and extensions are minimal and easy to use.

Put together, our system is efficient and general, and can run many standard Linux programs. The resultant machine runs at up to 11KHz on a 1Gbps LAN and supports MBs of RAM.

Zero-Knowledge (ZK) proofs (ZKP) are foundational in cryptography. Most recent ZK research focuses on non-interactive proofs (NIZK) of small statements, useful in blockchain scenarios. Another line, and our focus, instead targets proofs of large statements that are useful, e.g., in proving properties of programs in ZK.

We specify a zero-knowledge processor that executes arbitrary programs written in a simple instruction set and proves in ZK the correctness of the execution. Such an approach is well-suited for constructing ZK proofs of large statements as it efficiently supports complex programming constructs, such as loops and RAM access.

We propose several novel ZK improvements that make our approach concretely efficient: (1) an efficient arithmetic representation with conversions to/from Boolean, (2) an efficient read-only memory that uses $2 \log n$ OTs per access, and (3) an efficient read-write memory, BubbleRAM, which uses $1/2 \log^2 n$ OTs per access. BubbleRAM beats linear scan for RAM of size > 3 elements! Prior ZK systems used generic ORAM costing orders of magnitude more.

We cast our system as a garbling scheme that can be plugged into the ZK protocol of [Jawurek et al, CCS’13].

Put together, our system is concretely efficient: for a processor instantiated with 512KB of main memory, each processor cycle costs 24KB of communication. We implemented our approach in C++. On a 1Gbps LAN, our implementation realizes a 2.1KHz processor.

We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are a lattice extractor to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on $L^1$ distance and KL divergence, respectively, which are of independent interest. We prove the existence of secrecy-good lattices under $L^1$ distance and KL divergence, whose $L^1$ and KL flatness factors vanish for volume-to-noise ratios up to $2\pi e$. This improves upon the volume-to-noise ratio threshold $2\pi$ of the $L^{\infty}$ flatness factor.