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#### 24 March 2023

###### Mathieu Gross, Robert Kunzelmann, Georg Sigl

ePrint Report
FPGA-SoCs are a popular platform for accelerating a wide
range of applications due to their performance and flexibility. From a
security point of view, these systems have been shown to be vulnerable
to various attacks, especially side-channel attacks where an attacker can
obtain the secret key of a cryptographic algorithm via laboratory mea-
surement equipment or even remotely with sensors implemented inside
the FPGA logic itself. Fortunately, a variety of countermeasures on the
algorithmic level have been proposed to mitigate this threat. Beyond side-
channel attacks, covert channels constitute another threat which enables
communication through a hidden channel. In this work, we demonstrate
the possibility of implementing a covert channel between the CPU and
an FPGA by modulating the usage of the Power Distribution Network.
We show that this resource is especially vulnerable since it can be easily
controlled and observed, resulting in a stealthy communication and a
high transmission data rate. The power usage is modulated using simple
and inconspicuous instructions executed on the CPU. Additionally, we
use Time-to-Digital Converter sensors to observe these power variations.
The sensor circuits are programmed into the FPGA fabric using only
standard logic components. Our covert channel achieves a transmission
rate of up to 16.7 kbit/s combined with an error rate of 2.3%. Besides
a good transmission quality, our covert channel is also stealthy and can
be used as an activation function for a hardware trojan.

###### Yu Li, Li-Ping Wang

ePrint Report
With the advancement of NIST PQC standardization, three of the four candidates in Round 4 are code-based schemes, namely Classic McEliece, HQC and BIKE. Currently, one of the most important tasks is to further analyze their security levels for the suggested parameter sets. At PKC 2022 Esser and Bellini restated the major information set decoding (ISD) algorithms by using nearest neighbor search and then applied these ISD algorithms to estimate the bit security of Classic McEliece, HQC and BIKE under the suggested parameter sets. However, all major ISD algorithms consume a large amount of memory, which in turn affects their time complexities. In this paper, we reestimate the bit-security levels of the parameter sets suggested by these three schemes in low memory by applying $K$-list sum algorithms to ISD algorithms. Compared with Esser-Bellini's results, our results achieve the best gains for Classic McEliece, HQC, and BIKE, with reductions in bit-security levels of $11.09$, $12.64$, and $12.19$ bits, respectively.

###### Fabrice Benhamouda, Shai Halevi, Hugo Krawczyk, Tal Rabin, Yiping Ma

ePrint Report
We describe high-throughput threshold protocols with guaranteed output delivery for generating Schnorr-type signatures. The protocols run a single message-independent interactive ephemeral randomness generation procedure (e.g., DKG) followed by a \emph{non-interactive} multi-message signature generation procedure. The protocols offer significant increase in throughput already for as few as ten parties while remaining highly-efficient for many hundreds of parties with thousands of signatures generated per minute (and over 10,000 in normal optimistic case).

These protocols extend seamlessly to the dynamic/proactive setting, where each run of the protocol uses a new committee, and they support sub-sampling the committees from among an effectively unbounded number of nodes. The protocols work over a broadcast channel in both synchronous and asynchronous networks.

The combination of these features makes our protocols a good match for implementing a signature service over an (asynchronous) public blockchain with many validators, where guaranteed output delivery is an absolute must. In that setting, there is a system-wide public key, where the corresponding secret signature key is distributed among the validators. Clients can submit messages (under suitable controls, e.g. smart contracts), and authorized messages are signed relative to the global public key.

Asymptotically, when running with committees of $n$ parties, our protocols can generate $\Omega(n^2)$ signatures per run, while providing resilience against $\Omega(n)$ corrupted nodes, and using broadcast bandwidth of only $O(n^2)$ group elements and scalars. For example, we can sign about $n^2/16$ messages using just under $2n^2$ total bandwidth while supporting resilience against $n/4$ corrupted parties, or sign $n^2/8$ messages using just over $2n^2$ total bandwidth with resilience against $n/5$ corrupted parties.

We prove security of our protocols by reduction to the hardness of the discrete logarithm problem in the random-oracle model.

These protocols extend seamlessly to the dynamic/proactive setting, where each run of the protocol uses a new committee, and they support sub-sampling the committees from among an effectively unbounded number of nodes. The protocols work over a broadcast channel in both synchronous and asynchronous networks.

The combination of these features makes our protocols a good match for implementing a signature service over an (asynchronous) public blockchain with many validators, where guaranteed output delivery is an absolute must. In that setting, there is a system-wide public key, where the corresponding secret signature key is distributed among the validators. Clients can submit messages (under suitable controls, e.g. smart contracts), and authorized messages are signed relative to the global public key.

Asymptotically, when running with committees of $n$ parties, our protocols can generate $\Omega(n^2)$ signatures per run, while providing resilience against $\Omega(n)$ corrupted nodes, and using broadcast bandwidth of only $O(n^2)$ group elements and scalars. For example, we can sign about $n^2/16$ messages using just under $2n^2$ total bandwidth while supporting resilience against $n/4$ corrupted parties, or sign $n^2/8$ messages using just over $2n^2$ total bandwidth with resilience against $n/5$ corrupted parties.

We prove security of our protocols by reduction to the hardness of the discrete logarithm problem in the random-oracle model.

###### Hyungrok Jo, Shingo Sato, Junji Shikata

ePrint Report
We present a tightly secure identity-based signature (IBS) scheme based on the supersingular isogeny problems. Although Shaw and Dutta proposed an isogeny-based IBS scheme with provable security, the security reduction is non-tight. For an IBS scheme with concrete security, the tightness of its security reduction affects the key size and signature size. Hence, it is reasonable to focus on a tight security proof for an isogeny-based IBS scheme. In this paper, we propose an isogeny-based IBS scheme based on the lossy CSI-FiSh signature scheme and give a tight security reduction for this scheme. While the existing isogeny-based IBS has the square-root advantage loss in the security proof, the security proof for our IBS scheme avoids such advantage loss, due to the properties of lossy CSI-FiSh.

###### Keita Emura

ePrint Report
Chen et al. (IEEE Transactions on Cloud Computing 2022) introduced dual-server public key authenticated encryption with keyword search (DS-PAEKS), and proposed a DS-PAEKS scheme under the decisional Diffie-Hellman assumption. In this paper, we propose a generic construction of DS-PAEKS from PAEKS, public key encryption, and signatures. By providing a concrete attack, we show that the DS-PAEKS scheme of Chen et al. is vulnerable. That is, the proposed generic construction yields the first DS-PAEKS schemes. Our attack with a slight modification works against the Chen et al. dual-server public key encryption with keyword search (DS-PEKS) scheme (IEEE Transactions on Information Forensics and Security 2016). Moreover, we demonstrate that the Tso et al. generic construction of DS-PEKS from public key encryption (IEEE Access 2020) is also vulnerable. We also analyze other pairing-free PAEKS schemes (Du et al., Wireless Communications and Mobile Computing 2022 and Lu and Li, IEEE Transactions on Mobile Computing 2022). Though we did not find any attack against these schemes, we show that at least their security proofs are wrong.

###### Shuichi Hirahara, Rahul Ilango, Zhenjian Lu, Mikito Nanashima, Igor C. Oliveira

ePrint Report
Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that relates the complexity of a pair of strings and their conditional complexities. Understanding if this property holds in the time-bounded setting is a longstanding open problem. In the nineties, Longpré and Mocas (1993) and Longpré and Watanabe (1995) established that if SoI holds for time-bounded Kolmogorov complexity then cryptographic one-way functions do not exist, and asked if a converse holds.

We show that one-way functions exist if and only if (probabilistic) time-bounded SoI fails on average, i.e., if there is a samplable distribution of pairs (x,y) of strings such that SoI for pK$^t$ complexity fails for many of these pairs. Our techniques rely on recent perspectives offered by probabilistic Kolmogorov complexity and meta-complexity, and reveal further equivalences between inverting one-way functions and the validity of key properties of Kolmogorov complexity in the time-bounded setting: (average-case) language compression and (average-case) conditional coding.

Motivated by these results, we investigate correspondences of this form for the worst-case hardness of NP (i.e., NP ⊄ BPP) and for the average-case hardness of NP (i.e., DistNP ⊄ HeurBPP), respectively. Our results establish the existence of similar dualities between these computational assumptions and the failure of results from Kolmogorov complexity in the time-bounded setting. In particular, these characterizations offer a novel way to investigate the main hardness conjectures of complexity theory (and the relationships among them) through the lens of Kolmogorov complexity and its properties.

We show that one-way functions exist if and only if (probabilistic) time-bounded SoI fails on average, i.e., if there is a samplable distribution of pairs (x,y) of strings such that SoI for pK$^t$ complexity fails for many of these pairs. Our techniques rely on recent perspectives offered by probabilistic Kolmogorov complexity and meta-complexity, and reveal further equivalences between inverting one-way functions and the validity of key properties of Kolmogorov complexity in the time-bounded setting: (average-case) language compression and (average-case) conditional coding.

Motivated by these results, we investigate correspondences of this form for the worst-case hardness of NP (i.e., NP ⊄ BPP) and for the average-case hardness of NP (i.e., DistNP ⊄ HeurBPP), respectively. Our results establish the existence of similar dualities between these computational assumptions and the failure of results from Kolmogorov complexity in the time-bounded setting. In particular, these characterizations offer a novel way to investigate the main hardness conjectures of complexity theory (and the relationships among them) through the lens of Kolmogorov complexity and its properties.

###### Nina Bindel, Britta Hale

ePrint Report
This draft presents work-in-progress concerning hybrid/composite signature schemes. More concretely, we give several tailored combinations of Fiat-Shamir based signature schemes (such as Dilithium) or Falcon with RSA or DSA. We observe that there are a number of signature hybridization goals, few of which are not achieved through parallel signing or concatenation approaches. These include proof composability (that the post-quantum hybrid signature security can easily be linked to the component algorithms), weak separability, strong separability, backwards compatibility, hybrid generality (i.e., hybrid compositions that can be instantiated with different algorithms once proven to be secure), and simultaneous verification. We do not consider backwards compatibility in this work, but aim in our constructions to show the feasibility of achieving all other properties. As a work-in-progress, the constructions are presented without the accompanying formal security analysis, to be included in an update.

###### Sven Bauer, Fabrizio De Santis

ePrint Report
We describe a fault attack against the deterministic variant of the Falcon signature scheme. It is the first fault attack that exploits specific properties of deterministic Falcon. The attack works under a very liberal and realistic single fault random model. The main idea is to inject a fault into the pseudo-random generator of the pre-image trapdoor sampler, generate different signatures for the same input, find reasonably short lattice vectors this way, and finally use lattice reduction techniques to obtain the private key. We investigate the relationship between fault location, the number of faults, computational effort for a possibly remaining exhaustive search step and success probability.

###### Islam Faisal

ePrint Report
This work is motivated by the following question: can an untrusted quantum server convince a classical verifier of the answer to an efficient quantum computation using only polylogarithmic communication? We show how to achieve this in the quantum random oracle model (QROM), after a non-succinct instance-independent setup phase.

We introduce and formalize the notion of post-quantum interactive oracle arguments for languages in QMA, a generalization of interactive oracle proofs (Ben-Sasson-Chiesa-Spooner). We then show how to compile any non-adaptive public-coin interactive oracle argument (with private setup) into a succinct argument (with setup) in the QROM.

To conditionally answer our motivating question via this framework under the post-quantum hardness assumption of LWE, we show that the XZ local Hamiltonian problem with at least inverse-polylogarithmic relative promise gap has an interactive oracle argument with instance-independent setup, which we can then compile.

Assuming a variant of the quantum PCP conjecture that we introduce called the weak XZ quantum PCP conjecture, we obtain a succinct argument for QMA (and consequently the verification of quantum computation) in the QROM (with non-succinct instance-independent setup) which makes only black-box use of the underlying cryptographic primitives.

We introduce and formalize the notion of post-quantum interactive oracle arguments for languages in QMA, a generalization of interactive oracle proofs (Ben-Sasson-Chiesa-Spooner). We then show how to compile any non-adaptive public-coin interactive oracle argument (with private setup) into a succinct argument (with setup) in the QROM.

To conditionally answer our motivating question via this framework under the post-quantum hardness assumption of LWE, we show that the XZ local Hamiltonian problem with at least inverse-polylogarithmic relative promise gap has an interactive oracle argument with instance-independent setup, which we can then compile.

Assuming a variant of the quantum PCP conjecture that we introduce called the weak XZ quantum PCP conjecture, we obtain a succinct argument for QMA (and consequently the verification of quantum computation) in the QROM (with non-succinct instance-independent setup) which makes only black-box use of the underlying cryptographic primitives.

###### Laurane Marco, Abdullah Talayhan, Serge Vaudenay

ePrint Report
The Bitcoin architecture heavily relies on the ECDSA signature scheme which is broken by quantum adversaries as the secret key can be computed from the public key in quantum polynomial time. To mitigate this attack, bitcoins can be paid to the hash of a public key (P2PKH). However, the first payment reveals the public key so all bitcoins attached to it must be spent at the same time (i.e. the remaining amount must be transferred to a new wallet). Some problems remain with this approach: the owners are vulnerable against rushing adversaries between the time the signature is made public and the time it is committed to the blockchain. Additionally, there is no equivalent mechanism for threshold signatures. Finally, no formal analysis of P2PKH has been done.
In this paper, we formalize the security notion of a digital signature with a hidden public key and we propose and prove the security of a generic transformation that converts a classical signature to a post-quantum one that can be used only once. We compare it with P2PKH. Namely, our proposal relies on pre-image resistance instead of collision resistance as for P2PKH, so allows for shorter hashes. Additionally, we propose the notion of a delay signature to address the problem of the rushing adversary when used with a public ledger and discuss the advantages and disadvantages of our approach. We further extend our results to threshold signatures.

###### Nick Frymann, Daniel Gardham, Mark Manulis

ePrint Report
Asynchronous Remote Key Generation (ARKG), introduced by Frymann et al. at CCS 2020, allows for the generation of unlinkable public keys by third parties, for which corresponding private keys may be later learned only by the key pair's legitimate owner. These key pairs can then be used in common public-key cryptosystems, including signatures, PKE, KEMs, and schemes supporting delegation, such as proxy signatures. The only known instance of ARKG generates discrete-log-based keys.

In this paper, we introduce new ARKG constructions for lattice-based cryptosystems. The key pairs generated using our ARKG scheme can be applied to lattice-based signatures and KEMs, which have recently been selected for standardisation in the NIST PQ process, or as alternative candidates.

In particular, we address challenges associated with the noisiness of lattice hardness assumptions, which requires a new generalised definition of ARKG correctness, whilst preserving the security and privacy properties of the former instantiation. Our ARKG construction uses key encapsulation techniques by Brendel et al. (SAC 2020) coined Split KEMs. As an additional contribution, we also show that Kyber (Bos et al., EuroS&P 2018) can be used to construct a Split KEM. The security of our protocol is based on standard LWE assumptions. We also discuss its use with selected candidates from the NIST process and provide an implementation and benchmarks.

In this paper, we introduce new ARKG constructions for lattice-based cryptosystems. The key pairs generated using our ARKG scheme can be applied to lattice-based signatures and KEMs, which have recently been selected for standardisation in the NIST PQ process, or as alternative candidates.

In particular, we address challenges associated with the noisiness of lattice hardness assumptions, which requires a new generalised definition of ARKG correctness, whilst preserving the security and privacy properties of the former instantiation. Our ARKG construction uses key encapsulation techniques by Brendel et al. (SAC 2020) coined Split KEMs. As an additional contribution, we also show that Kyber (Bos et al., EuroS&P 2018) can be used to construct a Split KEM. The security of our protocol is based on standard LWE assumptions. We also discuss its use with selected candidates from the NIST process and provide an implementation and benchmarks.

###### Benny Applebaum, Eliran Kachlon, Arpita Patra

ePrint Report
In STOC 1989, Rabin and Ben-Or (RB) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with statistical (information-theoretic) security in the presence of an active (aka Byzantine) rushing adversary that controls up to half of the parties. We study the round complexity of general secure multiparty computation and several related tasks in the RB model.

Our main result shows that every functionality can be realized in only four rounds of interaction which is known to be optimal. This completely settles the round complexity of statistical actively-secure optimally-resilient MPC, resolving a long line of research.

Along the way, we construct the first round-optimal statistically-secure verifiable secret sharing protocol (Chor, Goldwasser, Micali, and Awerbuch; STOC 1985), show that every single-input functionality (e.g., multi-verifier zero-knowledge) can be realized in 3 rounds, and prove that the latter bound is optimal. The complexity of all our protocols is exponential in the number of parties, and the question of deriving polynomially-efficient protocols is left for future research.

Our main technical contribution is a construction of a new type of statistically-secure signature scheme whose existence was open even for smaller resiliency thresholds. We also describe a new statistical compiler that lifts up passively-secure protocols to actively-secure protocols in a round-efficient way via the aid of protocols for single-input functionalities. This compiler can be viewed as a statistical variant of the GMW compiler (Goldreich, Micali, Wigderson; STOC, 1987) that originally employed zero-knowledge proofs and public-key encryption.

Our main result shows that every functionality can be realized in only four rounds of interaction which is known to be optimal. This completely settles the round complexity of statistical actively-secure optimally-resilient MPC, resolving a long line of research.

Along the way, we construct the first round-optimal statistically-secure verifiable secret sharing protocol (Chor, Goldwasser, Micali, and Awerbuch; STOC 1985), show that every single-input functionality (e.g., multi-verifier zero-knowledge) can be realized in 3 rounds, and prove that the latter bound is optimal. The complexity of all our protocols is exponential in the number of parties, and the question of deriving polynomially-efficient protocols is left for future research.

Our main technical contribution is a construction of a new type of statistically-secure signature scheme whose existence was open even for smaller resiliency thresholds. We also describe a new statistical compiler that lifts up passively-secure protocols to actively-secure protocols in a round-efficient way via the aid of protocols for single-input functionalities. This compiler can be viewed as a statistical variant of the GMW compiler (Goldreich, Micali, Wigderson; STOC, 1987) that originally employed zero-knowledge proofs and public-key encryption.

###### Isaac A. Canales-Martínez, Igor Semaev

ePrint Report
Cryptanalysis of modern symmetric ciphers may be done by using linear equation systems with multiple right hand sides, which describe the encryption process. The tool was introduced by Raddum and Semaev where several solving methods were developed. In this work, the probabilities are ascribed to the right hand sides and a statistical attack is then applied. The new approach is a multivariate generalisation of the correlation attack by Siegenthaler. A fast version of the attack is provided too. It may be viewed as an extension of the fast correlation attack by Meier and Staffelbach, based on exploiting so called parity-checks for linear recurrences. Parity-checks are a particular case of the relations that we introduce in the present work. The notion of a relation is irrelevant to linear recurrences. We show how to apply the method to some LFSR-based stream ciphers including those from the Grain family. The new method generally requires a lower number of the keystream bits to recover the initial states than other techniques reported in the literature.

###### Asaf Cohen, Paweł Cyprys, Shlomi Dolev

ePrint Report
Self-masking allows the masking of success criteria, part of a problem instance (such as the sum in a subset-sum instance) that restricts the number of solutions. Self-masking is used to prevent the leakage of helpful information to attackers; while keeping the original solution valid and, at the same time, not increasing the number of unplanned solutions.
Self-masking can be achieved by xoring the sums of two (or more) independent subset sum instances \cite{DD20, CDM22}, and by doing so, eliminate all known attacks that use the value of the sum of the subset to find the subset fast, namely, in a polynomial time; much faster than the naive exponential exhaustive search.
We demonstrate that the concept of self-masking can be applied to a single instance of the subset sum and a single instance of the permuted secret-sharing polynomials.
We further introduce the benefit of permuting the bits of the success criteria, avoiding leakage of information on the value of the $i$'th bit of the success criteria, in the case of a single instance, or the parity of the $i$'th bit of the success criteria in the case of several instances.
In the case of several instances, we permute the success criteria bits of each instance prior to xoring them with each other. One basic permutation and its nesting versions (e.g., $\pi^i$) are used, keeping the solution space small and at the same time, attempting to create an ``all or nothing'' effect, where the result of a wrong $\pi$ trials does not imply much.

###### Giovanni Deligios, Aarushi Goel, Chen-Da Liu-Zhang

ePrint Report
To overcome the limitations of traditional secure multi-party computation (MPC) protocols that consider a static set of participants, in a recent work, Choudhuri et al. [CRYPTO 2021] introduced a new model called Fluid MPC, which supports {\em dynamic} participants. Protocols in this model allow parties to join and leave the computation as they wish. Unfortunately, known fluid MPC protocols (even with strong honest-majority), either only achieve security with abort, or require strong computational and trusted setup assumptions.

In this work, we also consider the "hardest" setting --- called the maximally-fluid model --- where each party can leave the computation after participating in a single round. We study the problem of designing information-theoretic maximally-fluid MPC protocols that achieve security with guaranteed output delivery (without relying on trusted setup), and obtain the following main results:

(1) We design a perfectly secure maximally-fluid MPC protocol, that achieves guaranteed output delivery against unbounded adversaries who are allowed to corrupt less than a third of the parties in every round/committee.

(2) We show that the corruption threshold in the above protocol is optimal. In particular, we prove that in fluid MPC, when the adversary can corrupt a third (or more) of the parties in any round, it is impossible to achieve information-theoretic security and guaranteed output delivery simultaneously --- even assuming a common random string (CRS) setup.

Additionally, for the case where the adversary is allowed to corrupt up to half of the parties in each committee, we present a new computationally secure maximally-fluid MPC protocol with guaranteed output delivery. Unlike prior works that require correlated setup and NIZKs, our construction only uses a common random string setup and is based on linearly-homomorphic equivocal commitments.

In this work, we also consider the "hardest" setting --- called the maximally-fluid model --- where each party can leave the computation after participating in a single round. We study the problem of designing information-theoretic maximally-fluid MPC protocols that achieve security with guaranteed output delivery (without relying on trusted setup), and obtain the following main results:

(1) We design a perfectly secure maximally-fluid MPC protocol, that achieves guaranteed output delivery against unbounded adversaries who are allowed to corrupt less than a third of the parties in every round/committee.

(2) We show that the corruption threshold in the above protocol is optimal. In particular, we prove that in fluid MPC, when the adversary can corrupt a third (or more) of the parties in any round, it is impossible to achieve information-theoretic security and guaranteed output delivery simultaneously --- even assuming a common random string (CRS) setup.

Additionally, for the case where the adversary is allowed to corrupt up to half of the parties in each committee, we present a new computationally secure maximally-fluid MPC protocol with guaranteed output delivery. Unlike prior works that require correlated setup and NIZKs, our construction only uses a common random string setup and is based on linearly-homomorphic equivocal commitments.

###### Guru-Vamsi Policharla, Bas Westerbaan, Armando Faz-Hernández, Christopher A Wood

ePrint Report
It is known that one can generically construct a post-quantum anonymous credential scheme, supporting the showing of arbitrary predicates on its attributes using general-purpose zero-knowledge proofs secure against quantum adversaries [Fischlin, CRYPTO 2006].
Traditionally, such a generic instantiation is thought to come with impractical sizes and performance. We show that with careful choices and optimizations, such a scheme can perform surprisingly well.
In fact, it performs competitively against state-of-the-art post-quantum blind signatures, for the simpler problem of post-quantum unlinkable tokens, required for a post-quantum version of Privacy Pass.

To wit, a post-quantum Privacy Pass constructed in this way using zkDilithium, our proposal for a STARK-friendly variation on Dilithium2, allows for a trade-off between token size (85–175KB) and generation time (0.3–5s) with a proof security level of 115 bits. Verification of these tokens can be done in 20–30ms. We argue that these tokens are reasonably practical, adding less than a second upload time over traditional tokens, supported by a measurement study.

Finally, we point out a clear advantage of our approach: the flexibility afforded by the general purpose zero-knowledge proofs. We demonstrate this by showing how we can construct a rate-limited variant of Privacy Pass that doesn't not rely on non-collusion for privacy.

To wit, a post-quantum Privacy Pass constructed in this way using zkDilithium, our proposal for a STARK-friendly variation on Dilithium2, allows for a trade-off between token size (85–175KB) and generation time (0.3–5s) with a proof security level of 115 bits. Verification of these tokens can be done in 20–30ms. We argue that these tokens are reasonably practical, adding less than a second upload time over traditional tokens, supported by a measurement study.

Finally, we point out a clear advantage of our approach: the flexibility afforded by the general purpose zero-knowledge proofs. We demonstrate this by showing how we can construct a rate-limited variant of Privacy Pass that doesn't not rely on non-collusion for privacy.

###### Miran Kim, Dongwon Lee, Jinyeong Seo, Yongsoo Song

ePrint Report
Lattice-based homomorphic encryption (HE) schemes are based on the noisy encryption technique, where plaintexts are masked with some random noise for security. Recent advanced HE schemes rely on a decomposition technique to manage the growth of noise, which involves a conversion of a ciphertext entry into a short vector followed by multiplication with an evaluation key. Prior to this work, the decomposition procedure turns out to be the most time-consuming part, as it requires discrete Fourier transforms (DFTs) over the base ring for efficient polynomial arithmetic. In this paper, an expensive decomposition operation over a large modulus is replaced with relatively cheap operations over a ring of integers with a small bound. Notably, the cost of DFTs is reduced from quadratic to linear with the level of a ciphertext without any extra noise growth. We demonstrate the implication of our approach by applying it to the key-switching procedure. Our experiments show that the new key-switching method achieves a speedup of 1.2--2.3 or 2.1--3.3 times over the previous method, when the dimension of a base ring is $2^{15}$ or $2^{16}$, respectively.

###### Keita Emura

ePrint Report
Forward security is a fundamental requirement in searchable encryption, where a newly generated ciphertext is not allowed to be searched by previously generated trapdoors. However, forward security is somewhat overlooked in the public key encryption with keyword search (PEKS) context and there are few proposals, whereas forward security has been stated as a default security notion in the (dynamic) symmetric searchable encryption (SSE) context. In the PEKS context, forward secure PEKS (FS-PEKS) is essentially the same as public key encryption with temporary keyword search (PETKS) proposed by Abdalla et al. (JoC 2016) which can be constructed generically from hierarchical identity-based encryption (HIBE) with level-1 anonymity. Alternatively, Zeng et al. (IEEE Transactions on Cloud Computing 2022) also proposed a generic construction of FS-PEKS from attribute-based searchable encryption supporting OR gates. In the public key authenticated encryption with keyword search (PAEKS) context, a concrete forward secure PAEKS (FS-PAEKS) construction has been proposed by Jiang et al. (The Computer Journal 2022), and no generic construction has been proposed to date. In this paper, we propose a generic construction of FS-PAEKS from PAEKS. In addition to PAEKS, we employ 0/1 encodings proposed by Lin et al. (ACNS 2005). We also show that the Jiang et al. FS-PAEKS scheme does not provide forward security, and thus our generic construction yields the first secure FS-PAEKS schemes. Our generic construction is quite simple, and it can also be applied to construct FS-PEKS. Our generic construction yields a comparably efficient FS-PEKS scheme compared to the previous scheme.
Moreover, it eliminates the hierarchical structure or attribute-based feature of the previous generic constructions which is meaningful from a feasibility perspective.

###### Vikas Srivastava, Anubhab Baksi, Sumit Kumar Debnath

ePrint Report
Digital signatures are one of the most basic cryptographic building blocks which are utilized to provide attractive security features like authenticity, unforgeability, and undeniability. The security of existing state of the art digital signatures is based on hardness of number theoretic hardness assumptions like discrete logarithm and integer factorization. However, these hard problems are insecure and face a threat in the quantum world. In particular, quantum algorithms like Shor’s algorithm can be used to solve the above mentioned hardness problem in polynomial time. As an alternative, a new direction of research called post-quantum cryptography (PQC) is supposed to provide a new generation of quantum-resistant digital signatures. Hash based signature is one such candidate to provide post quantum secure digital signatures. Hash based signature schemes are a type of digital signature scheme that use hash functions as their central building block. They are efficient, flexible, and can be used in a variety of applications. In this document, we provide an overview of the hash based signatures. Our presentation of the topic covers a wide range of aspects that are not only comprehensible for readers without expertise in the subject matter, but also serve as a valuable resource for experts seeking reference material.

###### Alper Cakan, Vipul Goyal, Chen-Da Liu-Zhang, João Ribeiro

ePrint Report
Side-channel attacks, which aim to leak side information on secret system components, are ubiquitous. Even simple attacks, such as measuring time elapsed or radiation emitted during encryption and decryption procedures, completely break textbook versions of many cryptographic schemes. This has prompted the study of leakage-resilient cryptography, which remains secure in the presence of side-channel attacks.

Classical leakage-resilient cryptography must necessarily impose restrictions on the type of leakage one aims to protect against. As a notable example, the most well-studied leakage model is that of bounded leakage, where it is assumed that an adversary learns at most $\ell$ bits of leakage on secret components, for some leakage bound $\ell$. Although this leakage bound is necessary, it is unclear if such a bound is realistic in practice since many practical side-channel attacks cannot be captured by bounded leakage.

In this work, we investigate the possibility of designing cryptographic schemes that provide guarantees against arbitrary side-channel attacks:

- Using techniques from uncloneable quantum cryptography, we design several basic leakage-resilient primitives, such as secret sharing, (weak) pseudorandom functions, digital signatures, and public- and private-key encryption, which remain secure under (polynomially) unbounded classical leakage. In particular, this leakage can be much longer than the (quantum) secret being leaked upon. In our view, leakage is the result of observations of quantities such as power consumption and hence is most naturally viewed as classical information. - In the even stronger adversarial setting where the adversary is allowed to obtain unbounded quantum leakage (and thus leakage-resilience is impossible), we design schemes for many cryptographic tasks which support leakage-detection. This means that we can efficiently check whether the security of such a scheme has been compromised by a side-channel attack. These schemes are based on techniques from cryptography with certified deletion. - We also initiate a study of classical cryptographic schemes with (bounded) post-quantum leakage-resilience. These schemes resist side-channel attacks performed by adversaries with quantum capabilities which may even share arbitrary entangled quantum states. That is, even if such adversaries are non-communicating, they can still have "spooky" communication via entangled states.

Classical leakage-resilient cryptography must necessarily impose restrictions on the type of leakage one aims to protect against. As a notable example, the most well-studied leakage model is that of bounded leakage, where it is assumed that an adversary learns at most $\ell$ bits of leakage on secret components, for some leakage bound $\ell$. Although this leakage bound is necessary, it is unclear if such a bound is realistic in practice since many practical side-channel attacks cannot be captured by bounded leakage.

In this work, we investigate the possibility of designing cryptographic schemes that provide guarantees against arbitrary side-channel attacks:

- Using techniques from uncloneable quantum cryptography, we design several basic leakage-resilient primitives, such as secret sharing, (weak) pseudorandom functions, digital signatures, and public- and private-key encryption, which remain secure under (polynomially) unbounded classical leakage. In particular, this leakage can be much longer than the (quantum) secret being leaked upon. In our view, leakage is the result of observations of quantities such as power consumption and hence is most naturally viewed as classical information. - In the even stronger adversarial setting where the adversary is allowed to obtain unbounded quantum leakage (and thus leakage-resilience is impossible), we design schemes for many cryptographic tasks which support leakage-detection. This means that we can efficiently check whether the security of such a scheme has been compromised by a side-channel attack. These schemes are based on techniques from cryptography with certified deletion. - We also initiate a study of classical cryptographic schemes with (bounded) post-quantum leakage-resilience. These schemes resist side-channel attacks performed by adversaries with quantum capabilities which may even share arbitrary entangled quantum states. That is, even if such adversaries are non-communicating, they can still have "spooky" communication via entangled states.