## IACR News

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#### 10 May 2022

###### Xiao Sui, Sisi Duan, Haibin Zhang

ePrint Report
As the first Byzantine fault-tolerant (BFT) protocol with linear communication complexity, HotStuff (PODC 2019) has received significant attention. HotStuff has three round-trips for both normal case operations and view change protocols. Follow-up studies attempt to reduce the number of phases for HotStuff. These protocols, however, all give up of one thing in return for another.

This paper presents Marlin, a BFT protocol with linearity, having two phases for normal case operations and two or three phases for view changes. Marlin uses the same cryptographic tools as in HotStuff and introduces no additional assumptions. We implement a new and efficient Golang library for Marlin and HotStuff, showing Marlin outperforms HotStuff for both the common case and the view change.

This paper presents Marlin, a BFT protocol with linearity, having two phases for normal case operations and two or three phases for view changes. Marlin uses the same cryptographic tools as in HotStuff and introduces no additional assumptions. We implement a new and efficient Golang library for Marlin and HotStuff, showing Marlin outperforms HotStuff for both the common case and the view change.

###### Tim Ruffing, Viktoria Ronge, Elliott Jin, Jonas Schneider-Bensch, Dominique Schröder

ePrint Report
Bitcoin and other cryptocurrencies have recently introduced support for Schnorr signatures whose cleaner algebraic structure, as compared to ECDSA, allows for simpler and more practical constructions of highly demanded "$t$-of-$n$" threshold signatures. However, existing Schnorr threshold signature schemes (like their ECDSA counterparts) still fall short of the needs of real-world applications due to their assumption that the network is synchronous and due to their lack of robustness, i.e., the guarantee that $t$ honest signers are able to obtain a valid signature even in the presence of other malicious signers who try to disrupt the protocol. This hinders the adoption of threshold signatures in the cryptocurrency ecosystem, e.g., in second-layer protocols built on top of cryptocurrencies.

In this work, we propose $\mathsf{ROAST}$, a simple wrapper that turns a given threshold signature scheme into a scheme with a robust and asynchronous signing protocol, as long as the underlying signing protocol is semi-interactive (i.e., has one preprocessing round and one actual signing round), provides identifiable aborts, and is unforgeable under concurrent signing sessions. When applied to the state-of-the-art Schnorr threshold signature scheme $\mathsf{FROST}$, which fulfills these requirements, we obtain a simple, efficient, and highly practical Schnorr threshold signature scheme.

In this work, we propose $\mathsf{ROAST}$, a simple wrapper that turns a given threshold signature scheme into a scheme with a robust and asynchronous signing protocol, as long as the underlying signing protocol is semi-interactive (i.e., has one preprocessing round and one actual signing round), provides identifiable aborts, and is unforgeable under concurrent signing sessions. When applied to the state-of-the-art Schnorr threshold signature scheme $\mathsf{FROST}$, which fulfills these requirements, we obtain a simple, efficient, and highly practical Schnorr threshold signature scheme.

###### Sora Suegami

ePrint Report
We propose a cryptographic obfuscation scheme for smart contracts from one-time programs using a blockchain, a garbled circuit, and witness encryption. The proposed scheme protects not only the privacy of its input data and states but also the privacy of its algorithm and hardcoded secrets. Its security depends on existing secure blockchains and does not require the honest majority of secure multiparty computation and trusted hardware. This scheme is more efficient than obfuscating an entire program with indistinguishability obfuscation. In addition, it needs a trusted setup, but its security is protected unless all participants of the setup process are malicious.

###### Yuyu Wang, Jiaxin Pan

ePrint Report
We construct the first non-interactive zero-knowledge (NIZK) proof systems in the fine-grained setting where adversaries’ resources are bounded and honest users have no more resources than an adversary. More concretely, our setting is the NC1-fine-grained setting, namely, all parties (including adversaries and honest participants) are in NC1.
Our NIZK systems are for circuit satisfiability (SAT) under the worst-case assumption, NC1 being unequal to Parity-L/poly. As technical contributions, we propose two approaches to construct NIZKs in the NC1-fine-grained setting. In stark contrast to the classical Fiat-Shamir transformation, both our approaches start with a simple Sigma protocol and transform it into NIZKs for circuit SAT without random oracles. Additionally, our second approach firstly proposes a fully homomorphic encryption (FHE) scheme in the fine-grained setting, which was not known before, as a building block. Compared with the first approach, the resulting NIZK only supports circuits with constant multiplicative depth, while its proof size is independent of the statement circuit size.
Extending our approaches, we obtain two NIZK systems in the uniform reference string model and two non-interactive zaps (namely, non-interactive witness-indistinguishability proof systems in the plain model). While the previous constructions from Ball, Dachman-Soled, and Kulkarni (CRYPTO 2020) require provers to run in polynomial-time, our constructions are the first one with provers in NC1.

###### GyuChol.Kim, YongBok.Jong

ePrint Report
In this paper, we propose the method to speed up signature generation in RSA with small public exponent. We first divide the signing algorithm into two stages. One is message generating stage and the other is signing stage. Next, we modify the RSA signature so that the bulk of the calculation cost is allocated to message generating stage. This gives the possibility to propose the RSA signature schemes which have fast signature generation and very fast verification. Our schemes are suited for the applications in which a message is generated offline, but needs to be quickly signed and verified online.

###### Sarisht Wadhwa, Jannis Stoeter, Fan Zhang, Kartik Nayak

ePrint Report
Hashed Time-Locked Contracts (HTLCs) are a widely used primitive in blockchain systems. Unfortunately, HTLC is incentive-incompatible and is vulnerable to bribery attacks.
MAD-HTLC (Oakland'21) is an elegant solution aiming to address the incentive incompatibility of HTLC.

In this paper, we show that MAD-HTLC is also incentive-incompatible. The crux of the issue is that MAD-HTLC only considers passively rational miners. We argue that such a model fails to capture active rational behaviors. We demonstrate the importance of taking actively rational behaviors into consideration by showing three novel reverse-bribery attacks against MAD-HTLC that can be implemented using Trusted Execution Environments (TEEs) or zero-knowledge proofs (ZKPs). We further show that reverse bribery can be combined with original delaying attacks to render MAD-HTLC insecure regardless of the relationship between collateral and deposit. Based on the learnings from our attacks, we devise a new smart contract specification, He-HTLC, which is lightweight and inert to incentive manipulation attacks. HE-HTLC, according to us, is the first specification to meet the HTLC specification even in the presence of actively rational miners.

In this paper, we show that MAD-HTLC is also incentive-incompatible. The crux of the issue is that MAD-HTLC only considers passively rational miners. We argue that such a model fails to capture active rational behaviors. We demonstrate the importance of taking actively rational behaviors into consideration by showing three novel reverse-bribery attacks against MAD-HTLC that can be implemented using Trusted Execution Environments (TEEs) or zero-knowledge proofs (ZKPs). We further show that reverse bribery can be combined with original delaying attacks to render MAD-HTLC insecure regardless of the relationship between collateral and deposit. Based on the learnings from our attacks, we devise a new smart contract specification, He-HTLC, which is lightweight and inert to incentive manipulation attacks. HE-HTLC, according to us, is the first specification to meet the HTLC specification even in the presence of actively rational miners.

###### Elisaweta Masserova, Deepali Garg, Ken Mai, Lawrence Pileggi, Vipul Goyal, Bryan Parno

ePrint Report
Due to the complexity and the cost of producing integrated circuits, most hardware circuit designers outsource the manufacturing of their circuits to a third-party foundry. However, a dishonest foundry may abuse its access to the circuit's design in a variety of ways that undermine the designer's investment or potentially introduce vulnerabilities.

To combat these issues, the hardware community has developed the notion of logic locking, which allows the designer to send the foundry a ``locked'' version of the original circuit. After the locked circuit has been manufactured, authorized users can unlock the original functionality with a secret key.

Unfortunately, most logic locking schemes are analyzed using informal security notions, leading to a cycle of attacks and ad hoc defenses that impedes the adoption of logic locking.

In this work, we propose a formal simulation-based security definition for logic locking. We then show that a construction based on universal circuits provably satisfies the definition. More importantly, we explore ways to efficiently realize our construction in actual hardware. This entails the design of alternate approaches and optimizations, and our evaluation (based on standard hardware metrics like power, area, and performance) illuminates tradeoffs between these designs.

To combat these issues, the hardware community has developed the notion of logic locking, which allows the designer to send the foundry a ``locked'' version of the original circuit. After the locked circuit has been manufactured, authorized users can unlock the original functionality with a secret key.

Unfortunately, most logic locking schemes are analyzed using informal security notions, leading to a cycle of attacks and ad hoc defenses that impedes the adoption of logic locking.

In this work, we propose a formal simulation-based security definition for logic locking. We then show that a construction based on universal circuits provably satisfies the definition. More importantly, we explore ways to efficiently realize our construction in actual hardware. This entails the design of alternate approaches and optimizations, and our evaluation (based on standard hardware metrics like power, area, and performance) illuminates tradeoffs between these designs.

###### Donghoon Chang, Deukjo Hong, Jinkeon Kang

ePrint Report
Ascon-128 and Ascon-80pq use 12-round Ascon permutation for initialization and finalization phases and 6-round Ascon permutation for processing associate data and message. In a nonce-misuse setting, we present a new partial-state-recovery conditional-cube attack on Ascon-128 and Ascon-80pq, where 192 bits out of 320-bit state are recovered. For our partial state-recovery attack, its required data complexity, \(D\), is about \(2^{44.8}\) and its required memory complexity, \(M\), is negligible. After a 192-bit partial state is recovered, in a nonce-misuse setting, we can further recover the full 320-bit state with time complexity, \(T=2^{128}\), and then we can recover the secret key with extra data complexity of \(2^{31.5}\), extra time complexity of \(2^{129.5}\), and memory complexity of \(2^{31.5}\). A similar attack of recovering the partial state was independently developed by Baudrin et al. at NIST fifth Lightweight Cryptography workshop. Note that our attack does not violate the NIST LWC security requirements on Ascon-128 and Ascon-80pq as well as the designers' claims.

###### Aram Jivanyan, Aaron Feickert

ePrint Report
Electronic voting has long been an area of active and challenging research. Security properties relevant to physical voting in elections with a variety of threat models and priorities are often difficult to reproduce in cryptographic systems and protocols. Existing work in this space often focuses on the privacy of ballot contents, assurances to voters that their votes are tabulated, and verification that election results are correct; however, privacy of voter identity is often offloaded to trust requirements on election organizers or tallying authorities, or implies other kinds of trust related to cryptographic construction instantiation. Here we introduce Aura, an election protocol that reduces trust on tallying authorities and organizers while ensuring voter privacy. Ballots in Aura are dissociated from voter identity cryptographically, use verifiable encryption and threshold decryption to diffuse trust in tallying authorities, require no trusted setup for cryptographic primitives, and use efficient proving systems to reduce computation and communication complexity. These properties make Aura a competitive candidate for use in a variety of applications where trust minimization is desirable or necessary.

###### Mathias Hall-Andersen, Jesper Buus Nielsen

ePrint Report
In his landmark paper at TCC 2008 Paul Valiant introduced the notion of ``incrementally verifiable computation''
which enables a prover to incrementally compute a succinct proof of correct execution of a (potentially) long running process. The paper later won the 2019 TCC test of time award. The construction was proven secure in the random oracle model without any further computational assumptions. However, the overall proof was given using a non-standard version of the random-oracle methodology where sometimes the hash function is a random oracle and sometimes it has a short description as a circuit. Valiant clearly noted that this model is non-standard, but conjectured that the standard random oracle methodology would not suffice. This conjecture has been open for 14 years. We prove that under some mild extra assumptions on the proof system the conjecture is true: the standard random-oracle model does not allow incrementally verifiable computation without making computational assumptions. Two extra assumptions under which we can prove the conjecture are 1) the proof system is also zero-knowledge or 2) when the proof system makes a query to its random oracle it can know with non-negligible probability whether the query is fresh or was made by the proof system earlier in the construction of the proof.

###### Sandro Coretti, Aggelos Kiayias, Cristopher Moore, Alexander Russell

ePrint Report
One of the most successful applications of peer-to-peer communication networks is in the context of blockchain protocols, which—in Satoshi Nakamoto's own words—rely on the "nature of information being easy to spread and hard to stifle." Significant efforts were invested in the last decade into analyzing the security of these protocols, and invariably the security arguments known for longest-chain Nakamoto-style consensus use an idealization of this tenet.

Unfortunately, the real-world implementations of peer-to-peer gossip-style networks used by blockchain protocols rely on a number of ad-hoc attack mitigation strategies that leave a glaring gap between the idealized communication layer assumed in formal security arguments for blockchains and the real world, where a wide array of attacks have been showcased.

In this work we bridge this gap by presenting a Byzantine-resilient network layer for blockchain protocols. For the first time we quantify the problem of network-layer attacks in the context of blockchain security models, and we develop a design that thwarts resource restricted adversaries.

Importantly, we focus on the proof-of-stake setting due to its vulnerability to Denial-of-Service (DoS) attacks stemming from the well-known deficiency (compared to the proof-of-work setting) known as nothing at stake.

We present a Byzantine-resilient gossip protocol, and we analyze it in the Universal Composition framework. In order to prove security, we show novel results on expander properties of random graphs. Importantly, our gossip protocol can be based on any given bilateral functionality that determines a desired interaction between two "adjacent" peers in the networking layer and demonstrates how it is possible to use application-layer information to make the networking-layer resilient to attacks.

Despite the seeming circularity, we demonstrate how to prove the security of a Nakamoto-style longest-chain protocol given our gossip networking functionality, and hence, we demonstrate constructively how it is possible to obtain provable security across protocol layers, given only bare-bone point-to-point networking, majority of honest stake, and a verifiable random function.

Unfortunately, the real-world implementations of peer-to-peer gossip-style networks used by blockchain protocols rely on a number of ad-hoc attack mitigation strategies that leave a glaring gap between the idealized communication layer assumed in formal security arguments for blockchains and the real world, where a wide array of attacks have been showcased.

In this work we bridge this gap by presenting a Byzantine-resilient network layer for blockchain protocols. For the first time we quantify the problem of network-layer attacks in the context of blockchain security models, and we develop a design that thwarts resource restricted adversaries.

Importantly, we focus on the proof-of-stake setting due to its vulnerability to Denial-of-Service (DoS) attacks stemming from the well-known deficiency (compared to the proof-of-work setting) known as nothing at stake.

We present a Byzantine-resilient gossip protocol, and we analyze it in the Universal Composition framework. In order to prove security, we show novel results on expander properties of random graphs. Importantly, our gossip protocol can be based on any given bilateral functionality that determines a desired interaction between two "adjacent" peers in the networking layer and demonstrates how it is possible to use application-layer information to make the networking-layer resilient to attacks.

Despite the seeming circularity, we demonstrate how to prove the security of a Nakamoto-style longest-chain protocol given our gossip networking functionality, and hence, we demonstrate constructively how it is possible to obtain provable security across protocol layers, given only bare-bone point-to-point networking, majority of honest stake, and a verifiable random function.

###### Katarzyna Anna Kowalska, Davide Fogliano, Jose Garcia Coello

ePrint Report
At Crypta Labs we are developing Quantum Random Number Generator technology and are using different random number test suites to assess the quality of our products. Among these is the NIST 800-22 suite. When testing our datasets, we found that we were consistently failing one particular test: the Overlapping Template Matching test. This was surprising to us, so we fed data from a known PRNG source into the same test and discovered that NIST approved PRNG was also failing in a similar fashion. At this point we decided to debug NIST's code. We did indeed find an error within the probability calculations and, once corrected, ran the tests again and passed. The code for this test had previously been revised by NIST due to an incorrect calculation of the probabilities, however, later in the revised source code the corrected calculations were calculated again using the originally incorrect formulas, and these overwrote the revised fix. Furthermore, the NIST 800-22 Test suite is currently under revision and our paper is a contribution towards it.

###### Yawning Angel, Benjamin Dowling, Andreas Hülsing, Peter Schwabe, Florian Weber

ePrint Report
We introduce PQNoise, a post-quantum variant of the Noise framework. We demonstrate that it is possible to replace the Diffie-Hellman key-exchanges in Noise with KEMs in a secure way. A challenge is the inability to combine key pairs of KEMs, which can be resolved by certain forms of randomness-hardening for which we introduce a formal abstraction. We provide a generic recipe to turn classical Noise patterns into PQNoise patterns. We prove that the resulting PQNoise patterns achieve confidentiality and authenticity in the fACCE-model. Moreover we show that for those classical Noise-patterns that have been conjectured or proven secure in the fACCE-model our matching PQNoise-patterns eventually achieve the same security. Our security proof is generic and applies to any valid PQNoise pattern. This is made possible by another abstraction, called a hash-object, which hides the exact workings of how keying material is processed in an abstract stateful object that outputs pseudorandom keys under different corruption patterns. We also show that the hash chains used in Noise are a secure hash-object. Finally, we demonstrate the practicality of PQNoise delivering benchmarks for several base patterns.

###### Patrick Karl, Jonas Schupp, Tim Fritzmann, Georg Sigl

ePrint Report
CRYSTALS-Dilithium and Falcon are digital signature algorithms based on cryptographic lattices, that are considered secure even if large-scale quantum computers will be able to break conventional public-key cryptography. Both schemes are third round candidates in the ongoing NIST post-quantum competition. In this work, we present a RISC-V HW/SW codesign that aims to combine the advantages of software- and hardware implementations, i.e. flexibility and performance. It shows the use of flexible hardware accelerators, which have been previously used for Public-Key Encryption (PKE) and Key-Encapsulation Mechanism (KEM), for post-quantum signatures. It is optimized for Dilithium as a generic signature scheme but also accelerates applications that require fast verification of Falcon’s compact signatures. We provide a comparison with previous works showing that for Dilithium and Falcon, cycle counts are significantly reduced, such that our design is faster than previous software implementations or other HW/SW codesigns. In addition to that, we present a compact Globalfoundries 22 nm ASIC design that runs at 800 MHz. By using hardware acceleration, energy consumption for Dilithium is reduced by up to 92.2%, and up to 67.5% for Falcon’s signature verification.

###### Jincheol Ha, Seongkwang Kim, Byeonghak Lee, Jooyoung Lee, Mincheol Son

ePrint Report
A transciphering framework converts a symmetric ciphertext into a homomorphic ciphertext on the server-side, reducing computational and communication overload on the client-side. In Asiacrypt 2021, Cho et al. proposed the RtF framework that supports approximate computation.

In this paper, we propose a family of noisy ciphers, dubbed Rubato, with a novel design strategy of introducing noise to a symmetric cipher of a low algebraic degree. With this strategy, the multiplicative complexity of the cipher is significantly reduced, compared to existing HE-friendly ciphers, without degrading the overall security. More precisely, given a moderate block size (16 to 64), Rubato enjoys a low multiplicative depth (2 to 5) and a small number of multiplications per encrypted word (2.1 to 6.25) at the cost of slightly larger ciphertext expansion (1.26 to 1.31). The security of Rubato is supported by comprehensive analysis including symmetric and LWE cryptanalysis. Compared to HERA within the RtF framework, client-side and server-side throughput is improved by 22.9% and 32.2%, respectively, at the cost of only 1.6% larger ciphertext expansion.

In this paper, we propose a family of noisy ciphers, dubbed Rubato, with a novel design strategy of introducing noise to a symmetric cipher of a low algebraic degree. With this strategy, the multiplicative complexity of the cipher is significantly reduced, compared to existing HE-friendly ciphers, without degrading the overall security. More precisely, given a moderate block size (16 to 64), Rubato enjoys a low multiplicative depth (2 to 5) and a small number of multiplications per encrypted word (2.1 to 6.25) at the cost of slightly larger ciphertext expansion (1.26 to 1.31). The security of Rubato is supported by comprehensive analysis including symmetric and LWE cryptanalysis. Compared to HERA within the RtF framework, client-side and server-side throughput is improved by 22.9% and 32.2%, respectively, at the cost of only 1.6% larger ciphertext expansion.

###### Sabyasachi Dey, Hirendra Kumar Garai, Santanu Sarkar, Nitin Kumar Sharma

ePrint Report
In this paper, we provide several improvements over the existing differential-linear attacks on ChaCha. ChaCha is a stream cipher which has $20$ rounds. At CRYPTO $2020$, Beierle et al. observed a differential in the $3.5$-th round if the right pairs are chosen. They produced an improved attack using this, but showed that to achieve a right pair, we need $2^5$ iterations on average.
In this direction, we provide a technique to find the right pairs with the help of listing. Also, we provide a strategical improvement in PNB construction, modification of complexity calculation and an alternative attack method using two input-output pairs.
Using these, we improve the time complexity, reducing it to $2^{221.95}$ from $2^{230.86}$ reported by Beierle et al. for $256$ bit version of ChaCha. Also, after a decade, we improve existing complexity (Shi et al: ICISC 2012) for a $6$-round of
$128$ bit version of ChaCha by more than 11 million times and produce the first-ever attack on 6.5-round ChaCha$128$ with time complexity $2^{123.04}.$

###### Damiano Abram, Peter Scholl, Sophia Yakoubov

ePrint Report
Structured random strings (SRSs) and correlated randomness are important for many cryptographic protocols. In settings where interaction is expensive, it is desirable to obtain such randomness in as few rounds of communication as possible; ideally, simply by exchanging one reusable round of messages which can be considered public keys.

In this paper, we describe how to generate any SRS or correlated randomness in such a single round of communication, using, among other things, indistinguishability obfuscation. We introduce what we call a distributed sampler, which enables $n$ parties to sample a single public value (SRS) from any distribution. We construct a semi-malicious distributed sampler in the plain model, and use it to build a semi-malicious public-key PCF (Boyle et al, FOCS 2020) in the plain model. A public-key PCF can be thought of as a distributed correlation sampler; instead of producing a public SRS, it gives each party a private random value (where the values satisfy some correlation).

We introduce a general technique called an anti-rusher which compiles any one-round protocol with semi-malicious security without inputs to a similar one-round protocol with active security by making use of a programmable random oracle. This gets us actively secure distributed samplers and public-key PCFs in the random oracle model.

Finally, we explore some tradeoffs. Our first PCF construction is limited to reverse-sampleable correlations (where the random outputs of honest parties must be simulatable given the random outputs of corrupt parties); we additionally show a different construction without this limitation, but which does not allow parties to hold secret parameters of the correlation. We also describe how to avoid the use of a random oracle at the cost of relying on sub-exponentially secure indistinguishability obfuscation.

In this paper, we describe how to generate any SRS or correlated randomness in such a single round of communication, using, among other things, indistinguishability obfuscation. We introduce what we call a distributed sampler, which enables $n$ parties to sample a single public value (SRS) from any distribution. We construct a semi-malicious distributed sampler in the plain model, and use it to build a semi-malicious public-key PCF (Boyle et al, FOCS 2020) in the plain model. A public-key PCF can be thought of as a distributed correlation sampler; instead of producing a public SRS, it gives each party a private random value (where the values satisfy some correlation).

We introduce a general technique called an anti-rusher which compiles any one-round protocol with semi-malicious security without inputs to a similar one-round protocol with active security by making use of a programmable random oracle. This gets us actively secure distributed samplers and public-key PCFs in the random oracle model.

Finally, we explore some tradeoffs. Our first PCF construction is limited to reverse-sampleable correlations (where the random outputs of honest parties must be simulatable given the random outputs of corrupt parties); we additionally show a different construction without this limitation, but which does not allow parties to hold secret parameters of the correlation. We also describe how to avoid the use of a random oracle at the cost of relying on sub-exponentially secure indistinguishability obfuscation.

###### Renas Bacho (CISPA Helmholtz Center for Information Security), Julian Loss (CISPA Helmholtz Center for Information Security)

ePrint Report
Threshold signatures are a crucial tool for many distributed protocols. As shown by Cachin, Kursawe, and Shoup (PODC `00), schemes with unique signatures are of particular importance, as they allow to implement distributed coin flipping very efficiently and without any timing assumptions. This makes them an ideal building block for (inherently randomized) asynchronous consensus protocols. The threshold-BLS signature of Boldyreva (PKC `03) is both unique and very compact, but unfortunately lacks a security proof against adaptive adversaries. Thus, current consensus protocols either rely on less efficient alternatives or are not adaptively secure. In this work, we revisit the security of the threshold BLS signature by showing the following results, assuming $t$ adaptive corruptions:

- We give a modular security proof that follows a two-step approach: 1) We introduce a new security notion for distributed key generation protocols (DKG). We show that it is satisfied by several protocols that previously only had a static security proof. 2) Assuming any DKG protocol with this property, we then prove unforgeability of the threshold BLS scheme. Our reductions are tight and can be used to substantiate real-world parameter choices.

- To justify our use of strong assumptions such as the algebraic group model (AGM) and the hardness of one-more-discrete logarithm (OMDL), we prove two impossibility results: 1) Without the AGM, there is no tight security reduction from $(t+1)$-OMDL. 2) Even in the AGM, $(t+1)$-OMDL is the weakest assumption from which any (possibly loose) security reduction exists.

- We give a modular security proof that follows a two-step approach: 1) We introduce a new security notion for distributed key generation protocols (DKG). We show that it is satisfied by several protocols that previously only had a static security proof. 2) Assuming any DKG protocol with this property, we then prove unforgeability of the threshold BLS scheme. Our reductions are tight and can be used to substantiate real-world parameter choices.

- To justify our use of strong assumptions such as the algebraic group model (AGM) and the hardness of one-more-discrete logarithm (OMDL), we prove two impossibility results: 1) Without the AGM, there is no tight security reduction from $(t+1)$-OMDL. 2) Even in the AGM, $(t+1)$-OMDL is the weakest assumption from which any (possibly loose) security reduction exists.

###### M. Rajululkahf

ePrint Report
This paper proposes Băhēm; a symmetric cipher that, when given a
random-looking key k, a true random number generator (TRNG) and a cleartext
message m to encrypt, no cryptanalysis can degrade its security below
min[H(m), H(k)] bits of entropy, even under Grover's algorithm or even if
it turned out that P = NP.

Aside from the cost of memory access and input/output processing, Băhēm requires only three additions (one per-session, two per-block) and one XOR operation in order to encrypt or decrypt, and is also highly parallelise-able.

Despite Băhēm's 1-bit overhead per cleartext bit, its early prototype, Alyal, achieved similar run-time speeds to OpenSSL's ChaCha20; slightly faster decryption, while slightly slower encryption when the TRNG was prepared in a file in advance. This demonstrates that Băhēm is practicality usable for many real-world application scenarios.

Later implementations, with better TRNG optimisations and parallelism, must allow the prototype a faster run-time for both, encryption and decryption.

Aside from the cost of memory access and input/output processing, Băhēm requires only three additions (one per-session, two per-block) and one XOR operation in order to encrypt or decrypt, and is also highly parallelise-able.

Despite Băhēm's 1-bit overhead per cleartext bit, its early prototype, Alyal, achieved similar run-time speeds to OpenSSL's ChaCha20; slightly faster decryption, while slightly slower encryption when the TRNG was prepared in a file in advance. This demonstrates that Băhēm is practicality usable for many real-world application scenarios.

Later implementations, with better TRNG optimisations and parallelism, must allow the prototype a faster run-time for both, encryption and decryption.

###### Joon-Woo Lee, Eunsang Lee, Young-Sik Kim, Jong-Seon No

ePrint Report
In the artificial intelligence as a service (AIaaS) system in the client-server model, where the clients provide the data on the cloud and the server processes the data by using the deep neural network in the cloud, data privacy via homomorphic encryption is getting more important. Brakerski/Fan-Vercauteran (BFV) and Cheon-Kim-Kim-Song (CKKS) schemes are two representative homomorphic encryption schemes which support various arithmetic operations for encrypted data in the single-instruction multiple-data (SIMD) manner. As the homomorphic operations in these schemes are performed component-wisely for encrypted message vectors, the rotation operations for various cyclic shifts of the encrypted message vector are required for useful advanced operations such as bootstrapping, matrix multiplication, and convolution in convolutional neural networks. Since the rotation operation requires different Galois keys for different cyclic shifts, the servers using the conventional BFV and CKKS schemes should ask the clients having their secret keys to generate and send all of the required Galois keys. In particular, in the advanced services that require rotation operations for many cyclic shifts such as deep convolutional neural networks, the total Galois key size can be hundreds of gigabytes. It imposes substantial burdens on the clients in the computation and communication cost aspects. In this paper, we propose a new concept of \emph{hierarchical Galois key generation method} for homomorphic encryption to reduce the burdens of the clients and the server running BFV and CKKS schemes. The main concept in the proposed method is the hierarchical Galois keys, such that after the client generates and transmits a few Galois keys in the highest key level to the server, the server can generate any required Galois keys from the public key and the smaller set of Galois keys in the higher key level. This proposed method significantly reduces the number of the clients' operations for Galois key generation and the communication cost for the Galois key transmission. Since the server can generate the required Galois keys by using the received small set of Galois keys from the client, the server does not need to request additional Galois keys to the clients or to store all possible Galois keys for future use. For example, if we implement the standard ResNet-20 network for the CIFAR-10 dataset and the ResNet-18 network for the ImageNet dataset with pre-trained parameters of the CKKS scheme with the polynomial modulus degree $N=2^{16}$ and $N=2^{17}$, respectively, the server requires 265 and 617 Galois keys, which occupy 105.6GB and 197.6GB of memory, respectively. If we use the proposed three-level hierarchical Galois key system, the Galois key size generated and transmitted by the client can be reduced from 105.6GB to 3.4GB for ResNet-20 model for CIFAR-10, and reduced from 197.6GB to 3.9GB for ResNet-18 model for ImageNet.