## IACR News

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#### 01 January 2022

###### Wenshuo Guo, Fang-Wei Fu
ePrint Report
This paper presents a key recovery attack on the cryptosystem proposed by Lau and Tan in a talk at ACISP 2018. The Lau-Tan cryptosystem uses Gabidulin codes as the underlying decodable code. To hide the algebraic structure of Gabidulin codes, the authors chose a matrix of column rank $n$ to mix with a generator matrix of the secret Gabidulin code. The other part of the public key, however, reveals crucial information about the private key. Our analysis shows that the problem of recovering the private key can be reduced to solving a multivariate linear system, rather than solving a multivariate quadratic system as claimed by the authors. Apparently, this attack costs polynomial time, and therefore completely breaks the cryptosystem.
###### Akiko Inoue, Tetsu Iwata, Kazuhiko Minematsu
ePrint Report
We study the provable security claims of two NIST Lightweight Cryptography (LwC) finalists, GIFT-COFB and Photon-Beetle, and present several attacks whose complexities contradict their claimed bounds in their final round specification documents. For GIFT-COFB, we show an attack using $q_e$ encryption queries and no decryption query to break privacy (IND-CPA). The success probability is $O(q_e/2^{n/2})$ for $n$-bit block while the claimed bound contains $O(q^2_e/2^{n})$. This positively solves an open question posed in~[Khairallah, ePrint~2021/648]. For Photon-Beetle, we show attacks using $q_e$ encryption queries (using a small number of input blocks) followed by a single decryption query and no primitive query to break authenticity (INT-CTXT). The success probability is $O(q^2_e/2^{b})$ for $b$-bit block permutation, and it is significantly larger than what the claimed bound tells. We also analyze other (improved/modified) bounds of Photon-Beetle shown in the subsequent papers~[Chakraborty et al., ToSC 2020(2) and Chakraborty et al., ePrint~2019/1475].

We emphasize that our results do not contradict the claimed bit security'' in the LwC specification documents for any of the schemes that we studied. That is, we do not negate the claims that GIFT-COFB is $(n/2 - \log n)$-bit secure for $n=128$, and Photon-Beetle is $(b/2 - \log b/2)$-bit secure for $b=256$ and $r=128$, where $r$ is a rate.

#### 31 December 2021

###### Mao Wenbo, Wang Wenxiang
ePrint Report
GoUncle is a blockchain for permissionless participation by modest computers. As in GHOST (Greedy Heaviest Observed SubTree, in successful implementation and use by the Ethereum blockchain's Proofs-of-Work version), GoUncle blocks also record the public-key IDs of some temporary forking blocks finders who are dearly called uncles'' (poorly named orphans'' in Bitcoin). While GHOST uncles are for saving PoW computations, GoUncle assigns jobs for its uncles to do. In a payload distillation job, uncles choose from block payloads only the logs which comply with the blockchain database (DB) policy to announce for to survive the blockchain gossip protocol. With uncles distillations, the blockchain address, aka height, for a no-longer-need-to-trust block, is deterministic right upon the block extending the blockchain. The deterministic blockchain addresses can index partition the distributed DB into small files to store in nowadays over provisioned external storage even for a low-cost computer. The index partitioned DB files can be fast operable for input, output, lookup, insert, update, manage, ..., etc., as a standard DB management system (DBMS) can. It is the fast operable property of the DBMS, even by a modest computer, that secures the blockchain DBMS by a hop-by-hop firewall among vast semantics gossipers who each looks up the local DBMS to judge either writing to the DB correct uncles distillations and forwarding them on, or discarding incorrect ones, both operations being quick. Since the hop-by-hop firewall works exactly as correctness probability amplification by repeated execution of a randomized probabilistic (RP) algorithm, the GoUncle work establishes:

$\mbox{Blockchains} \subset \mbox{RP}.$

Also to be manifested in the present work are more general blockchain consensus layer computations that uncles can and should execute and disseminate the execution output as No-Spam and No-Single-Point-of-Failure (No-SPOF) set of blockchain servers.
###### Akira Takahashi, Greg Zaverucha
ePrint Report
Verifiable encryption (VE) is a protocol where one can provide assurance that an encrypted plaintext satisfies certain properties. It is an important buiding block in cryptography with many useful applications, such as key escrow, group signatures, optimistic fair exchange, etc. However, a majority of previous VE schemes are restricted to instantiation with specific public-key encryption schemes or relations.

In this work, we propose a novel framework that realizes VE protocols using the MPC-in-the-head zero-knowledge proof systems (Ishai et al. STOC 2007). Our generic compiler can turn a large class of MPC-in-the-head ZK proofs into secure VE protocols for any CPA secure public-key encryption (PKE) schemes with the undeniability property, a notion that essentially guarantees binding of encryption when used as a commitment scheme.

Our framework is versatile: because the circuit proven by the MPC-in-the-head prover is decoupled from a complex encryption function, the prover’s work can be focused on proving properties (i.e. relation) about the encrypted data, not the proof of plaintext knowledge. Hence, our approach allows for instantiation with various combinations of properties about encrypted data and encryption functions. As concrete applications we describe new approaches to verifiably encrypting discrete logarithms in any prime order group and AES private keys.
###### Hao Chen
ePrint Report
In this paper we propose the linear hull construction for block ciphers with quadratic Maiorana-McFarland structure round functions. The search for linear trails with high squared correlations from our Maiorana-McFarland structure based constructive linear cryptanalysis is linear algebraic. Hence from this linear algebraic essence, the space of all linear trails has the structure such that good linear hulls can be constructed. We apply our method to construct better linear hulls for the Simon and Simeck block cipher family. Then for Simon2n and its variants, the linear hull with the fixed input and output masks at arbitrary long rounds, and with the potential bigger than $\frac{1}{2^{2n}}$ can be constructed.

On the other hand we propose the Maiorana-McFarland structure based constructive differential cryptanalysis for symmetric-key primitives. The new search for good differential trails for Simon variants is linear algebraic. The problem of real existent differential trails is reduced to the finding of a solution of algebraic equations. We apply our method to the Simon2n variants with arbitrary long rounds and prove that the expected differential probability is bigger than $\frac{1}{2^{\frac{n}{2}}}$ under the independence assumptions. It seems that at least theoretically Simon2n is insecure for the key-recovery attack based on our new constructed linear hulls and key-recovery attack based on our constructed differential trails.
###### Anand Agrawal, Urbi Chatterjee, Rajib Ranjan Maiti
ePrint Report
Recently, a number of attacks have been demonstrated (like key reinstallation attack, called KRACK) on WPA2 protocol suite in Wi-Fi WLAN. As the firmware of the WLAN devices in the context of IoT, industrial systems, and medical devices is often not patched, detecting and preventing such attacks is challenging. In this paper, we design and implement a system, called CheckShake, to passively detect anomalies in the handshake of Wi-Fi security protocols, in particular WPA2, between a client and an access point using COTS radios. Our proposed system works without decrypting any traffic. It passively monitors multiple wireless channels in parallel in the neighborhood and uses a state machine model to characterize and detect the attacks. In particular, we develop a state machine model for grouping Wi-Fi handshake packets and then perform deep packet inspection to identify the symptoms of the anomaly in specific stages of a handshake session. Our implementation of CheckShake does not require any modification to the firmware of the client or the access point or the COTS devices, it only requires to be physically placed within the range of the access point and its clients. We use both the publicly available dataset and our own data set for performance analysis of CheckShake. Using gradient boosting-based supervised machine learning models, we show that an accuracy around 93.39% and a false positive rate of 5.08% can be achieved using CheckShake
###### Ma Yanlong
ePrint Report
The hidden discrete logarithm problem(HDLP) over non-commutative associative algebras (FNAAs) in [1] was broken in [8] by reducing to discrete logarithm problem(DLP) in a finite field through analyzing the eigenvalues of the representation matrix. A generalized form of HDLP(GHDLP) was proposed in [11], which is claimed to be computationally hard under quantum computers. Based on this, several schemes are proposed. In this paper, we will show that GHDLP can also be reduced to DLP in a finite field by algebraic representation. With all the instruments in hand, we will show how some schemes based on GHDLP can be broken. Thus we conclude that these schemes are not secure under quantum attack. So constructing schemes based on GHDLP is fundamentally wrong.

#### 30 December 2021

###### Helger Lipmaa
ePrint Report
We propose a general framework for non-universal SNARKs. It contains (1) knowledge-sound and non-black-box any-simulation-extractable (ASE), (2) zero-knowledge and subversion-zero knowledge SNARKs for the well-known QAP, SAP, QSP, and QSP constraint languages that all by design have \emph{relatively} simple security proofs. The knowledge-sound zero-knowledge SNARK is similar to Groth's SNARK from EUROCRYPT 2016, except having fewer trapdoors, while the ASE subversion-zero knowledge SNARK relies on few additional conditions. We prove security in a weaker, more realistic version of the algebraic group model. We characterize SAP, SSP, and QSP in terms of QAP; this allows one to use a SNARK for QAP directly for other languages. Our results allow us to construct a family of SNARKs for different languages and with different security properties following the same proof template. Some of the new SNARKs are more efficient than prior ones. In other cases, the new SNARKs cover gaps in the landscape, e.g., there was no previous ASE or Sub-ZK SNARK for SSP or QSP.
###### Hiroki Okada, Atsushi Takayasu, Kazuhide Fukushima, Shinsaku Kiyomoto, Tsuyoshi Takagi
ePrint Report
We propose a lattice-based digital signature scheme MLWRSign by modifying Dilithium, which is one of the third-Round finalists of NIST’s call for post-quantum cryptographic standards. To the best of our knowledge, our scheme MLWRSign is the first signature scheme whose security is based on the (module) learning with rounding (LWR) problem. Due to the simplicity of the LWR, the secret key size is reduced by approximately 30% in our scheme compared to Dilithium, while achieving the same level of security. Moreover, we implemented MLWRSign and observed that the running time of MLWRSign is comparable to that of Dilithium.
ePrint Report
We describe and analyze a simple protocol for $n$ parties that implements a randomness beacon: a sequence of high entropy values, continuously emitted at regular intervals, with sub-linear communication per value. The algorithm can tolerate a $(1 - \epsilon)/2$ fraction of the $n$ players to be controlled by an adaptive adversary that may deviate arbitrarily from the protocol. The randomness mechanism relies on verifiable random functions (VRF), modeled as random functions, and effectively stretches an initial $\lambda$-bit seed to an arbitrarily long public sequence so that (i) with overwhelming probability in $k$--the security parameter--each beacon value has high min-entropy conditioned on the full history of the algorithm, and (ii) the total work and communication required per value is $O(k)$ cryptographic operations.

The protocol can be directly applied to provide a qualitative improvement in the security of several proof-of-stake blockchain algorithms, rendering them safe from grinding'' attacks.
###### Andrea Basso, Furkan Aydin, Daniel Dinu, Joseph Friel, Avinash Varna, Manoj Sastry, Santosh Ghosh
ePrint Report
Secure communication often require both encryption and digital signatures to guarantee the confidentiality of the message and the authenticity of the parties. However, post-quantum cryptographic protocols are often studied independently. In this work, we identify a powerful synergy between two finalist protocols in the NIST standardization process. In particular, we propose a technique that enables SABER and Dilithium to share the exact same polynomial multiplier. Since polynomial multiplication plays a key role in each protocol, this has a significant impact on hardware implementations that support both SABER and Dilithium. We estimate that existing Dilithium implementations can add support for SABER with only a 4% increase in LUT count. A minor trade-off of the proposed multiplier is that it can produce inexact results with some limited inputs. We thus carry out a thorough analysis of such cases, where we prove that the probability of these events occurring is near zero, and we show that this characteristic does not affect the security of the implementation. We then implement the proposed multiplier in hardware to obtain a design that offers competitive performance/area trade-offs. Our NTT implementation achieves a latency of 519 cycles while consuming 2,012 LUTs and only 331 flip-flops when implemented on an Artix-7 FPGA. We also propose a shuffling-based method to provide side-channel protection with low overhead during polynomial multiplication. Finally, we evaluate the side-channel security of the proposed design on a Sakura-X FPGA board.
###### Yu Long Chen, Bart Mennink, Bart Preneel
ePrint Report
A growing number of lightweight block ciphers are proposed for environments such as the Internet of Things. An important contribution to the reduced implementation cost is a block length n of 64 or 96 bits rather than 128 bits. As a consequence, encryption modes and message authentication code (MAC) algorithms require security beyond the 2^{n/2} birthday bound. This paper provides an extensive treatment of MAC algorithms that offer beyond birthday bound PRF security for both nonce-respecting and nonce-misusing adversaries. We study constructions that use two block cipher calls, one universal hash function call and an arbitrary number of XOR operations.

We start with the separate problem of generically identifying all possible secure n-to-n-bit pseudorandom functions (PRFs) based on two block cipher calls. The analysis shows that the existing constructions EDM, SoP, and EDMD are the only constructions of this kind that achieve beyond birthday bound security.

Subsequently we deliver an exhaustive treatment of MAC algorithms, where the outcome of a universal hash function evaluation on the message may be entered at any point in the computation of the PRF. We conclude that there are a total amount of nine schemes that achieve beyond birthday bound security, and a tenth construction that cannot be proven using currently known proof techniques. For these former nine MAC algorithms, three constructions achieve optimal n-bit security in the nonce-respecting setting, but are completely insecure if the nonce is reused. The remaining six constructions have 3n/4-bit security in the nonce-respecting setting, and only four out of these six constructions still achieve beyond the birthday bound security in the case of nonce misuse.
###### Lorenzo Grassi, Silvia Onofri, Marco Pedicini, Luca Sozzi
ePrint Report
Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over $\mathbb F_p$ for a large prime $p$ have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps $x\mapsto x^d$. In this paper, we start an analysis of new non-linear permutation functions over $\mathbb F_p^n$ that can be used as building blocks in such symmetric-key primitives. Given a local map $F:\mathbb F_p^m \rightarrow \mathbb F_p$, we limit ourselves to focus on S-Boxes over $\mathbb F_p^n$ for $n\ge m$ defined as $\mathcal S(x_0, x_1, \ldots, x_{n-1}) = y_0\| y_1\| \ldots \| y_{n-1}$ where $y_i := F(x_i, x_{i+1}, \ldots, x_{i+m-1} )$. As main results, we prove that

- given any quadratic function $F:\mathbb F_p^2 \rightarrow \mathbb F_p$, the corresponding S-Box $\mathcal S$ over $\mathbb F_p^n$ for $n\ge 3$ is never invertible;

- similarly, given any quadratic function $F:\mathbb F_p^3 \rightarrow \mathbb F_p$, the corresponding S-Box $\mathcal S$ over $\mathbb F_p^n$ for $n\ge 5$ is never invertible.

Moreover, for each $p\ge 3$, we present (1st) generalizations of the Lai-Massey construction over $\mathbb F_p^n$ defined as before via functions $F:\mathbb F_p^m \rightarrow \mathbb F_p$ for each $n=m\ge 2$ and (2nd) (non-trivial) quadratic functions $F:\mathbb F_p^3 \rightarrow \mathbb F_p$ such that $\mathcal S$ over $\mathbb F_p^n$ for $n\in \{3,4\}$ is invertible. As an open problem for future work, we conjecture that for each $m\ge 1$ there exists a finite integer $n_{max}(m)$ such that $\mathcal S$ over $\mathbb F_p^n$ defined as before via a quadratic function $F:\mathbb F_p^m \rightarrow \mathbb F_p$ is not invertible for each $n\ge n_{max}(m)$.

Finally, as a concrete application, we propose Neptune, a variant of the sponge hash function Poseidon, whose non-linear layer is designed by taking into account the results presented in this paper. We show that this variant leads to a concrete multiplication reduction with respect to Poseidon.
###### Ferran Alborch, Ramiro Martínez, Paz Morillo
ePrint Report
Ever since the appearance of quantum computers, prime factoring and discrete logarithm based cryptography has been put in question, giving birth to the so called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain difficult lattice problems like Learning With Errors (LWE) or Ring Learning With Errors (RLWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also seen to a great interest in distributed cryptography. In this work we will give two original threshold protocols based in the lattice problem RLWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems and we will give a rough implementation of the protocols in C to give some tentative results about their viability.
###### Tjerand Silde
ePrint Report
In this work we present a direct construction for verifiable decryption for the BGV encryption scheme by combining existing zero-knowledge proofs for linear relations and bounded values. This is one of the first constructions of verifiable decryption protocols for lattice-based cryptography, and we give a protocol that is simpler and at least as efficient as the state of the art when amortizing over many ciphertexts.

To prove its practicality we provide concrete parameters, resulting in proof size of less than $47 \tau$ KB for $\tau$ ciphertexts with message space $2048$ bits. Furthermore, we provide an open source implementation showing that the amortized cost of the verifiable decryption protocol is only $90$ ms per message when batching over $\tau = 2048$ ciphertexts.
###### Alexandtros Bakas, Antonis Michalas, Tassos Dimitriou
ePrint Report
The use of data combined with tailored statistical analysis have presented a unique opportunity to organizations in diverse fields to observe users' behaviors and needs, and accordingly adapt and fine-tune their services. However, in order to offer utilizable, plausible, and personalized alternatives to users, this process usually also entails a breach of their privacy. The use of statistical databases for releasing data analytics is growing exponentially, and while many cryptographic methods are utilized to protect the confidentiality of the data -- a task that has been ably carried out by many authors over the years -- only a few %rudimentary number of works focus on the problem of privatizing the actual databases. Believing that securing and privatizing databases are two equilateral problems, in this paper, we propose a hybrid approach by combining Functional Encryption with the principles of Differential Privacy. Our main goal is not only to design a scheme for processing statistical data and releasing statistics in a privacy-preserving way but also to provide a richer, more balanced, and comprehensive approach in which data analytics and cryptography go hand in hand with a shift towards increased privacy.
###### Tomoyuki Morimae, Takashi Yamakawa
ePrint Report
All known constructions of classical or quantum commitments require at least one-way functions. Are one-way functions really necessary for commitments? In this paper, we show that non-interactive quantum commitments (for classical messages) with computational hiding and statistical binding exist if pseudorandom quantum states exist. Pseudorandom quantum states are sets of quantum states that are efficiently generated but computationally indistinguishable from Haar random states [Z. Ji, Y.-K. Liu, and F. Song, CRYPTO 2018]. It is known that pseudorandom quantum states exist even if BQP=QMA (relative to a quantum oracle) [W. Kretschmer, TQC 2021], which means that pseudorandom quantum states can exist even if no quantum-secure classical cryptographic primitive exists. Our result therefore shows that quantum commitments can exist even if no quantum-secure classical cryptographic primitive exists. In particular, quantum commitments can exist even if no quantum-secure one-way function exists. We also show that one-time secure signatures with quantum public keys exist if pseudorandom quantum states exist. In the classical setting, the existence of signatures is equivalent to the existence of one-way functions. Our result, on the other hand, suggests that quantum signatures can exist even if no quantum-secure classical cryptographic primitive (including quantum-secure one-way functions) exists.
###### Yaqi Xu, Baofeng Wu, Dongdai Lin
ePrint Report
In this paper, we formulate a new framework of cryptanalysis called rotational-linear attack on ARX ciphers. We firstly build an efficient distinguisher for the cipher $E$ consisted of the rotational attack and the linear attack together with some intermediate variables. Then a key recovery technique is introduced with which we can recover some bits of the last whitening key in the related-key scenario. To decrease data complexity of our attack, we also apply a new method, called bit flipping, in the rotational cryptanalysis for the first time and the effective partitioning technique to the key-recovery part. Applying the new framework of attack to the MAC algorithm Chaskey, we build a full-round distinguisher over it. Besides, we have recovered $21$ bits of information of the key in the related-key scenario, for keys belonging to a large weak-key class based on 6-round distinguisher. The data complexity is $2^{38.8}$ and the time complexity is $2^{46.8}$. Before our work, the rotational distinguisher can only be used to reveal key information by checking weak-key conditions. This is the first time it is applied in a last-rounds key-recovery attack. We build a 17-round rotational-linear distinguisher for ChaCha permutation as an improvement compared to single rotational cryptanalysis over it.
###### Baofeng Wu
ePrint Report
In this note, we prove the conjecture posed by Keller and Rosemarin at Eurocrypt 2021 on the nullity of a matrix polynomial of a block matrix with Hadamard type blocks over commutative rings of characteristic 2. Therefore, it confirms the conjectural optimal bound on the dimension of invariant subspace of the Starkad cipher using the HADES design strategy. We also give characterizations of the algebraic structure formed by Hadamard matrices over commutative rings.
###### Eunsang Lee, Joon-Woo Lee, Junghyun Lee, Young-Sik Kim, Yongjune Kim, Jong-Seon No, Woosuk Choi
ePrint Report
Privacy-preserving machine learning on fully homomorphic encryption (FHE) is one of the most influential applications of the FHE scheme. Recently, Lee et al. [16] implemented the standard ResNet-20 model for the CIFAR-10 dataset with residue number system variant Cheon-Kim-Kim-Song (RNS-CKKS) scheme, one of the most promising FHE schemes, for the first time. However, its implementation should be improved because it requires large number of key-switching operations, which is the heaviest operation in the RNS-CKKS scheme. In order to reduce the number of key-switching operations, it should be studied to efficiently perform neural networks on the RNS-CKKS scheme utilizing full slots of RNS-CKKS ciphertext as much as possible. In particular, since the packing density is reduced to 1/4 whenever a convolution of stride two is performed, it is required to study convolution that maintains packing density of the data. On the other hand, when bootstrapping should be performed, it is desirable to use sparse slot bootstrapping that requires fewer key-switching operations instead of full slot bootstrapping. In this paper, we propose a new packing method that makes several tensors for multiple channels to be multiplexed into one tensor. Then, we propose new convolution method that outputs a multiplexed tensor for the input multiplexed tensor, which makes it possible to maintain a high packing density during the entire ResNet network with strided convolution. In addition, we propose a method that parallelly performs convolutions for multiple output channels using repeatedly packed input data, which reduces the running time of convolution. Further, we fine-tune the parameters to reach the standard 128-bit security level and to further reduce the number of the bootstrapping operations. As a result, the number of key-switching operations is reduced to 1/107 compared to Lee et al's implementation in the ResNet-20 model on the RNS-CKKS scheme. The proposed method takes about 37 minutes with only one thread for classification of one CIFAR-10 image compared to 3 hours with 64 threads of Lee et al.'s implementation. Furthermore, we even implement ResNet-32/44/56/110 models for the first time on RNS-CKKS scheme with the linear time of the number of layers, which is generally difficult to be expected in the leveled homomorphic encryption. Finally, we successfully classify the CIFAR-100 dataset on RNS-CKKS scheme for the first time using standard ResNet-32 model, and we obtain a running time of 3,942s and an accuracy of 69.4% close to the accuracy of backbone network 69.5%.