## IACR News

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#### 25 July 2021

###### Dan Boneh, Hart Montgomery, Ananth Raghunathan
ePrint Report
We construct an algebraic pseudorandom function (PRF) that is more efficient than the classic Naor- Reingold algebraic PRF. Our PRF is the result of adapting the cascade construction, which is the basis of HMAC, to the algebraic settings. To do so we define an augmented cascade and prove it secure when the underlying PRF satisfies a property called parallel security. We then use the augmented cascade to build new algebraic PRFs. The algebraic structure of our PRF leads to an efficient large-domain Verifiable Random Function (VRF) and a large-domain simulatable VRF.
###### Gachon University, Korea
Job Posting
Post-doctoral fellow position in Department of Computer Engineering at Gachon University in the field of information security including cryptography for at least two year appointment. Applicants should have their Ph.D degrees as of August 31, 2021. Please email with subject ‘Postdoc position’ statement of research, CV, recommendation letters or referees, and publications records to sohwang (at) gachon.ac.kr Closing date for applications: 07 August 2021 More information: https://ai-security.github.io/index_e.htm

Closing date for applications:

Contact: Contact Professor Seong Oun Hwang at sohwang (at) gachon.ac.kr

#### 23 July 2021

###### Hanno Becker, Vincent Hwang, Matthias J. Kannwischer, Bo-Yin Yang, Shang-Yi Yang
ePrint Report
We present new speed records on the Arm-v8A architecture for the lattice-based schemes Dilithium, Kyber, and Saber. The core novelty in this paper is the combination of Montgomery multiplication and Barrett reduction resulting in “Barrett multiplication” which allows particularly efficient modular one-known-factor multiplication using the Arm-v8A Neon vector instructions. These novel techniques combined with fast two-unknown-factor Montgomery multiplication, Barrett reduction sequences, and interleaved multi-stage butterflies result in significantly faster code. We also introduce “asymmetric multiplication” which is an improved technique for caching the results of the incomplete NTT, used e.g. for matrix-to-vector polynomial multiplication. Our implementations target the Arm Cortex-A72 CPU, on which our speed is 1.7× that of the state-of-the-art matrix-to-vector polynomial multiplication in Kyber [Nguyen–Gaj 2021]. For Saber, NTTs are far superior to Toom–Cook multiplication on the Arm-v8A architecture, outrunning the matrix-to-vector polynomial multiplication by 2.1×. On the Apple M1, our matrix-vector products run 2.1× and 1.9× faster for Kyber and Saber respectively.
###### Karim Lounis
ePrint Report
Due to the heterogeneity and the particular security requirements of IoT (Internet of Things), developing secure, low-cost, and lightweight authentication protocols has become a serious challenge. This has excited the research community to design and develop new authentication protocols that meet IoT requirements. An interesting hardware technology, called PUFs (Physical Unclonable Functions), has been the subject of many subsequent publications on lightweight, low-cost, and secure-by-design authentication protocols for the past six years. In 2020, a lightweight PUF-based authenticated key-exchange (AKE) scheme was proposed. The scheme claimed to provide mutual authentication and key establishment. The protocol was demonstrated to be vulnerable to a spoofing attack, where an attacker is able to compromise the authentication claims that are made during the execution of the protocol. Recently, some researchers have argued the validity of the attack due to a misunderstanding of security protocol specification principles. In this paper, we show how the authentication claim, as well as the key-establishment claim of the authentication protocol, can be compromised by spoofing the server and fooling the meter.
###### Alan Szepieniec
ePrint Report
This paper proposes the use of Legendre symbols as component gates in the design of ciphers tailored for use in cryptographic proof systems. Legendre symbols correspond to high-degree maps, but can be evaluated much faster. As a result, a cipher that uses Legendre symbols can offer the same security as one that uses high-degree maps but without incurring the penalty of a comparatively slow evaluation time.

After discussing the design considerations induced by the use of Legendre symbol gates, we present a concrete design that follows this strategy, along with an elaborate security analysis thereof. This cipher is called Grendel.
###### Elena Fuchs, Kristin Lauter, Matthew Litman, Austin Tran
ePrint Report
Cryptographic hash functions from expander graphs were proposed by Charles, Goren, and Lauter in [CGL] based on the hardness of finding paths in the graph. In this paper, we propose a new candidate for a hash function based on the hardness of finding paths in the graph of Markoff triples modulo p. These graphs have been studied extensively in number theory and various other fields, and yet finding paths in the graphs remains difficult. We discuss the hardness of finding paths between points, based on the structure of the Markoff graphs. We investigate several possible avenues for attack and estimate their running time to be greater than O(p). In particular, we analyze a recent groundbreaking proof in [BGS1] that such graphs are connected and discuss how this proof gives an algorithm for finding paths.
###### Anubhab Baksi, Kyungbae Jang, Gyeongju Song, Hwajeong Seo, Zejun Xiang
ePrint Report
With the advancement of the quantum computing technologies, a large body of research work is dedicated to revisit the security claims for ciphers being used. An adversary with access to a quantum computer can employ certain new attacks which would not be possible in the current pre-quantum era. In particular, the Grover's search algorithm is a generic attack against symmetric key cryptographic primitives, that can reduce the search complexity to square root. To apply the Grover's search algorithm, one needs to implement the target cipher as a quantum circuit. Although relatively recent, this field of research has attracted serious attention from the research community, as several ciphers (like AES, GIFT, SPECK, SIMON etc.) are being implemented as quantum circuits. In this work, we target the lightweight block cipher RECTANGLE and the Authenticated Encryption with Associated Data (AEAD) KNOT which is based on RECTANGLE; and implement those in the ProjectQ library (an open-source quantum compatible library designed by researchers from ETH Zurich). AEADs are considerably more complex to implement than a typical block/stream cipher, and ours is among the first works to do this.
###### Sudharshan Swaminathan, Lukasz Chmielewski, Guilherme Perin, Stjepan Picek
ePrint Report
Side-channel attacks (SCA) focus on vulnerabilities caused by insecure implementations and exploit them to deduce useful information about the data being processed or the data itself through leakages obtained from the device. There have been many studies exploiting these side-channel leakages, and most of the state-of-the-art attacks have been shown to work on systems implementing AES. The methodology is usually based on exploiting leakages for the outer rounds, i.e., the first and the last round. In some cases, due to partial countermeasures or the nature of the device itself, it might not be possible to attack the outer round leakages. In this case, the attacker has to resort to attacking the inner rounds.

This work provides a generalization for inner round side-channel attacks on AES and experimentally validates it with non-profiled and profiled attacks. This work \textit{formulates the computation of the hypothesis values of any byte in the intermediate rounds}. The more inner the AES round is, the higher is the attack complexity in terms of the number of bits to be guessed for the hypothesis. We discuss the main limitations for obtaining predictions in inner rounds and, in particular, we compare the performance of Correlation Power Analysis (CPA) against deep learning-based profiled side-channel attacks (DL-SCA). We demonstrate that because trained deep learning models require fewer traces in the attack phase, they also have fewer complexity limitations to attack inner AES rounds than non-profiled attacks such as CPA. This paper is the first to propose deep learning-based profiled attacks on inner rounds of AES under several time and memory constraints to the best of our knowledge.
###### University of Birmingham
Job Posting
The School of Computer Science at the University of Birmingham seeks to recruit outstanding computer scientists for the role of Lecturer/Senior Lecturer in Cyber Security. Candidates are welcome from both early career and established stages with an emphasis on a growing international reputation. Particular strengths of the group include: • Applied cryptography • Hardware-based security • Embedded systems security (including automotive security) • Side-channel and fault-based attacks • Security protocol analysis • Health data security • Blockchain security • Artificial intelligence and machine learning security • Fintech security • Industrial control systems security

Closing date for applications:

Contact: Mark Ryan

###### Cambridge Quantum, London, UK
Job Posting

Cambridge Quantum (CQ) is a quantum computing software and algorithms company aiming to allow our customers to get the most out of quantum computers both now and in the future. Our cybersecurity division is developing quantum-related technologies including the world’s only quantum random number generator (QRNG) that uses quantum computers to produce verifiably high-quality entropy.

In this role will work in our quantum cryptography team and bring your expertise in computer science and/or classical cryptography to find solutions to the different problems faced both by classical cryptography in a post-quantum world but also the ones faced by quantum cryptography.

Role overview
• Research and design new cryptography applications with a quantum advantage, together with their security proofs.
• Find innovative solutions to the problems faced by classical cryptography in a quantum world and to the challenges faced in quantum cryptography.
Key Requirements
• PhD in Computer Science, Mathematics, Physics or related field (or equivalent experience).
• Expertise in one or more of the following: post-quantum cryptography (E.g. lattice-based crypto), multi-party computation, zero-knowledge proofs, formal verification tools, information-theoretic security, cryptanalysis.
• Track record of publications in relevant fields.
Desirable
• Job experience in research either as a postdoc or with a company.
• Familiarity with quantum-based cryptography.
• An interest in the discussions and issues surrounding the transition to post-quantum cryptography.
• Good programming skills (E.g. Python, C/C++ and/or other).
• Ability to mentor and coach colleagues.
Full details including information on our current projects, benefits, and how to apply available via main link.

Closing date for applications:

Contact: Ela Lee (ela dot lee at cambridgequantum dot com)

#### 22 July 2021

###### Kyoungbae Jang, Gyeong Ju Song, Hyunji Kim, Hyeokdong Kwon, Wai-Kong Lee, Zhi Hu, Hwajeong Seo
ePrint Report
Optimizing arithmetic operations into quantum circuits to utilize quantum algorithms, such as the Shor algorithm and Grover search algorithm for cryptanalysis, is an active research field in cryptography implementation. In particular, reducing quantum resources is important for efficient implementation. In this paper, binary field ($GF(2^n)$) Montgomery multiplication in quantum circuits is presented. We utilize the bit-level Montgomery algorithm to efficiently compute the Montgomery product $C = A \cdot B \cdot r^{-1}$ in the binary field $GF(2^n)$. Additionally, we also present an efficient Montgomery multiplication quantum circuit in the case where the modulus of $GF(2^n)$ is specified.
###### Nicholas Franzese, Jonathan Katz, Steve Lu, Rafail Ostrovsky, Xiao Wang, Chenkai Weng
ePrint Report
We show a constant-overhead interactive zero-knowledge (ZK) proof system for RAM programs, that is, a ZK proof in which the communication complexity as well as the running times of the prover and verifier scale linearly in the size of the memory N and the running time T of the underlying RAM program. Besides yielding an asymptotic improvement of prior work, our implementation gives concrete performance improvements for RAM-based ZK proofs. In particular, our implementation supports ZK proofs of private read/write accesses to 64 MB of memory (2^{24} 32-bit words) using only 34 bytes of communication per access, a more than 80\times improvement compared to the recent BubbleRAM protocol. We also design a lightweight RISC CPU that can efficiently emulate the MIPS-I instruction set, and for which our ZK proof communicates only \approx 320 bytes per cycle, more than 10\times less than the BubbleRAM CPU. In a 100 Mbps network, we can perform zero-knowledge executions of our CPU (with 64 MB of main memory and 4 MB of program memory) at a clock rate of 6.6 kHz.
###### Donghang Lu, Albert Yu, Aniket Kate, Hemanta Maji
ePrint Report
While the practicality of secure multi-party computation (MPC) has been extensively analyzed and improved over the past decade, we are hitting the limits of efficiency with the traditional approaches of representing the computed functionalities as generic arithmetic or Boolean circuits. This work follows the design principle of identifying and constructing fast and provably-secure MPC protocols to evaluate useful high-level algebraic abstractions; thus, improving the efficiency of all applications relying on them. We present Polymath, a constant-round secure computation protocol suite for the secure evaluation of (multi-variate) polynomials of scalars and matrices, functionalities essential to numerous data-processing applications. Using precise natural precomputation and high-degree of parallelism prevalent in the modern computing environments, Polymath can make latency of secure polynomial evaluations of scalars and matrices independent of polynomial degree and matrix dimensions.

We implement our protocols over the HoneyBadgerMPC library and apply them to two prominent secure computation tasks: privacy-preserving evaluation of decision trees and privacy-preserving evaluation of Markov processes. For the decision tree evaluation problem, we demonstrate the feasibility of evaluating high-depth decision tree models in a general n-party setting. For the Markov process application, we demonstrate that Polymath can compute large powers of transition matrices with better online time and less communication.
###### Yuval Ishai, Hang Su, David J. Wu
ePrint Report
Zero-knowledge succinct arguments of knowledge (zkSNARKs) enable efficient privacy-preserving proofs of membership for general NP languages. Our focus in this work is on post-quantum zkSNARKs, with a focus on minimizing proof size. Currently, there is a $1000\times$ gap in the proof size between the best pre-quantum constructions and the best post-quantum ones. Here, we develop and implement new lattice-based zkSNARKs in the designated-verifier preprocessing model. With our construction, after an initial preprocessing step, a proof for an NP relation of size $2^{20}$ is just over 16 KB. Our proofs are $10.3\times$ shorter than previous post-quantum candidates. Compared to previous lattice-based zkSNARKs (also in the designated-verifier preprocessing model), we obtain a $42\times$ reduction in proof size and a $60\times$ reduction in the prover's running time, all while achieving a much higher level of soundness. Finally, compared to the shortest pre-quantum zkSNARKs by Groth (Eurocrypt 2016), the proof size in our lattice-based construction is $131\times$ longer, but the prover's running time is $1.2\times$ faster.

Our construction follows the general blueprint of Bitansky et al. (TCC 2013) and Boneh et al. (Eurocrypt 2017) of combining a linear probabilistically checkable proof (linear PCP) together with a linear-only vector encryption scheme. We develop a concretely-efficient lattice-based instantiation of this compiler by considering quadratic extension fields of moderate characteristic and using linear-only vector encryption over rank-2 module lattices.
###### Sayantan Mukherjee, Avishek Majumder
ePrint Report
Broadcast Encryption allows a sender to send a message to more than one receiver. In a typical broadcast encryption, the broadcaster decides the privileged set as in who all can decrypt a particular ciphertext. Gritti et al. (IJIS'16) introduced a new primitive called Broadcast Encryption with Dealership (BED), where the dealer/wholesaler decides the privileged set. This rather recently introduced primitive allows a wholesaler to buy content from the broadcaster and sell it to users. Following their construction, to date, three more constructions of broadcast encryption with dealership have been proposed. Among them, the first showed the BED construction of Gritti et al. (IJIS'16) to be insecure.

All the state-of-the-arts works were unable to fully identify the requirements of a BED scheme. We first identify and propose a new security requirement that has not been considered before. After formally defining a BED scheme, we show simple pairing-based attacks on all previous constructions rendering all of them useless. We then give the first secure BED construction in the composite-order pairing groups. This construction achieves constant-size ciphertext and secret keys but achieves selectively secure message hiding only. We then give our second construction from Li and Gong's (PKC'18) anonymous broadcast encryption. This construction achieves adaptively secure message hiding but has ciphertext size dependent on the size of the privileged set. Following that, we propose our third and final construction that achieves constant size ciphertext in the standard model and achieves adaptive message hiding security.
###### Mugurel Barcau, Cristian Lupascu, Vicentiu Pasol, George C. Turcas
ePrint Report
The present work investigates morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by Gentry to produce fully homomorphic encryption schemes, we exhibit a general recipe for the construction of bridges and we give various examples. We shall also present an example of a bridge that does not fall in this category.
###### Yi-Fan Tseng, Chun-I Fan, Zi-Cheng Liu
ePrint Report
Nowadays, it is convenient for people to store their data on clouds. To protect the privacy, people tend to encrypt their data before uploading them to clouds. Due to the widespread use of cloud services, public key searchable encryption is necessary for users to search the encrypted files efficiently and correctly. However, the existing public key searchable encryption schemes supporting monotonic queries suffer from either infeasibility in keyword testing or inefficiency such as heavy computing cost of testing, large size of ciphertext or trapdoor, and so on. In this work, we first propose a novel and efficient anonymous key-policy attribute-based encryption (KP-ABE). Then by applying Shen et al.'s generic construction proposed to the proposed anonymous KP-ABE, we obtain an efficient and expressive public key searchable encryption, which to the best of our knowledge achieves the best performance in testing among the existing such schemes. Only 2 pairings is needed in testing. Besides, we also implement our scheme and others with Python for comparing the performance. From the implementation results, our scheme owns the best performance on testing, and the size of ciphertexts and trapdoors are smaller than most of the existing schemes.
###### Michał Andrzejczak, Kris Gaj
ePrint Report
Lattice sieving is currently the leading class of algorithms for solving the shortest vector problem over lattices. The computational difficulty of this problem is the basis for constructing secure post-quantum public-key cryptosystems based on lattices. In this paper, we present a novel massively parallel approach for solving the shortest vector problem using lattice sieving and hardware acceleration. We combine previously reported algorithms with a proper caching strategy and develop hardware architecture. The main advantage of the proposed approach is eliminating the overhead of the data transfer between a CPU and a hardware accelerator. The authors believe that this is the first such architecture reported in the literature to date and predict to achieve up to 8 times higher throughput when compared to a multi-core high-performance CPU. Presented methods can be adapted for other sieving algorithms hard to implement in FPGAs due to the communication and memory bottleneck
###### Alexander May, Julian Nowakowski, Santanu Sarkar
ePrint Report
Let $(N,e)$ be an RSA public key, where $N=pq$ is the product of equal bitsize primes $p,q$. Let $d_p, d_q$ be the corresponding secret CRT-RSA exponents.

Using a Coppersmith-type attack, Takayasu, Lu and Peng (TLP) recently showed that one obtains the factorization of $N$ in polynomial time, provided that $d_p, d_q \leq N^{0.122}$. Building on the TLP attack, we show the first Partial Key Exposure attack on short secret exponent CRT-RSA. Namely, let $N^{0.122} \leq d_p, d_q \leq N^{0.5}$. Then we show that a constant known fraction of the least significant bits (LSBs) of both $d_p, d_q$ suffices to factor $N$ in polynomial time.

Naturally, the larger $d_p,d_q$, the more LSBs are required. E.g. if $d_p, d_q$ are of size $N^{0.13}$, then we have to know roughly a $\frac 1 5$-fraction of their LSBs, whereas for $d_p, d_q$ of size $N^{0.2}$ we require already knowledge of a $\frac 2 3$-LSB fraction. Eventually, if $d_p, d_q$ are of full size $N^{0.5}$, we have to know all of their bits. Notice that as a side-product of our result we obtain a heuristic deterministic polynomial time factorization algorithm on input $(N,e,d_p,d_q)$.
###### Lior Rotem, Gil Segev
ePrint Report
The Schnorr identification and signature schemes have been amongst the most influential cryptographic protocols of the past three decades. Unfortunately, although the best-known attacks on these two schemes are via discrete-logarithm computation, the known approaches for basing their security on the hardness of the discrete logarithm problem encounter the square-root barrier''. In particular, in any group of order $p$ where Shoup's generic hardness result for the discrete logarithm problem is believed to hold (and is thus used for setting concrete security parameters), the best-known $t$-time attacks on the Schnorr identification and signature schemes have success probability $t^2/p$, whereas existing proofs of security only rule out attacks with success probabilities $(t^2/p)^{1/2}$ and $(q_{\mathcal{H}} \cdot t^2/p)^{1/2}$, respectively, where $q_{\mathcal{H}}$ denotes the number of random-oracle queries issued by the attacker.

We establish tighter security guarantees for identification and signature schemes which result from $\Sigma$-protocols with special soundness based on the hardness of their underlying relation, and in particular for Schnorr's schemes based on the hardness of the discrete logarithm problem. We circumvent the square-root barrier by introducing a high-moment generalization of the classic forking lemma, relying on the assumption that the underlying relation is $d$-moment hard'': The success probability of any algorithm in the task of producing a witness for a random instance is dominated by the $d$-th moment of the algorithm's running time.

In the concrete context of the discrete logarithm problem, already Shoup's original proof shows that the discrete logarithm problem is $2$-moment hard in the generic-group model, and thus our assumption can be viewed as a highly-plausible strengthening of the discrete logarithm assumption in any group where no better-than-generic algorithms are currently known. Applying our high-moment forking lemma in this context shows that, assuming the $2$-moment hardness of the discrete logarithm problem, any $t$-time attacker breaks the security of the Schnorr identification and signature schemes with probabilities at most $(t^2/p)^{2/3}$ and $(q_{\mathcal{H}} \cdot t^2/p)^{2/3}$, respectively.