International Association
for Cryptologic Research

Known constructions of (efficient) blind signatures either rely on non-standard hardness assumptions or require parameters that grow linearly with the number of concurrently issued signatures. This holds true even in the random oracle model.

Katz, Loss and Rosenberg (ASIACRYPT 2021) presented a generic construction that boosts a scheme supporting logarithmically many concurrent signing sessions to a scheme that supports polynomially many. Unfortunately, this construction has two drawbacks: 1) the communication between the signer and the user still grows linearly with the number of issued signatures 2) their schemes inherit a very loose security bound from the underlying scheme and, as a result, require impractical parameter sizes.

In this paper, we eliminate these two drawbacks by proposing two highly practical blind signature schemes from the CDH and RSA assumptions. Our resulting schemes have communication which grows only logarithmically in the number of issued signatures. In addition, we introduce new techniques to mitigate the large security loss in the construction of Katz et al. Overall, we obtain the following parameter sizes (providing 128 bits of security):

- Our main scheme PIKA is based on the BLS blind signature scheme (Boldyreva, PKC 2003) and is secure under the \cdh assumption over a standard-sized group. Signatures are of size roughly 3KB and communication per signature is roughly 150KB. - Our RSA-based scheme is based on the Okamoto-Guillou-Quisquater blind signature scheme (Okamoto, CRYPTO 1992). It has signatures and communication of roughly 9KB and 8KB, respectively.

Lattice-based blind signature schemes have been receiving some recent attention lately. Earlier efficient 3-round schemes (Asiacrypt 2010, Financial Cryptography 2020) were recently shown to have mistakes in their proofs, and fixing them turned out to be extremely inefficient and limited the number of signatures that a signer could send to less than a dozen (Crypto 2020). In this work we propose a round-optimal, 2-round lattice-based blind signature scheme which produces signatures of length 150KB. The running time of the signing protocol is linear in the maximum number signatures that can be given out, and this limits the number of signatures that can be signed per public key. Nevertheless, the scheme is still quite efficient when the number of signatures is limited to a few dozen thousand, and appears to currently be the most efficient lattice-based candidate.

The generation of pseudorandom binary sequences is of a great importance in numerous applications stretching from simulation and gambling to cryptography. Pseudorandom bit generators (PRBGs) can be split into two classes depending on their claimed security. The first includes PRBGs that are provably secure (such as the Blum-Blum-Shub one). Security of the second class rests on heuristic arguments. Sadly, PRBG from the first class are inherently inefficient and some PRBG are insecure against quantum attacks. While, their siblings from the second class are very efficient, but security relies on their resistance against known cryptographic attacks.

This work presents a construction of PRBG from the asymmetric numeral system (ANS) compression algorithm. We define a family of PRBGs for $2^R$ ANS states and prove that it is indistinguishable from a truly random one for a big enough $R$. To make our construction efficient, we investigate PRBG built for smaller $R=7,8,9$ and show how to remove local correlations from output stream. We permute output bits using rotation and Keccak transformations and show that permuted bits pass all NIST tests. Our PRBG design is provably secure (for a large enough $R$) and heuristically secure (for a smaller $R$). Besides, we claim that our PRBG is secure against quantum adversaries.

We present a new construction for publicly verifiable anonymous tokens with private metadata. This primitive enables an issuer to generate an anonymous authentication token for a user while embedding a single private metadata bit. The token can be publicly verified, while the value of the private metadata is only accessible to the party holding the secret issuing key and remains hidden to any other party, even to the user. The security properties of this primitive also include unforgeability, which guarantees that only the user can generate new valid tokens, and unlinkability that guarantees that tokens issued with the same private metadata bit are indistinguishable. Our anonymous tokens scheme builds on the top of blind Schnorr signatures.

We analyze its security in the algebraic group model and prove its security under the modified ROS assumption, one-more discrete logarithm, and decisional Diffie-Hellman assumptions.

Blind signature schemes are one of the best and best-studied tools for privacy-preserving authentication. It has a blind signing protocol in which a signer learns nothing about the message being signed or the resulting signature; thus such a signature can serve as an anonymous authentication token. Thus, constructing efficient blind signatures secure under realistic cryptographic assumptions is an important goal.

A recent paper by Benhamouda, Lepoint, Loss, Orr\`u, and Raykova (Eurocrypt '21) showed that a large class of blind signature schemes secure in the stand-alone setting are no longer secure when multiple instances of the blind signing protocol are executed concurrently. The best known technique to salvage the security of such blind signatures was recently proposed by Katz, Loss, and Rosenberg (Asiacrypt '21). For the security parameter $\kappa$, their technique transforms blind signature schemes that are secure for $\mathcal{O}(\log \kappa)$ concurrent executions of the blind signing protocol into ones that are secure for any $N = \mathsf{poly}(\kappa)$ concurrent executions. The resulting, transformed blind signing protocol needs $\mathcal{O}(N)$ times more computation and communication than the original one.

In this paper, we give an improved transform for obtaining a secure blind signing protocol tolerating $N = \mathsf{poly}(\kappa)$ concurrent executions from one that is secure for $\mathcal{O}(\log \kappa)$ concurrent executions. Our technique still needs $\mathcal{O}(N)$ times more computation, but only $\mathcal{O}(\log N)$ more communication than the original blind signature.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.