International Association
for Cryptologic Research

Fault Injection Analysis is seen as a powerful attack against implementations of cryptographic algorithms. Over the last two decades, researchers proposed a plethora of countermeasures to secure such implementations. However, the design process and implementation are still error-prone, complex, and manual tasks which require long-standing experience in hardware design and physical security. Moreover, the validation of the claimed security is often only done by empirical testing in a very late stage of the design process. To prevent such empirical testing strategies, approaches based on formal verification are applied instead providing the designer early feedback.

In this work, we present a fault verification framework to validate the security of countermeasures against fault-injection attacks designed for ICs. The verification framework works on netlist-level, parses the given digital circuit into a model based on Binary Decision Diagrams, and performs symbolic fault injections. This verification approach constitutes a novel strategy to evaluate protected hardware designs against fault injections offering new opportunities as performing full analyses under a given fault models.

Eventually, we apply the proposed verification framework to real-world implementations of well-established countermeasures against fault-injection attacks. Here, we consider protected designs of the lightweight ciphers CRAFT and LED-64 as well as AES. Due to several optimization strategies, our tool is able to perform more than 90 million fault injections in a single-round CRAFT design and evaluate the security in under 50 min while the symbolic simulation approach considers all $2^128$ primary inputs.

Oblivious Transfer (OT) is a fundamental primitive in cryptography, supporting protocols such as Multi-Party Computation and Private Set Intersection (PSI), that are used in applications like contact discovery, remote diagnosis and contact tracing. Due to its fundamental nature, it is utterly important that its execution is secure even if arbitrarily composed with other instances of the same, or other protocols. This property can be guaranteed by proving its security under the Universal Composability model. Herein, a 3-round Random Oblivious Transfer (ROT) protocol is proposed, which achieves high computational efficiency, in the Random Oracle Model. The security of the protocol is based on the Ring Learning With Errors assumption (for which no quantum solver is known). ROT is the basis for OT extensions and, thus, achieves wide applicability, without the overhead of compiling ROTs from OTs. Finally, the protocol is implemented in a server-class Intel processor and four application-class ARM processors, all with different architectures. The usage of vector instructions provides on average a 40% speedup. The implementation shows that our proposal is at least one order of magnitude faster than the state-of-the-art, and is suitable for a wide range of applications in embedded systems, IoT, desktop, and servers. From a memory footprint perspective, there is a small increase (16%) when compared to the state-of-the-art. This increase is marginal and should not prevent the usage of the proposed protocol in a multitude of devices. In sum, the proposal achieves up to 37k ROTs/s in an Intel server-class processor and up to 5k ROTs/s in an ARM application-class processor. A PSI application, using the proposed ROT, is up to 6.6 times faster than related art.

We provide new constructions for zero-knowledge commit-and-prove SNARKs (CP-SNARKs) with a universal updatable SRS. Informally, a commit-and-prove argument system is one that can efficiently prove relations over committed inputs. They have many applications, including allowing for efficient composition of proof systems with different strength points.

We first show a general technique to compile Algebraic Holographic Proofs (AHP) with special ``decomposition'' properties into an efficient CP-SNARK with universal and updatable SRS. We require that the polynomials in an AHP can be easily decomposed into components that refer to the committed part of the witness and the rest of the witness respectively.

We then show that some of the most efficient AHP constructions---Marlin, PLONK, and Sonic---satisfy our compilation requirements. To obtain succinct instantiations of our protocols we rely on recent advancements in compressed $\Sigma$-protocol theory (Attema and Cramer, Crypto '20). Our constructions retain the succinct proof size of the underlying AHP and only impose an additional proof size that grows logarithmically with the size of the committed component of the witness.

To factor an integer $N$ we construct $n$ triples of $p_n$-smooth integers $u,v,|u-vN|$ for the $n$-th prime $p_n$. Denote such triple a fac-relation. We get fac-relations from a nearly shortest vector of the lattice $\mathcal L(\mathbf R_{n, f})$ with basis matrix $\mathbf R_{n, f} \in \mathbb R^{(n+1)\times(n+1)}$ where $f\colon [1, n]\to[1, n]$ is a permutation of $[1, 2, \ldots, n]$ and $(f(1),\ldots,f(n),N'\ln N)$ is the diagonal and $(N' \ln p_1,\ldots, N' \ln p_n,N' \ln N)$ for $N' = N^{\frac{1}{n+1}}$ is the last line of $\mathbf R_{n, f}$. An independent permutation $f'$ yields an independent fac-relation. We find sufficiently short lattice vectors by strong primal-dual reduction of $\mathbf R_{n, f}$. We factor $N\approx 2^{400}$ by $n = 47$ and $N\approx 2^{800}$ by $n = 95$. Our accelerated strong primal-dual reduction of [GN08] factors integers $N\approx 2^{400}$ and $N\approx 2^{800}$ by $4.2\cdot 10^9$ and $8.4\cdot 10^{10}$ arithmetic operations, much faster then the quadratic sieve and the number field sieve and using much smaller primes $p_n$. This destroys the RSA cryptosystem.

A succinct functional commitment (SFC) scheme for a circuit class $\mathbf{CC}$ enables, for any circuit $\mathcal{C} \in \mathbf{CC}$, the committer to first succinctly commit to a vector $\vec{\alpha}$, and later succinctly open the commitment to $\mathcal{C} (\vec{\alpha}, \vec{\beta})$, where the verifier chooses $\vec{\beta}$ at the time of opening. Unfortunately, SFC commitment schemes are known only for severely limited function classes like the class of inner products. By making non-black-box use of SNARK-construction techniques, we propose an SFC scheme for the large class of semi-sparse polynomials. The new SFC scheme can be used to, say, efficiently (1) implement sparse polynomials, and (2) aggregate various interesting SFC (e.g., vector commitment and polynomial commitment) schemes. The new scheme is evaluation-binding under a new instantiation of the computational uber-assumption. We provide a thorough analysis of the new assumption.

FlexAEAD is a block cipher candidate submitted to the NIST Lightweight Cryptography standardization project, based on repeated application of an Even-Mansour construction. In order to optimize performance, the designers chose a relatively small number of rounds, using properties of the mode and bounds on differential and linear characteristics to substantiate their security claims. Due to a forgery attack with complexity $2^{46}$, FlexAEAD was not selected to the second round of evaluation in the NIST project.

In this paper we present a practical key recovery attack on FlexAEAD, using clusters of differentials for the internal permutation and the interplay between different parts of the mode. Our attack, which was fully verified in practice, allows recovering the secret subkeys of FlexAEAD-64 with a time complexity of less than $2^{31}$ encryptions (with an experimental success rate of $75\,\%$). This is the first practical key recovery attack on a candidate of the NIST standardization project.

In this document we describe the Darlin proof carrying data scheme for the distributed computation of block and epoch proofs in a Latus sidechain of Zendoo (IACR eprint 2020/123). Recursion as well as base proofs rest on Marlin using the Pasta cycle of curves and the ‘dlog’ polynomial commitment scheme introduced by Bootle et al. EUROCRYPT 2016. We apply the amortization technique from Halo (IACR eprint 2019/099) to the non-succinct parts of the verifier, and we adapt their strategy for bivariate circuit encoding polynomials to aggregate Marlin’s inner sumchecks across the nodes of the proof carrying data scheme. Regarding performance, the advantage of Darlin over a scheme without inner sumcheck aggregation is about 30% in a tree-like scenario as ours, and beyond when applied to linear recursion.

The Sidon cryptosystem is a new multivariate encryption scheme based on the theory of Sidon spaces which was presented at PKC 2021. As is usual for this kind of schemes, its security relies on the hardness of solving particular instances of the MQ problem and of the MinRank problem. A nice feature of the scheme is that it enjoys a homomorphic property due the bilinearity of its public polynomials. Unfortunately, we will show that the Sidon cryptosystem can be broken by a polynomial time key-recovery attack. This attack relies on the existence of solutions to the underlying MinRank instance which lie in a subfield and which are inherent to the structure of the secret Sidon space. We prove that such solutions can be found in polynomial time. Our attack consists in recovering an equivalent key for the cryptosystem by exploiting these particular solutions, and this task can be performed very efficiently.

Many recent stream ciphers use Galois NFSRs as their main building blocks, such as the hardware-oriented finalists Grain and Trivium in the eSTREAM project. Previous work has found some types of Galois NFSRs equivalent to Fibonacci ones, including that used in Grain. Based on the observability of an NFSR on [0,N-1], which means any two initial states of an NFSR are distinguishable from their corresponding output sequences of length N, the paper first presents two easily verifiable necessary and sufficient conditions for Galois NFSRs equivalent to Fibonacci ones. It then validates both conditions by the Galois NFSRs previously found (not) equivalent to Fibonacci ones. As an application, the paper finally reveals that the 288-stage Galois NFSR used in Trivium is neither equivalent to a 288-stage Fibonacci NFSR, nor observable on [0,287], theoretically verifying Trivium's good design criteria of confusion and diffusion.

Many of the recent advanced lattice-based $\Sigma$-/public-coin honest verifier (HVZK) interactive protocols based on the techniques developed by Lyubashevsky (Asiacrypt'09, Eurocrypt'12) can be transformed into a non-interactive zero-knowledge (NIZK) proof in the random oracle model (ROM) using the Fiat-Shamir transform. Unfortunately, although they are known to be secure in the $\mathit{classical}$ ROM, existing proof techniques are incapable of proving them secure in the $\mathit{quantum}$ ROM (QROM). Alternatively, while we could instead rely on the Unruh transform (Eurocrypt'15), the resulting QROM secure NIZK will incur a large overhead compared to the underlying interactive protocol.

In this paper, we present a new simple semi-generic transform that compiles many existing lattice-based $\Sigma$-/public-coin HVZK interactive protocols into QROM secure NIZKs. Our transform builds on a new primitive called $\textit{extractable linear homomorphic commitment}$ protocol. The resulting NIZK has several appealing features: it is not only a proof of knowledge but also straight-line extractable; the proof overhead is smaller compared to the Unruh transform; it enjoys a relatively small reduction loss; and it requires minimal background on quantum computation. To illustrate the generality of our technique, we show how to transform the recent Bootle et al.'s 5-round protocol with an exact sound proof (Crypto'19) into a QROM secure NIZK by increasing the proof size by a factor of $2.6$. This compares favorably to the Unruh transform that requires a factor of more than $50$.

We show that Yao’s garbling scheme is adaptively indistinguishable for the class of Boolean circuits of size S and treewidth w with only a S^O(w) loss in security. For instance, circuits with constant treewidth are as a result adaptively indistinguishable with only a polynomial loss. This (partially) complements a negative result of Applebaum et al. (Crypto 2013), which showed (assuming one-way functions) that Yao’s garbling scheme cannot be adaptively simulatable. As main technical contributions, we introduce a new pebble game that abstracts out our security reduction and then present a pebbling strategy for this game where the number of pebbles used is roughly O(d w log(S)), d being the fan-out of the circuit. The design of the strategy relies on separators, a graph-theoretic notion with connections to circuit complexity.

Dijk et al. presents Remote Attestation (RA) for secure processor technology which is secure in the presence of an All Digital State Observing (ADSO) adversary. The scheme uses a combination of hardware security primitives and design principles together with a new cryptographic primitive called a Public Key Session based One-Time Signature Scheme with Secret Key Exposure (OTS-SKE). Dijk et al. show a hash based realization of OTS-SKE which is post quantum secure but suffers long $8.704$ KB signatures for 128-bit quantum security or 256-bit classical security. From a classical cryptographic perspective we complete the picture by introducing a bilinear map based OTS-SKE with short $0.125$ KB signatures, $65$ times shorter, and for which the security reduces to the Computational Diffie-Hellman Problem (CDHP) -- at the cost of a $9\times$ longer initialization phase in the RA scheme if implemented in software (this can be improved with appropriate elliptic curve hardware acceleration). Signing takes 560 ms at most $60\%$ of the $>936$ ms needed for the hash based scheme.

Digital signatures following the methodology of “Fiat-Shamir with Aborts”, proposed by Lyubashevsky, are capable of achieving the smallest public-key and signature sizes among all the existing lattice signature schemes based on the hardness of the Ring-SIS and Ring-LWE problems. Since its introduction, several variants and optimizations have been proposed, and two of them (i.e., Dilithium and qTESLA) entered the second round of the NIST post-quantum cryptography standardization. This method of designing signatures relies on rejection sampling during the signing process. Rejection sampling is crucial for ensuring both the correctness and security of these signature schemes. In this paper, we investigate the possibility of removing the two rejection conditions used both in Dilithium and qTESLA. First, we show that removing one of the rejection conditions is possible, and provide a variant of Lyubashevsky’s signature with comparable parameters with Dilithium and qTESLA. Second, we give evidence on the difficulty of removing the other rejection condition, by showing that two very general approaches do not yield a signature scheme with correctness or security.

Roughly four decades ago, Taher ElGamal put forward what is today one of the most widely known and best understood public key encryption schemes. ElGamal encryption has been used in many different contexts, chiefly among them by the OpenPGP standard. Despite its simplicity, or perhaps because of it, in reality there is a large degree of ambiguity on several key aspects of the cipher. Each library in the OpenPGP ecosystem seems to have implemented a slightly different "flavour" of ElGamal encryption. While --taken in isolation-- each implementation may be secure, we reveal that in the interoperable world of OpenPGP, unforeseen cross-configuration attacks become possible. Concretely, we propose different such attacks and show their practical efficacy by recovering plaintexts and even secret keys.

Digital signature is one of the most important public key cryptographic primitive for message authentication. In a digital signature scheme, receiver of a message-signature pair gets assurance about the fact that the message belongs to the sender and neither receiver nor any third party can manipulate the message. In the current state of art, most of the existing digital signatures' security relies on classical cryptographic assumption based hard problems, such as discrete log, integer factorization, etc. However, rapid development of quantum computing creates a security threat to these classical digital signature schemes. It indicates the recruitment of an alternative solution which can prevent quantum attacks. We focus on this concern by implementing a post-quantum secure isogeny based digital signature scheme without making use of SIDH and CSIDH. Our scheme achieves uf-cma security under a hard problem in isogeny. The proposed signature scheme incurs 256 byte public key size and 128 byte signature size to achieve 128-bit security level (NIST-1 level of security). In particular, the size of signature of our design is smaller than all other IBC based signature schemes at the 128-bit security level.

This paper presents a brand-new idea of masking the algebraic structure of linear codes used in code-based cryptography. Specially, we introduce the so-called semilinear transformations in coding theory, make a thorough study on their algebraic properties and then creatively apply them to the construction of code-based cryptosystems. Note that $\mathbb{F}_{q^m}$ can be viewed as an $\mathbb{F}_q$-linear space of dimension $m$, a semilinear transformation $\varphi$ is therefore defined to be an $\mathbb{F}_q$-linear automorphism of $\mathbb{F}_{q^m}$. After that, we impose this transformation to a linear code $\mathcal{C}$ over $\mathbb{F}_{q^m}$. Apparently $\varphi(\mathcal{C})$ forms an $\mathbb{F}_q$-linear space, but generally does not preserve the $\mathbb{F}_{q^m}$-linearity according to our analysis. Inspired by this observation, a new technique for masking the structure of linear codes is developed in this paper. Meanwhile, we endow the secret code with the so-called partial cyclic structure to make a reduction in public-key size. Compared to some other code-based cryptosystems, our proposal admits a much more compact representation of public keys. For instance, 1058 bytes are enough to reach the security of 256 bits, almost 1000 times smaller than that of the Classic McEliece entering the third round of the NIST PQC project.

We construct, under standard hardness assumptions, the first non-malleable commitments secure against quantum attacks. Our commitments are statistically binding and satisfy the standard notion of non-malleability with respect to commitment. We obtain the following instantiations:

\begin{itemize} \item A $\log^\star(\lambda)$-round classical protocol based on quantum fully-homomorphic encryption and the quantum hardness of Learning with Errors. \item A polynomial-round classical protocol based on post-quantum oblivious transfer.

\item A polynomial-round quantum protocol based on post-quantum one-way functions. \end{itemize}

Previously, non-malleable commitments with quantum security were only known against a restricted class of adversaries known as synchronizing adversaries. At the heart of our results is a general technique that allows to modularly obtain non-malleable commitments from any extractable commitment protocol, obliviously of the underlying extraction strategy (black-box or non-black-box), round complexity, and whether communication is quantum or classical. The transformation preserves the quantum security of the underlying extractable commitments, and is new even in the classical setting.

We prove that the path-finding problem in $\ell$-isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis. The presumed hardness of these problems is foundational for isogeny-based cryptography. As an essential tool, we develop a rigorous algorithm for the quaternion analog of the path-finding problem, building upon the heuristic method of Kohel, Lauter, Petit and Tignol. This problem, and its (previously heuristic) resolution, are both a powerful cryptanalytic tool and a building-block for cryptosystems.

Event date: 5 November to 8 November 2021
Submission deadline: 20 July 2021
Notification: 25 August 2021

The Cybersecurity - Identity Management group at the Hasso-Plattner-Institute (HPI), University of Potsdam is looking for motivated PhD students in the area of cryptography and privacy.

Your future tasks

• Development and analysis of provably secure cryptographic protocols for real-world problems. Topics of interest include (but are not limited to):
  • Privacy-enhancing technologies
  • Password-based cryptography
  • Foundations and solutions for real-world cryptography
• Publish and present results at top-tier international conferences
• Participate in teaching activities (depends on position)

Your skills

• Master’s degree in Computer Science, Mathematics, or a related area by the time of appointment
• Profound knowledge and interest in the areas of cryptography and IT security
• Fluency in English (written and spoken)

There are two types for the PhD positions: One position comes with a teaching obligation for which also sufficient German language skills are required. Review of applicants will start immediately until the position is filled. The starting date is flexible. The other is through the scholarship program of the HPI. Deadline for scholarship applications is August 15, and the positions usually start around October.

We look forward to your application including a CV, motivation letter and a list of attended Master courses and grades. Please submit your application documents (only as PDF) via email, and indicate the position you are interested in (teaching/scholarship).

Closing date for applications:

Contact: Anja Lehmann (anja . lehmann - at - hpi . de)

More information: https://hpi.de/lehmann/home.html