What a lovely hat

In response to the quantum threat, new post-quantum cryptographic algorithms will soon be deployed to replace existing public-key schemes. MAYO is a quantum-resistant digital signature scheme whose small keys and signatures make it suitable for widespread adoption, including on embedded platforms with limited security resources. This paper demonstrates two single-trace side-channel attacks on a MAYO implementation in ARM Cortex-M4 that recover a secret key with probabilities of 99.9% and...

We provide several attacks on the BASS signature scheme introduced by Grigoriev, Ilmer, Ovchinnikov and Shpilrain in 2023. We lay out a trivial forgery attack which generates signatures passing the scheme's probabilistic signature verification with high probability. Generating these forgeries is faster than generating signatures honestly. Moreover, we describe a key-only attack which allows us to recover an equivalent private key from a signer's public key. The time complexity of this...

As the industry prepares for the transition to post-quantum secure public key cryptographic algorithms, vulnerability analysis of their implementations is gaining importance. A theoretically secure cryptographic algorithm should also be able to withstand the challenges of physical attacks in real-world environments. MAYO is a candidate in the ongoing first round of the NIST post-quantum standardization process for selecting additional digital signature schemes. This paper demonstrates three...

Keccak acts as the hash algorithm and eXtendable-Output Function (XOF) specified in the NIST standard drafts for Kyber and Dilithium. The Keccak output is highly correlated with sensitive information. While in RSA and ECDSA, hash-like components are only used to process public information, such as the message. The importance and sensitivity of hash-like components like Keccak are much higher in Kyber and Dilithium than in traditional public-key cryptography. However, few works study Keccak...

In 2022, Wang et al. proposed the multivariate signature scheme SNOVA as a UOV variant over the non-commutative ring of $\ell \times \ell $ matrices over $\mathbb{F}_q$. This scheme has small public key and signature size and is a first round candidate of NIST PQC additional digital signature project. Recently, Ikematsu and Akiyama, and Li and Ding show that the core matrices of SNOVA with $v$ vinegar-variables and $o$ oil-variables are regarded as the representation matrices of UOV with...

To be competitive with other signature schemes, the MLWE instance $\bf (A,t)$ on which Dilithium is based is compressed: the least significant bits of $\bf t$, which are denoted $\textbf{t}_0$, are considered part of the secret key. Knowing $\bf t_0$ does not provide any information about the other data in the secret key, but it does allow the construction of much more efficient side-channel attacks. Yet to the best of our knowledge, there is no kown way to recover $\bf t_0$ from Dilithium...

Blockchain technology ensures accountability, transparency, and redundancy in critical applications, includ- ing IoT with embedded systems. However, the reliance on public-key cryptography (PKC) makes blockchain vulnerable to quantum computing threats. This paper addresses the urgent need for quantum-safe blockchain solutions by integrating Post- Quantum Cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization pro- cess, we aim to fortify...

WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using public-key cryptography. Users prove their identity by signing a challenge with a private key, which is stored on a device such as a cell phone or a USB security token. This approach avoids many of the common security problems with password-based authentication. WebAuthn's reliance on proof-of-possession leads to a usability issue, however: a user who loses access to their...

Hudoba proposed a public key encryption (PKE) scheme and conjectured its security to be based on the Planted Clique problem. In this note, we show that this scheme is not secure. We do so by devising an efficient algorithm for the even neighbor independent set problem proposed by Hudoba. This leaves open the possibility of building PKE based on Planted Clique.

In this paper, we present an efficient attack against ${\tt PROV}$, a recent variant of the popular Unbalanced Oil and Vinegar (${\tt UOV}$) multivariate signature scheme, that has been submitted to the ongoing ${\tt NIST}$ standardization process for additional post-quantum signature schemes. A notable feature of ${\tt PROV}$ is its proof of security, namely, existential unforgeability under a chosen-message attack (${\tt EUF-CMA}$), assuming the hardness of solving the system formed by the...

Kyber KEM, the NIST selected PQC standard for Public Key Encryption and Key Encapsulation Mechanisms (KEMs) has been subjected to a variety of side-channel attacks, through the course of the NIST PQC standardization process. However, all these attacks targeting the decapsulation procedure of Kyber KEM either require knowledge of the ciphertexts or require to control the value of ciphertexts for key recovery. However, there are no known attacks in a blind setting, where the attacker does not...

After NIST’s selection of Dilithium as the primary future standard for quantum-secure digital signatures, increased efforts to understand its implementation security properties are required to enable widespread adoption on embedded devices. Concretely, there are still many open questions regarding the susceptibility of Dilithium to fault attacks. This is especially the case for Dilithium’s randomized (or hedged) signing mode, which, likely due to devastating implementation attacks on the...

SNOVA is a multivariate signature scheme submitted to the ad- ditional NIST PQC standardization project started in 2022. SNOVA is con- structed by incorporating the structure of the matrix ring over a finite field into the UOV signature scheme, and the core part of its public key is the UOV public key whose coefficients consist of matrices. As a result, SNOVA dramatically reduces the public key size compared to UOV. In this paper, we recall the construction of SNOVA, and reconsider its...

We present a side-channel attack on CRYSTALS-Dilithium, a post-quantum secure digital signature scheme, with two variants of post-processing. The side-channel attack exploits information leakage in the secret key unpacking procedure of the signing algorithm to recover the coefficients of the polynomials in the secret key vectors ${\bf s}_1$ and ${\bf s}_2$ by profiled deep learning-assisted power analysis. In the first variant, one half of the coefficients of ${\bf s}_1$ and ${\bf s}_2$ is...

In their 2022 study, Kuang et al. introduced the Multivariable Polynomial Public Key (MPPK) cryptography, a quantum-safe public key cryptosystem leveraging the mutual inversion relationship between multiplication and division. MPPK employs multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded the cryptosystem into the Homomorphic Polynomial Public Key (HPPK), transforming product polynomials over...

Given a set of matrices $\mathbf{A} := \{A_0, \dotsc, A_{k-1}\}$, and a matrix $M$ guaranteed to be the product of some ordered subset of $\mathbf{L}\subset\mathbf{A}$, can $\mathbf{L}$ be efficiently recovered? We begin by observing that the answer is positive under some assumptions on $\mathbf{A}$. Noting that appropriate transformations seem to make $\mathbf{L}$'s recovery difficult we provide the blueprint of two new public-key cryptosystems based upon this problem. We term those...

Power analysis of public-key algorithms is a well-known approach in the community of side-channel analysis. We usually classify operations based on the differences in power traces produced by different basic operations (such as modular exponentiation) to recover secret information like private keys. The more accurate the segmentation of power traces, the higher the efficiency of their classification. There exist two commonly used methods: one is equidistant segmentation, which requires a...

Account recovery enables users to regain access to their accounts when they lose their authentication credentials. While account recovery is well established and extensively studied in the Web2 (traditional web) context, Web3 account recovery presents unique challenges. In Web3, accounts rely on a (cryptographically secure) private-public key pair as their credential, which is not expected to be shared with a single entity like a server owing to security concerns. This makes account recovery...

The McEliece cryptosystem is a strong contender for post-quantum schemes, including key encapsulation for confidentiality of key exchanges in network protocols. A McEliece secret key is a structured parity check matrix that is transformed via Gaussian elimination into an unstructured public key. We show that this transformation is a highly critical operation with respect to side-channel leakage. We assume leakage of the elementary row operations during Gaussian elimination, motivated by...

Clouds have replaced most local backup systems as they offer strong availability and reliability guarantees. Clouds, however, are not (and should not be) used as backup for cryptographic secrets. Cryptographic secrets might control financial assets (e.g., crypto wallets), hence, storing such secrets on the cloud corresponds to sharing ownership of the financial assets with the cloud, and makes the cloud a more attractive target for insider attacks. Can we have the best of the two worlds,...

We analyze REDOG, a public-key encryption system submitted to the Korean competition on post-quantum cryptography. REDOG is based on rank-metric codes. We prove its incorrectness and attack its implementation, providing an efficient message recovery attack. Furthermore, we show that the security of REDOG is much lower than claimed. We then proceed to mitigate these issues and provide two approaches to fix the decryption issue, one of which also leads to better security.

NIST has recently selected CRYSTALS-Kyber as a new public key encryption and key establishment algorithm to be standardized. This makes it important to evaluate the resistance of CRYSTALS-Kyber implementations to side-channel attacks. Software implementations of CRYSTALS-Kyber have already been thoroughly analysed. The discovered vulnerabilities helped improve the subsequently released versions and promoted stronger countermeasures against side-channel attacks. In this paper, we present the...

In response to side-channel attacks on masked implementations of post-quantum cryptographic algorithms, a new bitsliced higher-order masked implementation of CRYSTALS-Kyber has been presented at CHES'2022. The bitsliced implementations are typically more difficult to break by side-channel analysis because they execute a single instruction across multiple bits in parallel. However, in this paper, we reveal new vulnerabilities in the masked Boolean to arithmetic conversion procedure of this...

MQ-Sign is a variant of the UOV singature scheme proposed by Shim et al. It has been suggested as a candidate for the standardization of post-quantum cryptography in Republic of Korea (known as KpqC). However, recently Aulbach et al. proposed a practical key recovery attack against MQ-Sign-RS and MQ-Sign-SS with a simple secret key $\mathcal{S}$. In this paper, we propose another attack that is valid for the case of a general secret key $\mathcal{S}$.

Predicate inner product functional encryption (P-IPFE) is essentially attribute-based IPFE (AB-IPFE) which additionally hides attributes associated to ciphertexts. In a P-IPFE, a message x is encrypted under an attribute w and a secret key is generated for a pair (y, v) such that recovery of ⟨x, y⟩ requires the vectors w, v to satisfy a linear relation. We call a P-IPFE unbounded if it can encrypt unbounded length attributes and message vectors. • zero predicate IPFE. We construct the first...

CRYSTALS-Kyber has been selected by the NIST as a public-key encryption and key encapsulation mechanism to be standardized. It is also included in the NSA's suite of cryptographic algorithms recommended for national security systems. This makes it important to evaluate the resistance of CRYSTALS-Kyber's implementations to side-channel attacks. The unprotected and first-order masked software implementations have been already analysed. In this paper, we present deep learning-based message...

Shuffling is a well-known countermeasure against side-channel analysis. It typically uses the Fisher-Yates (FY) algorithm to generate a random permutation which is then utilized as the loop iterator to index the processing of the variables inside the loop. The processing order is scrambled as a result, making side-channel analysis more difficult. Recently, a side-channel attack on a masked and shuffled implementation of Saber requiring 61,680 power traces to extract the secret key was...

NTRU was the first practical public key encryption scheme constructed on a lattice over a polynomial-based ring and has been considered secure against significant cryptanalytic attacks over the past few decades. However, NTRU and its variants suffer from several drawbacks, including difficulties in achieving worst-case correctness error in a moderate modulus, inconvenient sampling distributions for messages, and relatively slower algorithms compared to other lattice-based schemes. In...

Passwords are difficult to remember, easy to guess and prone to hacking. While there have been several attempts to solve the aforementioned problems commonly associated with passwords, one of the most successful ones to date has been by the Fast Identity Online (FIDO) alliance. FIDO introduced a series of protocols that combine local authentication on a user device with remote validation on relying party servers using public-key cryptography. One of the fundamental problems of FIDO...

CRYSTALS-Kyber has been recently selected by the NIST as a new public-key encryption and key-establishment algorithm to be standardized. This makes it important to assess how well CRYSTALS-Kyber implementations withstand side-channel attacks. Software implementations of CRYSTALS-Kyber have been already analyzed and the discovered vulnerabilities were patched in the subsequently released versions. In this paper, we present a profiling side-channel attack on a hardware implementation of...

In this work, we recover the private key material of the FrodoKEM key exchange mechanism as submitted to the NIST Post Quantum Cryptography (PQC) standardization process. The new mechanism that allows for this is a Rowhammer-assisted \emph{poisoning} of the FrodoKEM Key Generation (KeyGen) process. The Rowhammer side-channel is a hardware-based security exploit that allows flipping bits in DRAM by “hammering” rows of memory adjacent to some target-victim memory location by repeated memory...

In this paper, we present the first side-channel attack on a higher-order masked implementation of an IND-CCA secure lattice-based key encapsulation mechanism (KEM). Our attack exploits a vulnerability in the procedure for the arithmetic to Boolean conversion which we discovered. On the example of Saber KEM, we demonstrate successful message and secret key recovery attacks on the second- and third-order masked implementations running on a different device than the profiling one. In our...

Creating a good deep learning (DL) model is an art which requires expertise in DL and a large set of labeled data for training neural networks. Neither is readily available. In this paper, we introduce a method which enables us to achieve good results with bad DL models. We use simple multilayer perceptron (MLP) networks, trained on a small dataset, which make strongly biased predictions if used without the proposed method. The core idea is to extend the attack dataset so that at least one...

Over the past decade, cryptocurrency has been undergoing a rapid development. Digital wallet, as the tool to store and manage the cryptographic keys, is the primary entrance for the public to access cryptocurrency assets. Hierarchical Deterministic Wallet (HDW), proposed in Bitcoin Improvement Proposal 32 (BIP32), has attracted much attention and been widely used in the community, due to its virtues such as easy backup/recovery, convenient cold-address management, and supporting trust-less...

We model and analyze the Signal end-to-end secure messaging protocol within the Universal Composability (UC) framework. Specifically: (1) We formulate an ideal functionality that captures end-to-end secure messaging in a setting with Public Key Infrastructure (PKI) and an untrusted server, against an adversary that has full control over the network and can adaptively and momentarily compromise parties at any time, obtaining their entire internal states. Our analysis captures the forward...

This work introduces new key recovery attacks against the Rainbow signature scheme, which is one of the three finalist signature schemes still in the NIST Post-Quantum Cryptography standardization project. The new attacks outperform previously known attacks for all the parameter sets submitted to NIST and make a key-recovery practical for the SL 1 parameters. Concretely, given a Rainbow public key for the SL 1 parameters of the second-round submission, our attack returns the corresponding...

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...

Deep Learning based Side-Channel Attacks (DL-SCA) are considered as fundamental threats against secure cryptographic implementations. Side-channel attacks aim to recover a secret key using the least number of leakage traces. In DL-SCA, this often translates in having a model with the highest possible accuracy. Increasing an attack’s accuracy is particularly important when an attacker targets public-key cryptographic implementations where the recovery of each secret key bits is directly...

This paper presents a side-channel analysis (SCA) on key encapsulation mechanism (KEM) based on the Fujisaki–Okamoto (FO) transformation and its variants. The FO transformation has been widely used in actively securing KEMs from passively secure public key encryption (PKE), as it is employed in most of NIST post-quantum cryptography (PQC) candidates for KEM. The proposed attack exploits side-channel leakage during execution of a psuedorandom function (PRF) in the re-encryption of KEM...

It is a well-known fact that the power consumption during certain stages of a cryptographic algorithm exhibits a strong correlation with the Hamming Weight of its underlying variables. This phenomenon has been widely exploited in the cryptographic literature in various attacks targeting a broad range of schemes such as block ciphers or public-key cryptosystems. A common way of breaking this correlation is through the inclusion of countermeasures involving additional randomness into the...

ROLLO was a candidate to the second round of NIST Post-Quantum Cryptography standardization process. In the last update in April 2020, there was a key encapsulation mechanism (ROLLO-I) and a public-key encryption scheme (ROLLO-II). In this paper, we propose an attack to recover the syndrome during the decapsulation process of ROLLO-I. From this syndrome, we explain how to perform a private key-recovery. We target two constant-time implementations: the C reference implementation and a C...

This paper presents two modifications for Loidreau’s code-based cryptosystem. Loidreau’s cryptosystem is a rank metric code-based cryptosystem constructed by using Gabidulin codes in the McEliece setting. Recently a polynomial-time key recovery attack was proposed to break Loidreau’s cryptosystem in some cases. To prevent this attack, we propose the use of subcodes to disguise the secret codes in Modification I. In Modification II, we choose a random matrix of low column rank over F q to mix...

With the NIST Post quantum cryptography competition in final round, the importance of implementation security is highlighted in the latest call. In this regard, we report practical side-channel assisted message recovery attacks over embedded implementations of several post-quantum public key encryption (PKE) and key encapsulation mechanisms (KEM) based on the Learning With Errors (LWE) and Learning With Rounding (LWR) problem, which include three finalists and three semi-finalist candidates...

Side-channel attacks targeting cryptography may leak only partial or indirect information about the secret keys. There are a variety of techniques in the literature for recovering secret keys from partial information. In this tutorial, we survey several of the main families of partial key recovery algorithms for RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman, the public-key cryptosystems in common use today. We categorize the known techniques by the structure of the information that is...

Quantum computing capability outperforms that of the classic computers overwhelmingly, which seriously threatens modern public-key cryptography. For this reason, the National Institute of Standards and Technology (NIST) and several other standards organizations are progressing the standardization for post-quantum cryptography (PQC). There are two contenders among those candidates, CRYSTALS-KYBER and SABER, lattice-based encryption algorithms in the third round finalists of NIST's PQC...

The HFEv- signature scheme is a twenty year old multivariate public key signature scheme. It uses the Minus and the Vinegar modifier on the original HFE scheme. An instance of the HFEv- signature scheme called GeMSS is one of the alternative candidates for signature schemes in the third round of the NIST Post Quantum Crypto (PQC) Standardization Project. In this paper, we propose a new key recovery attack on the HFEv- signature scheme. We show that the Minus modification does not enhance the...

We introduce Vetted Encryption (VE), a novel cryptographic primitive, which addresses the following scenario: a receiver controls, or vets, who can send them encrypted messages. We model this as a filter publicly checking ciphertext validity, where the overhead does not grow with the number of senders. The filter receives one public key for verification, and every user receives one personal encryption key. We present three versions: Anonymous, Identifiable, and Opaque VE (AVE, IVE and OVE),...

In most post-quantum signature protocols, the verification procedure leaks information about which signature is being verified, and/or which public key is being used to verify the signature, to timing and other side-channel attacks. In some applications, this information leak is a breach of user privacy or system security. One class of signature protocols, based on the parallel composition of many runs of one or more interactive cut-and-choose protocols, can be modified to enable...

When generating primes $p$ and $q$ for an RSA key, the algorithm specifies that they should be checked to see that $p-1$ and $q-1$ are relatively prime to the public exponent $e$, and regenerated if this is not the case. If this is not done, then the calculation of the decrypt exponent will fail. However, what if a software bug allows the generation of public parameters $N$ and $e$ of an RSA key with this property and then it is subsequently used for encryption? Though this may seem like a...

WebAuthn, forming part of FIDO2, is a W3C standard for strong authentication, which employs digital signatures to authenticate web users whilst preserving their privacy. Owned by users, WebAuthn authenticators generate attested and unlinkable public-key credentials for each web service to authenticate users. Since the loss of authenticators prevents users from accessing web services, usable recovery solutions preserving the original WebAuthn design choices and security objectives are...

Code-based public-key cryptosystems are promising candidates for standardization as quantum-resistant public-key cryptographic algorithms. Their security is based on the hardness of the syndrome decoding problem. Computing the syndrome in a finite field, usually $\mathbb{F}_2$, guarantees the security of the constructions. We show in this article that the problem becomes considerably easier to solve if the syndrome is computed in $\mathbb{N}$ instead. By means of laser fault injection, we...

We report an important implementation vulnerability exploitable through physical attacks for message recovery in five lattice-based public-key encryption schemes (PKE) and Key Encapsulation Mechanisms (KEM) - NewHope, Kyber, Saber, Round5 and LAC that are currently competing in the second round of NIST's standardization process for post-quantum cryptography. The reported vulnerability exists in the message decoding function which is a fundamental kernel present in lattice-based PKE/KEMs and...

The US National Institute of Standards and Technology (NIST) recently announced the public-key cryptosystems (PKC) that have passed to the second round of the post-quantum standardization process. Most of these PKC come in two flavours: a weak IND-CPA version and a strongly secure IND-CCA construction. For the weaker scheme, no level of security is claimed in the plaintext-checking attack (PCA) model. However, previous works showed that, for several NIST candidates, only a few PCA queries...

It is convenient and common for schemes in the random oracle model to assume access to multiple random oracles (ROs), leaving to implementations the task (we call it oracle cloning) of constructing them from a single RO. The first part of the paper is a case study of oracle cloning in KEM submissions to the NIST Post-Quantum Cryptography standardization process. We give key-recovery attacks on some submissions arising from mistakes in oracle cloning, and find other submissions using oracle...

Conditional differential attacks were proposed by Knellwolf et al. at ASIACRYPT 2010 which targeted at cryptographic primitives based on non-linear feedback shift registers. The main idea of conditional differential attacks lies in controlling the propagation of a difference through imposing some conditions on public/key variables. In this paper, we improve the conditional differential attack by introducing the mixed integer linear programming (MILP) method to it. Let...

We bypass impossibility results for the deterministic encryption of public-key-dependent messages, showing that, in this setting, the classical Encrypt-with-Hash scheme provides message-recovery security, across a broad range of message distributions. The proof relies on a new variant of the forking lemma in which the random oracle is reprogrammed on just a single fork point rather than on all points past the fork.

Substantial work on trapdoor functions (TDFs) has led to many powerful notions and applications. However, despite tremendous work and progress, all known constructions have prohibitively large public keys. In this work, we introduce new techniques for realizing so-called range-trapdoor hash functions with short public keys. This notion, introduced by Döttling et al. [Crypto 2019], allows for encoding a range of indices into a public key in a way that the public key leaks no information...

In this work, we demonstrate generic and practical side-channel assisted chosen ciphertext attacks on multiple LWE/LWR-based Public Key Encryption (PKE) and Key Encapsulation Mechanism (KEM) secure in the chosen ciphertext model (IND-CCA security). Firstly, we identified EM-based side-channel vulnerabilities in the error correcting codes (ECC) used in LWE/LWR-based schemes that enable to distinguish the value/validity of the codewords output from the decryption operation. We also identified...

Single-trace side-channel attacks are a considerable threat to implementations of classic public-key schemes. For lattice-based cryptography, however, this class of attacks is much less understood, and only a small number of previous works show attacks. Primas et al., for instance, present a single-trace attack on the Number Theoretic Transform (NTT), which is at the heart of many efficient lattice-based schemes. They, however, attack a variable-time implementation and also require a rather...

Recently, Castryck, Lange, Martindale, Panny, and Renes proposed CSIDH (pronounced "sea-side") as a candidate post-quantum "commutative group action." It has attracted much attention and interest, in part because it enables noninteractive Diffie--Hellman-like key exchange with quite small communication. Subsequently, CSIDH has also been used as a foundation for digital signatures. In 2003--04, Kuperberg and then Regev gave asymptotically subexponential quantum algorithms for "hidden shift"...

Twisted Reed-Solomon (TRS) codes are a family of codes that contains a large number of maximum distance separable codes that are non-equivalent to Reed--Solomon codes. TRS codes were recently proposed as an alternative to Goppa codes for the McEliece code-based cryptosystem, resulting in a potential reduction of key sizes. The use of TRS codes in the McEliece cryptosystem has been motivated by the fact that a large subfamily of TRS codes is resilient to a direct use of known algebraic...

Tan et al. proposed a rank metric code-based signature (TPL) in the 2018 International Symposium on Information Theory and Its Application [3]. Their proposal has compact key size ($8.29$KB, $1.97$KB and $2.90$KB for public key, private key and signature respectively) compared to other code-based signature submitted to the NIST call for Post-Quantum Cryptography Standardization at $128$-bit post-quantum security level. This short paper aims to discuss the practical security of the TPL...

Song, Huang, Mu, and Wu proposed a new code-based signature scheme, the Rank Quasi-Cyclic Signature (RQCS) scheme (PKC 2019, Cryptology ePrint Archive 2019/053), which is based on an IND-CCA2 KEM scheme, RQC, proposed by Aguilar Melchor et al. (NIST PQC Standardization Round 1). Their scheme is an analogue to the Schnorr signature scheme. In this short note, we investigate the security of the RQCS scheme. We report a key-recovery known-message attack by following the discussion in Aragon,...

In ASIACCS 2015, Nuñez, Agudo, and Lopez proposed a proxy re-encryption scheme, NTRUReEncrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator's public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee's private key. In addition to its potential resistance to quantum algorithm, the scheme was also considered to be efficient. However, in this paper we point out that the re-encryption process will increase the decryption error, and...

Quasi-cyclic moderate density parity check codes allow the design of McEliece-like public-key encryption schemes with compact keys and a security that provably reduces to hard decoding problems for quasi-cyclic codes. In particular, QC-MDPC are among the most promising code-based key encapsulation mechanisms (KEM) that are proposed to the NIST call for standardization of quantum safe cryptography (two proposals, BIKE and QC-MDPC KEM). The first generation of decoding algorithms suffers...

For years, researchers have been engaged in finding new cryptography schemes with high security and efficiency that can resist against the attacking from quantum computers. Lattice-based cryptography scheme is believed as a promising candidate. But to achieve both high efficiency and high security is not easy. Until recently, some Lattice-based schemes with enough efficiency have been proposed and submitted to the post-quantum cryptography standardization project that initiated by NIST....

A multitude of post-quantum key encapsulation mechanisms (KEMs) and public key encryption (PKE) schemes implicitly rely on a protocol by which Alice and Bob exchange public messages and converge on secret values that are identical up to some small noise. By our count, 24 out of 49 KEM or PKE submissions to the NIST Post-Quantum Cryptography Standardization project follow this strategy. Yet the notion of a noisy key agreement (NKA) protocol lacks a formal definition as a primitive in its own...

Post-quantum cryptography has attracted much attention from worldwide cryptologists. However, most research works are related to public-key cryptosystem due to Shor's attack on RSA and ECC ciphers. At CRYPTO 2016, Kaplan et al. showed that many secret-key (symmetric) systems could be broken using a quantum period finding algorithm, which encouraged researchers to evaluate symmetric systems against quantum attackers. In this paper, we continue to study symmetric ciphers against quantum...

During the last decade, constant-time cryptographic software has quickly transitioned from an academic construct to a concrete security requirement for real-world libraries. Most of OpenSSL's constant-time code paths are driven by cryptosystem implementations enabling a dedicated flag at runtime. This process is perilous, with several examples emerging in the past few years of the flag either not being set or software defects directly mishandling the flag. In this work, we propose a...

In 2013, Misoczki, Tillich, Sendrier and Barreto proposed a variant of the McEliece cryptosystem based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes. This proposal uses an iterative bit-flipping algorithm in its decryption procedure. Such algorithms fail with a small probability. At Asiacrypt 2016, Guo, Johansson and Stankovski (GJS) exploited these failures to perform a key recovery attack. They introduced the notion of the distance spectrum of a sparse vector and showed...

In 2017, Liu, Li, Kim and Nepal submitted a new public-key encryption scheme Compact-LWE to NIST as a candidate of the standard of post-quantum cryptography. Compact-LWE features its structure similar to LWE, but with different distribution of errors. Liu, Li, Kim and Nepal thought that the special error distribution they employed would protect Compact-LWE from the known lattice-based attacks. Furthermore, they recommended a set of small parameters to improve the efficiency of Compact-LWE...

In this paper, we consider a scenario where a sender transmits ciphertexts to multiple receivers using a public-key encryption scheme, and at a later point of time, wants to retrieve the plaintexts, without having to request the receivers' help in decrypting the ciphertexts, and without having to locally store a separate recovery key for every receiver the sender interacts with. This problem, known as public key encryption with sender recovery has intuitive solutions based on hybrid...

We investigate the security of a public-key encryption scheme, the Indeterminate Equation Cryptosystem (IEC), introduced by Akiyama, Goto, Okumura, Takagi, Nuida, and Hanaoka at SAC 2017 as postquantum cryptography. They gave two parameter sets PS1 (n,p,deg X,q) = (80,3,1,921601) and PS2 (n,p,deg X,q) = (80,3,2,58982400019). The paper gives practical key-recovery and message-recovery attacks against those parameter sets of IEC through lattice basis-reduction algorithms. We exploit the fact...

We show that the NISTPQC submission HILA5 is not secure against chosen-ciphertext attacks. Specifically, we demonstrate a key-recovery attack on HILA5 using an active attack on reused keys. The attack works around the error correction in HILA5. The attack applies to the HILA5 key-encapsulation mechanism (KEM), and also to the public-key encryption mechanism (PKE) obtained by NIST's procedure for combining the KEM with authenticated encryption. This contradicts the most natural interpretation...

The cryptographic community has widely acknowledged that the emergence of large quantum computers will pose a threat to most current public-key cryptography. Primitives that rely on order-finding problems, such as factoring and computing Discrete Logarithms, can be broken by Shor's algorithm (Shor, 1994). Symmetric primitives, at first sight, seem less impacted by the arrival of quantum computers: Grover's algorithm (Grover, 1996) for searching in an unstructured database finds a marked...

QcBits is a code-based public key algorithm based on a problem thought to be resistant to quantum computer attacks. It is a constant time implementation for a quasi-cyclic moderate density parity check (QC-MDPC) Niederreiter encryption scheme, and has excellent performance and small key sizes. In this paper, we present a key recovery attack against QcBits. We first used differential power analysis (DPA) against the syndrome computation of the decoding algorithm to recover partial information...

Although lattice-based cryptography has proven to be a particularly efficient approach to post-quantum cryptography, its security against side-channel attacks is still a very open topic. There already exist some first works that use masking to achieve DPA security. However, for public-key primitives SPA attacks that use just a single trace are also highly relevant. For lattice-based cryptography this implementation-security aspect is still unexplored. In this work, we present the first...

Several recent cryptographic constructions - including a public key encryption scheme, a fully homomorphic encryption scheme, and a candidate multilinear map construction - rely on the hardness of the short generator principal ideal problem (SG-PIP): given a $\mathbb{Z}$-basis of some principal (fractional) ideal in an algebraic number field that is guaranteed to have an exceptionally short generator with respect to the logarithmic embedding, find a shortest generator of the principal ideal....

We propose a public key infrastructure framework, inspired by modern distributed cryptocurrencies, that allows for tunable key escrow, where the availability of key escrow is only provided under strict conditions and enforced through cryptographic measures. We argue that any key escrow scheme designed for the global scale must be both inert --- requiring considerable effort to recover a key --- and public --- everybody should be aware of all key recovery attempts. To this end, one of the...

Cryptographic APIs like PKCS#11 are interfaces to trusted hardware where keys are stored; the secret keys should never leave the trusted hardware in plaintext. In PKCS#11 it is possible to give keys conflicting roles, leading to a number of key-recovery attacks. To prevent these attacks, one can authenticate the attributes of keys when wrapping, but this is not standard in PKCS#11. Alternatively, one can configure PKCS#11 to place additional restrictions on the commands permitted by the...

Algorithms for secure encryption in a post-quantum world are currently receiving a lot of attention in the research community, including several larger projects and a standardization effort from NIST. One of the most promising algorithms is the code-based scheme called QC-MDPC, which has excellent performance and a small public key size. In this work we present a very efficient key recovery attack on the QC-MDPC scheme using the fact that decryption uses an iterative decoding step and this...

Authenticated Key Exchange (AKE) is the backbone of internet security protocols such as TLS and IKE. A recent announcement by standardization bodies calling for a shift to quantum-resilient crypto has resulted in several AKE proposals from the research community. Because AKE can be generically constructed by combining a digital signature scheme with public key encryption (or a KEM), most of these proposals focused on optimizing the known KEMs and left the authentication part to the generic...

The BBCRS scheme is a variant of the McEliece public-key encryption scheme where the hiding phase is performed by taking the inverse of a matrix which is of the form T+R where T is a sparse matrix with average row/column weight equal to a very small quantity m, usually m<2, and R is a matrix of small rank z&#10878;1. The rationale of this new transformation is the reintroduction of families of codes, like generalized Reed-Solomon codes, that are famously known for representing insecure...

We present a cryptanalysis of the ASASA public key cipher introduced at Asiacrypt 2014. This scheme alternates three layers of affine transformations A with two layers of quadratic substitutions S. We show that the partial derivatives of the public key polynomials contain information about the intermediate layer. This enables us to present a very simple distinguisher between an ASASA public key and random polynomials. We then expand upon the ideas of the distinguisher to achieve a full...

The ASASA construction is a new design scheme introduced at Asiacrypt 2014 by Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public-key encryption schemes, a secret-key scheme, as well as super S-box subcomponents of a white-box scheme. However one of the two public-key cryptosystems was recently broken at Crypto 2015 by Gilbert, Plu&#770;t and Treger. As our main contribution, we propose a new algebraic key-recovery attack able to break at once the...

Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has been one of the major cryptanalysis techniques for lattice based cryptographic systems, key recovery cryptanalysis techniques for linear code based cryptographic sys- tems are generally scheme specific. In recent years, several important techniques such as...

Protecting user data entails providing authenticated users access to their data. The most prevalent and probably also the most feasible approach to the latter is by username and password. With password breaches through server compromise now reaching billions of affected passwords, distributing the password files and user data over multiple servers is not just a good idea, it is a dearly needed solution to a topical problem. Threshold password-authenticated secret sharing (TPASS) protocols...

At ACM-CCS 2014, Cheon, Lee and Seo introduced a new number-theoretic assumption, the co-approximate common divisor (Co-ACD) assumption, based on which they constructed several cryptographic primitives, including a particularly fast additively homomorphic encryption scheme. For their proposed parameters, they found that their scheme was the ``most efficient of those that support an additive homomorphic property''. In this paper, we analyze the security of the Cheon-Lee-Seo (CLS) homomorphic...

We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC'05] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over. Most notably are worst-case hardness and post-quantum resistance. In fact, LWEE's duality is...

We investigate the security of the family of MQQ public key cryptosystems using multivariate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular, the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature scheme MQQ-SIG and the encryption scheme MQQ-ENC, although using different types of MQQs, share a common algebraic structure that introduces a...

Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO '13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a finite field. We present an attack based on subspace differential invariants inherent to this methodology. The attack is is a structural key...

The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non trivial automorphism group. Such codes display then symmetries allowing compact parity-check or generator matrices. For instance, a key-reduction is obtained by taking quasi-cyclic (QC) or quasi-dyadic (QD) alternant/Goppa codes. We show that the use of such symmetric alternant/Goppa...

A very popular trend in code-based cryptography is to decrease the public-key size by focusing on subclasses of alternant/Goppa codes which admit a very compact public matrix, typically quasi-cyclic (QC), quasi-dyadic (QD), or quasi-monoidic (QM) matrices. We show that the very same reason which allows to construct a compact public-key makes the key-recovery problem intrinsically much easier. The gain on the public-key size induces an important security drop, which is as large as the...

In this paper, we propose the first provable secure certificate-based proxy signature with message recovery without bilinear pairing. The notion of certificate-based cryptography was initially introduced by Gentry in 2003, in order to simplify certificate management in traditional public key cryptography(PKC)and to solve the key escrow problem in identity-based cryptosystems. To date, a number of certificate-based proxy signature(CBPS)schemes from bilinear pairing have been proposed....

How is it possible to prevent the sharing of cryptographic functions? This question appears to be fundamentally hard to address since in this setting the owner of the key {\em is} the adversary: she wishes to share a program or device that (potentially only partly) implements her main cryptographic functionality. Given that she possesses the cryptographic key, it is impossible for her to be {\em prevented} from writing code or building a device that uses that key. She may though be {\em...

Most implementations of public key cryptography employ exponentiation algorithms. Side-channel attacks on secret exponents are typically bound to the leakage of single executions due to cryptographic protocols or side-channel countermeasures such as blinding. We propose for the first time, to use a well-established class of algorithms, i.e. unsupervised cluster classification algorithms such as the k-means algorithm to attack cryptographic exponentiations and recover secret exponents without...

We introduce and study a new notion of \emph{enhanced chosen-ciphertext security} (ECCA) for public-key encryption. Loosely speaking, in the ECCA security experiment, the decryption oracle provided to the adversary is augmented to return not only the output of the decryption algorithm on a queried ciphertext but also of a \emph{randomness recovery} algorithm associated to the scheme. Our results mainly concern the case where the randomness recovery algorithm is efficient. We provide...

&#8233;Elliptic curve cryptosystems have improved greatly in speed over the past few years. In this paper we outline a new elliptic curve signature and key agreement implementation which achieves record speeds while remaining relatively compact. For example, on Intel Sandy Bridge, a curve with about $2^{250}$ points produces a signature in just under 60k clock cycles, verifies in under 169k clock cycles, and computes a Diffie-Hellman shared secret in under 153k clock cycles. Our...

The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar (UOV) signature scheme (Eurocrypt '99) minimizing the length of the signatures. By now the Rainbow Band Separation attack is the best key recovery attack known. For some sets of parameters it is even faster than a direct attack on the public key. Unfortunately the available description of the attack is very ad hoc and does not provide deep insights. In this article we provide another...

Square is a multivariate quadratic encryption scheme proposed in 2009. It is a specialization of Hidden Field Equations by using only odd characteristic fields and also X^2 as its central map. In addition, it uses embedding to reduce the number of variables in the public key. However, the system was broken at Asiacrypt 2009 using a differential attack. At PQCrypto 2010 Clough and Ding proposed two new variants named Double-Layer Square and Square+. We show how to break Double-Layer Square...