What a lovely hat

A broadcast encryption scheme allows a user to encrypt a message to $N$ recipients with a ciphertext whose size scales sublinearly with $N$. While broadcast encryption enables succinct encrypted broadcasts, it also introduces a strong trust assumption and a single point of failure; namely, there is a central authority who generates the decryption keys for all users in the system. Distributed broadcast encryption offers an appealing alternative where there is a one-time (trusted) setup...

Kyber is a post-quantum lattice-based key encapsulation mechanism (KEM) selected by NIST for standardization as ML-KEM. The scheme is designed to ensure that the unintentional errors accumulated during decryption do not prevent the receiver to correctly recover the encapsulated key. This is done by using a simple error-correction code independently applied to each bit of the message, for which it is possible to show that the decryption failure rate (DFR) is negligible. Although there have...

At Eurocrypt $2021$, Li and Micciancio demonstrated that the IND-CPA notion of security is not sufficient to cover the passive security of approximate homomorphic encryption schemes, by outlining a key recovery attack against the CKKS scheme (Cheon, Kim, Kim, Seong, Asiacrypt $2017$). They proposed the notion of $q$-IND-CPA-D security, which allows an adversary to make $q$ calls to a restricted decryption oracle. Li and Micciancio left achieving $q$-IND-CPA-D security as an open problem, but...

We present a formally verified proof of the correctness and IND-CCA security of ML-KEM, the Kyber-based Key Encapsulation Mechanism (KEM) undergoing standardization by NIST. The proof is machine-checked in EasyCrypt and it includes: 1) A formalization of the correctness (decryption failure probability) and IND-CPA security of the Kyber base public-key encryption scheme, following Bos et al. at Euro S&P 2018; 2) A formalization of the relevant variant of the Fujisaki-Okamoto transform in...

In a recent work, Hövelmanns, Hülsing and Majenz introduced a new security proof for the Fujisaki-Okamoto transform in the quantum-accessible random oracle model (QROM) used in post-quantum key encapsulation mechanisms. While having a smaller security loss due to decryption failures present in many constructions, it requires two new security properties of the underlying public-key encryption scheme (PKE). In this work, we show that one of the properties, Find Failing Plaintexts - Non...

NTRU-like cryptosystems are among the most studied lattice-based post-quantum candidates. While most NTRU proposals have been introduced over a commutative ring of quotient polynomials, other rings can be used. Noncommutative algebra has been endorsed as a direction to build new variants of NTRU a long time ago. The first attempt to construct a noncommutative variant was due to Hoffstein and Silverman motivated by more resistance to lattice attack. The scheme has been built over the group...

The Module-NTRU problem, introduced by Cheon, Kim, Kim, Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehlé, Wallet, Xagawa (ASIACCS ’20), generalizes the versatile NTRU assump- tion. One of its main advantages lies in its ability to offer greater flexibil- ity on parameters, such as the underlying ring dimension. In this work, we present several lattice-based encryption schemes, which are IND-CPA (or OW-CPA) secure in the standard model based on the Module-NTRU and...

Cryptographic primitives are often validated through rigorous security proofs, but insecure implementations or software-level attacks can compromise control flows, potentially undermining these guarantees. To address this issue, we introduce a new security notion, IND-CFA, which formalizes decryption security in the presence of adversarially controlled execution flows. Using this notion, we investigate the control flows under which a cryptographic scheme remains secure, providing insights...

Threshold symmetric encryption (TSE), introduced by Agrawal et al. [DiSE, CCS 2018], provides scalable and decentralized solution for symmetric encryption by ensuring that the secret-key stays distributed at all times. They avoid having a single point of attack or failure, while achieving the necessary security requirements. TSE was further improved by Christodorescu et al. [ATSE, CCS 2021] to support an amortization feature which enables a “more privileged” client to encrypt records in bulk...

NIST released the draft standard for ML-KEM, and we can expect its widespread use in the embedded world in the near future. Several side-channel attacks have been proposed, and one line of research has focused on attacks against the comparison step of the FO-transform. A work published at TCHES 2022 stressed the need for secure higher-order masked comparisons beyond the $t$-probing model and proposed a higher-order masked comparison method. Subsequently, D'Anvers, Van Beirendonck, and...

This paper reviews common attacks in classical cryptography and plausible attacks in the post-quantum era targeted at CRYSTALS-Kyber. Kyber is a recently standardized post-quantum cryptography scheme that relies on the hardness of lattice problems. Although it has undergone rigorous testing by the National Institute of Standards and Technology (NIST), there have recently been studies that have successfully executed attacks against Kyber while showing their applicability outside of controlled...

The Fujisaki-Okamoto (FO) transformation is used in most proposals for post-quantum secure key encapsulation mechanisms (KEMs) like, e.g., Kyber [BDK+18]. The security analysis of FO in the presence of quantum attackers has made huge progress over the last years. Recently, [HHM22] made a particular improvement by giving a security proof that is agnostic towards how invalid ciphertexts are being treated: in contrast to previous proofs, it works regardless whether invalid ciphertexts are...

In an effort to circumvent the high cost of standard countermeasures against side-channel attacks in post-quantum cryptography, some works have developed low-cost detection-based countermeasures. These countermeasures try to detect maliciously generated input ciphertexts and react to them by discarding the ciphertext or secret key. In this work, we take a look at two previously proposed low-cost countermeasures: the ciphertext sanity check and the decapsulation failure check, and demonstrate...

In this paper, we present NEV -- a faster and smaller NTRU Encryption using Vector decoding, which is provably IND-CPA secure in the standard model under the decisional NTRU and RLWE assumptions over the cyclotomic ring $R_q = \mathbb{Z}_q[X]/(X^n+1)$. Our main technique is a novel and non-trivial way to integrate a previously known plaintext encoding and decoding mechanism into the provably IND-CPA secure NTRU variant by Stehl\'e and Steinfeld (Eurocrypt 2011). Unlike the original NTRU...

The Brakerski-Gentry-Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. For this reason, the parameters of BGV need to be estimated carefully, with a trade-off between security and error margin. The ciphertext space of BGV is the ring $\mathcal R_q=\mathbb...

Recently, NIST has announced Kyber, a lattice-based key encapsulation mechanism (KEM), as a post-quantum standard. However, it is not the most efficient scheme among the NIST's KEM finalists. Saber enjoys more compact sizes and faster performance, and Mera et al. (TCHES '21) further pushed its efficiency, proposing a shorter KEM, Sable. As KEM are frequently used on the Internet, such as in TLS protocols, it is essential to achieve high efficiency while maintaining sufficient security....

Code-based cryptography has received a lot of attention recently because it is considered secure under quantum computing. Among them, the QC-MDPC based scheme is one of the most promising due to its excellent performance. QC-MDPC based scheme is usually subject to a small rate of decryption failure, which can leak information about the secret key. This raises two crucial problems: how to accurately estimate the decryption failure rate and how to use the failure information to recover the...

TEE-based smart contracts are an emerging blockchain architecture, offering fully programmable privacy with better performance than alternatives like secure multiparty computation. They can also support compatibility with existing smart contract languages, such that existing (plaintext) applications can be readily ported, picking up privacy enhancements automatically. While previous analysis of TEE-based smart contracts have focused on failures of TEE itself, we asked whether other aspects...

We propose a REinforced modified Dual-Ouroboros based on Gabidulin codes, shortly called REDOG. This is a code-based cryptosystem based on the well-known rank metric codes, Gabidulin codes. The public key sizes of REDOG are 14KB, 33KB, 63KB at the security levels of 128, 192, 256 bits respectively. There is no decoding failure in decryption. REDOG is IND-CPA. As a new result, we give the performance results of implementing REDOG including the time for Key generation, encryption, and...

The Distorted Bounded Distance Decoding Problem (DBDD) was introduced by Dachman-Soled et al. [Crypto ’20] as an intermediate problem between LWE and unique-SVP (uSVP). They presented an approach that reduces an LWE instance to a DBDD instance, integrates side information (or “hints”) into the DBDD instance, and finally reduces it to a uSVP instance, which can be solved via lattice reduction. They showed that this principled approach can lead to algorithms for side-channel attacks that...

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...

Attribute based encryption (ABE) is a cryptographic technique allowing fine-grained access control by enabling one-to-many encryption. Existing ABE constructions suffer from at least one of the following limitations. First, single point of failure on security meaning that, once an authority is compromised, an adversary can either easily break the confidentiality of the encrypted data or effortlessly prevent legitimate users from accessing data; second, the lack of user and/or attribute...

In known security reductions for the Fujisaki-Okamoto transformation, decryption failures are handled via a reduction solving the rather unnatural task of finding failing plaintexts \emph{given the private key}, resulting in a Grover search bound. Moreover, they require an implicit rejection mechanism for invalid ciphertexts to achieve a reasonable security bound in the QROM. We present a reduction that has neither of these deficiencies: We introduce two security games related to finding...

Kyber is a candidate in the third round of the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) Standardization. However, because of the protocol's independence assumption, the bound on the decapsulation failure probability resulting from the original analysis is not tight. In this work, we give a rigorous mathematical analysis of the actual failure probability calculation, and provides the Kyber security estimation in reality rather than only in a...

In this work, we propose generic and novel side-channel assisted chosen-ciphertext attacks on NTRU-based key encapsulation mechanisms (KEMs). These KEMs are IND-CCA secure, that is, they are secure in the chosen-ciphertext model. Our attacks involve the construction of malformed ciphertexts. When decapsulated by the target device, these ciphertexts ensure that a targeted intermediate variable becomes very closely related to the secret key. An attacker, who can obtain information about the...

Cryptographic constructions based on $\textit{ring learning with errors}$ (RLWE) have emerged as one of the front runners for the standardization of post quantum public key cryptography. As the standardization process continues, optimizing specific parts of proposed schemes becomes a worthwhile endeavor. In this work we focus on using error correcting codes to alleviate a natural trade-off present in most schemes; namely, we would like a wider error distribution to increase security, but a...

Many lattice-based encryption schemes are subject to a very small probability of decryption failures. It has been shown that an adversary can efficiently recover the secret key using a number of ciphertexts that cause such a decryption failure. In PKC~2019, D'Anvers~et~al. introduced `failure boosting', a technique to speed up the search for decryption failures. In this work we first improve the state-of-the-art multitarget failure boosting attacks. We then improve the cost calculation of...

An information escrow (IE) service allows its users to encrypt a message such that the message is unlocked only when a user-specified condition is satisfied. Its instantiations include timed-release encryption and allegation escrows with applications ranging from e-auctions to the #metoo movement. The proposed IE systems typically employ threshold cryptography towards mitigating the single-point-of-failure problem. Here, a set of escrow agents securely realize the IE functionality as long as...

In 2013, Tao et al. introduced the ABC Simple Matrix Encryption Scheme, a multivariate public key encryption scheme. The scheme boasts great efficiency in encryption and decryption, though it suffers from very large public keys. It was quickly noted that the original proposal, utilizing square matrices, suffered from a very bad decryption failure rate. As a consequence, the designers later published updated parameters, replacing the square matrices with rectangular matrices and altering...

We analyze the multi-user security of the streaming encryption in Google's Tink library via an extended version of the framework of nonce-based online authenticated encryption of Hoang et al. (CRYPTO'15) to support random-access decryption. We show that Tink's design choice of using random nonces and a nonce-based key-derivation function indeed improves the concrete security bound. We then give two better alternatives that are more robust against randomness failure. In addition, we show how...

The Hamming Quasi-Cyclic (HQC) proposal is a promising candidate in the second round of the NIST Post-Quantum cryptography Standardization project. It features small public key sizes, precise estimation of its decryption failure rates and contrary to most of the code-based systems, its security does not rely on hiding the structure of an error-correcting code. In this paper, we propose the first power side-channel attack on the Key Encapsulation Mechanism (KEM) version of HQC. Our attack...

The QC-MDPC code-based KEM BIKE is one of the Round-2 candidates of the NIST PQC standardization project. Its specification document describes a version that is claimed to have IND-CCA security. The security proof uses the Fujisaki-Okamoto transformation and a de-coder that targeted a Decoding Failure Rate (DFR) of 2^{-128} (for Level-1 security). However, there are several aspects that need to be amended in order for the IND-CCA proof to hold. The main issue is that using a decoder with DFR...

Mersenne number schemes are a new strain of potentially quantum-safe cryptosystems that use sparse integer arithmetic modulo a Mersenne prime to encrypt messages. Two Mersenne number based schemes were submitted to the NIST post-quantum standardization process: Ramstake and Mersenne-756839. Typically, these schemes admit a low but non-zero probability that ciphertexts fail to decrypt correctly. In this work we show that the information leaked from failing ciphertexts can be used to gain...

We give a new proof that the decryption failure rate of NewHope512 is at most $2^{-398.8}$. As in previous work, this failure rate is with respect to random, honestly generated, secret key and ciphertext pairs. However, our technique can also be applied to a fixed secret key. We demonstrate our technique on some subsets of the NewHope1024 key space, and we identify a large subset of NewHope1024 keys with failure rates of no more than $2^{-439.5}$.

We propose a framework for cryptanalysis of lattice-based schemes, when side information---in the form of ``hints''--- about the secret and/or error is available. Our framework generalizes the so-called primal lattice reduction attack, and allows the progressive integration of hints before running a final lattice reduction step. Our techniques for integrating hints include sparsifying the lattice, projecting onto and intersecting with hyperplanes, and/or altering the distribution of the...

In this work we study the quantum security of public key encryption schemes (PKE). Boneh and Zhandry (CRYPTO'13) initiated this research area for PKE and symmetric key encryption (SKE), albeit restricted to a classical indistinguishability phase. Gagliardoni et al. (CRYPTO'16) advanced the study of quantum security by giving, for SKE, the first definition with a quantum indistinguishability phase. For PKE, on the other hand, no notion of quantum security with a quantum indistinguishability...

Aigis-Enc is an encryption algorithm based on asymmetrical LWE. In this algorithm, the compression process is utilized during both key generation and encryption (which is equivalent to add some LWR noise). Then encapsulation is realized by FO transformation. It is well known that FO transformation is not considered for discussing CPA security. On the other hand, since the security reduction of LWR is hard to proceed, it is not considered for discussing the CPA security of Aigis-Enc. But...

Encryption is an indispensable tool for securing digital infra- structures as it reduces the problem of protecting the data to just protecting decryption keys. Unfortunately, this also makes it easier for users to share protected data by simply sharing decryption keys. Kiayias and Tang (ACM CCS 2013) were the first to address this important issue pre-emptively rather than a posteriori like traitor tracing schemes do. They proposed leakage-deterring encryption schemes that work as follows....

Learning with Errors (LWE) and Ring-LWE (RLWE) problems allow the construction of efficient key exchange and public-key encryption schemes. However, while improving the security through the use of error distributions with large standard deviations, the decryption failure rate increases as well. Currently, the independence of individual coefficient failures is assumed to estimate the overall decryption failure rate of many LWE/RLWE schemes. However, previous work has shown that this...

In this article we put forward an encryption mechanism that dwells on the problem of identifying the correct subset of primes from a known set. By utilizing our specially constructed public key when computing the ciphertext equation, the decryption mechanism can correctly output the shared secret parameter. The scheme has short key length, no decryption failure issues, plaintext-to-ciphertext expansion of one-to-two as well as uses \simple" mathematics in order to achieve maximum simplicity...

Lattice-based encryption schemes are often subject to the possibility of decryption failures, in which valid encryptions are decrypted incorrectly. Such failures, in large number, leak information about the secret key, enabling an attack strategy alternative to pure lattice reduction. Extending the "failure boosting'' technique of D'Anvers et al. in PKC 2019, we propose an approach that we call "directional failure boosting'' that uses previously found "failing ciphertexts'' to accelerate...

The user of an imperfectly correct lattice-based public-key encryption scheme leaks information about their secret key with each decryption query that they answer---even if they answer all queries successfully. Through a refinement of the D'Anvers--Guo--Johansson--Nilsson--Vercauteren--Verbauwhede failure boosting attack, we show that an adversary can use this information to improve his odds of finding a decryption failure. We also propose a new definition of $\delta$-correctness, and we...

In 1998, Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman introduced the famous NTRU cryptosystem, and called it "A ring-based public key cryptosystem". Actually, it turns out to be a lattice based cryptosystem that is resistant to Shor's algorithm. There are several modifications to the original NTRU and two of them are selected as round 2 candidates of NIST post quantum public key scheme standardization. In this paper, we present a simple attack on the original NTRU scheme. The...

Rank metric is a very promising research direction for code-based cryptography. In fact, thanks to the high complexity of generic decoding attacks against codes in this metric, it is possible to easily select parameters that yield very small data sizes. In this paper we analyze cryptosystems based on Low-Rank Parity-Check (LRPC) codes, one of the classes of codes that are efficiently decodable in the rank metric. We show how to exploit the decoding failure rate, which is an inherent...

A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random...

[Modified slightly because MathJax doesn't render $U^{notbot}$ correctly] We revisit the construction of IND-CCA secure key encapsulation mechanisms (KEM) from public-key encryption schemes (PKE). We give new, tighter security reductions for several constructions. Our main result is a tight reduction for the security of the $U^{notbot}$-transform of Hofheinz, Hövelmanns, and Kiltz (TCC'17) which turns OW-CPA secure deterministic PKEs into IND-CCA secure KEMs. This result is enabled by a new...

This paper develops Central Limit arguments for analysing the noise in ciphertexts in two homomorphic encryption schemes that are based on Ring-LWE. The first main contribution of this paper is to present and evaluate an average-case noise analysis for the BGV scheme. Our approach relies on the recent work of Costache et al. (SAC 2023) that gives the approximation of a polynomial product as a multivariate Normal distribution. We show how this result can be applied in the BGV context and...

Lattice-based public-key encryption has a large number of design choices that can be combined in diverse ways to obtain different tradeoffs. One of these choices is the distribution from which secret keys are sampled. Numerous secret-key distributions exist in the state of the art, including (discrete) Gaussian, binomial, ternary, and fixed-weight ternary. Although the secret-key distribution impacts both the concrete security and the performance of the schemes, it has not been compared in a...

While error correcting codes (ECC) have the potential to significantly reduce the failure probability of post-quantum schemes, they add an extra ECC decoding step to the algorithm. Even though this additional step does not compute directly on the secret key, it is susceptible to side-channel attacks. We show that if no precaution is taken, it is possible to use timing information to distinguish between ciphertexts that result in an error before decoding and ciphertexts that do not contain...

Error-correcting codes can be useful in reducing decryption failure rate of several lattice-based and code-based public-key encryption schemes. Two schemes, namely LAC and HQC, in NIST’s round 2 phase of its post-quantum cryptography standardisation project use the strong error-correcting BCH code. However, direct application of the BCH code in decryption algorithms of public-key schemes could open new avenues to the attacks. For example, a recent attack exploited non-constant-time execution...

We present the ring-based configuration of the NIST submission Round5, a Ring Learning with Rounding (RLWR)- based IND-CPA secure public-key encryption scheme. It combines elements of the NIST candidates Round2 (use of RLWR as underlying problem, having $1+x+\ldots +x^n$ with $n+1$ prime as reduction polynomial, allowing for a large design space) and HILA5 (the constant-time error-correction code XEf). Round5 performs part of encryption, and decryption via multiplication in...

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...

Code-based cryptography is one of the main techniques enabling cryptographic primitives in a post-quantum scenario. In particular, the MDPC scheme is a basic scheme from which many other schemes have been derived. These schemes rely on iterative decoding in the decryption process and thus have a certain small probability $p$ of having a decryption (decoding) error. In this paper we show a very fundamental and important property of code-based encryption schemes. Given one initial error...

Current estimation techniques for the probability of decryption failures in Ring/Mod-LWE/LWR based schemes assume independence of the failures in individual bits of the transmitted message to calculate the full failure rate of the scheme. In this paper we disprove this assumption both theoretically and practically for schemes based on Ring/Mod-Learning with Errors/Rounding. We provide a method to estimate the decryption failure probability, taking into account the bit failure dependency. We...

In this paper we investigate the impact of decryption failures on the chosen-ciphertext security of (Ring/Module)-Learning With Errors and (Ring/Module)-Learning with Rounding based primitives. Our analysis is split in three parts: First, we use a technique to increase the failure rate of these schemes called failure boosting. Based on this technique we investigate the minimal effort for an adversary to obtain a failure in 3 cases: when he has access to a quantum computer, when he mounts a...

Standardization bodies such as NIST and ETSI are currently seeking quantum resistant alternatives to vulnerable RSA and elliptic curve-based public-key algorithms. In this context, we present Round5, a lattice-based cryptosystem providing a key encapsulation mechanism and a public-key encryption scheme. Round5 is based on the General Learning with Rounding problem, unifying non-ring and ring lattice rounding problems into one. Usage of rounding combined with a tight analysis leads to...

Thermal laser stimulation (TLS) is a failure analysis technique, which can be deployed by an adversary to localize and read out stored secrets in the SRAM of a chip. To this date, a few proof-of-concept experiments based on TLS or similar approaches have been reported in the literature, which do not reflect a real attack scenario. Therefore, it is still questionable whether this attack technique is applicable to modern ICs equipped with side-channel countermeasures. The primary aim of this...

Motivated by what we call "honest but lazy‚" parties in the context of secure multi party computation, we revisit the notion of multi-key FHE schemes (MFHE). In MFHE, any message encrypted using a public key $pk_i$ can be "expanded" so that the resulting ciphertext is encrypted with respect to a set of public keys $(pk_1,..,pk_n)$. Such expanded ciphertexts can be homomorphically evaluated with respect to any circuit to generate a ciphertext $ct$. Then, this ciphertext $ct$ can be partially...

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...

Lattice problems allow the construction of very efficient key exchange and public-key encryption schemes. When using the Learning with Errors (LWE) or Ring-LWE (RLWE) problem such schemes exhibit an interesting trade-off between decryption error rate and security. The reason is that secret and error distributions with a larger standard deviation lead to better security but also increase the chance of decryption failures. As a consequence, various message/key encoding or reconciliation...

In this paper, we propose NTRU-LPR IND-CPA, a new secure scheme based on the decisional variant of Bounded Distance Decoding problem over rings (DR-BDD). This scheme is IND-CPA secure and has two KEM variants IND-CCA2 secure in the random oracle model. NTRU-LPR IND-CPA is similar to NTRU LPRime and LPR Cryptosystem. NTRU-LPR IND-CPA does not have a problem of decryption failures. Our polynomial ring can be any ring of the form $\mathbb{Z}[x]/(q,f(x))$, where $f$ is a polynomial of degree...

We describe a new reconciliation method for Ring-LWE that has a significantly smaller failure rate than previous proposals while reducing ciphertext size and the amount of randomness required. It is based on a simple, deterministic variant of Peikert's reconciliation that works with our new ``safe bits'' selection and constant-time error correction techniques. The new method does not need randomized smoothing to achieve non-biased secrets. When used with the very efficient ``New Hope''...

We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight. We depart somewhat from Aleknovich's approach and propose an encryption scheme based on the difficulty of decoding random quasi-cyclic codes. We propose two new...

Some lattice-based public key cryptosystems allow one to transform ciphertext from one lattice or ring representation to another efficiently and without knowledge of public and private keys. In this work we explore this lattice transformation property from cryptographic engineering viewpoint. We apply ciphertext transformation to compress Ring-LWE ciphertexts and to enable efficient decryption on an ultra-lightweight implementation targets such as Internet of Things, Smart Cards, and RFID...

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 simple matrix encryption scheme (Tao-Diene-Tang-Ding, PQCrypto 2013) has a problem of decryption failures. Quite recently, Petzoldt-Ding-Wang (http://eprint.iacr.org/2016/010) proposed a new version of this scheme called the tensor simple matrix encryption scheme to remove decryption failures by using a tensor product of two small matrices as its secret key. However, it is much weaker than the original scheme. In this note, we show that the tensor simple matrix encryption scheme is...

The SimpleMatrix encryption scheme as proposed by Tao et al. \cite{TD13} is one of the very few existing approaches to create a secure and efficient encryption scheme on the basis of multivariate polynomials. However, in its basic version, decryption failures occur with non-negligible probability. Although this problem has been addressed in several papers \cite{DP14,TX15}, a general solution to it is still missing.\\ In this paper we propose an improved version of the SimpleMatrix scheme,...

An authenticated encryption scheme is deemed secure (AE) if ciphertexts both look like random bitstrings and are unforgeable. AE is a much stronger notion than the traditional IND--CCA. One shortcoming of AE as commonly understood is its idealized, all-or-nothing decryption: if decryption fails, it will always provide the \emph{same single} error message \emph{and nothing more}. Reality often turns out differently: encode-then-encipher schemes often output decrypted ciphertext before...

In threshold public-key encryption, the decryption key is divided into n shares, each one of which is given to a different decryption user in order to avoid single points of failure. In this study, we propose a simple and efficient non-interactive threshold public-key encryption scheme by using the hashed Diffie-Hellman assumption in bilinear groups. Compared with the other related constructions, the proposed scheme is more efficient.

We propose to relax the assumption that decryption failures are indistinguishable in security models for symmetric encryption. Our main purpose is to build models that better reflect the reality of cryptographic implementations, and to surface the security issues that arise from doing so. We systematically explore the consequences of this relaxation, with some surprising consequences for our understanding of this basic cryptographic primitive. Our results should be useful to practitioners...

We consider the impact of the possibility of decryption failures in proofs of security for padding schemes, where these failures are both message and key dependent. We explain that an average case failure analysis is not necessarily sufficient to achieve provable security with existing CCA2-secure schemes. On a positive note, we introduce NAEP, an efficient padding scheme similar to PSS-E designed especially for the NTRU one-way function. We show that with this padding scheme we can prove...