Key Encapsulation Mechanism with Explicit Rejection in the Quantum Random Oracle Model

The recent post-quantum cryptography standardization project launched by NIST increased the interest in generic key encapsulation mechanism (KEM) constructions in the quantum random oracle (QROM). Based on a OW-CPA-secure public-key encryption (PKE), Hofheinz, Hövelmanns and Kiltz (TCC 2017) first presented two generic constructions of an IND-CCA-secure KEM with quartic security loss in the QROM, one with implicit rejection (a pseudorandom key is return for an invalid ciphertext) and the other with explicit rejection (an abort symbol is returned for an invalid ciphertext). Both are widely used in the NIST Round-1 KEM submissions and the ones with explicit rejection account for 40%. Recently, the security reductions have been improved to quadratic loss under a standard assumption, and be tight under a nonstandard assumption by Jiang et al. (Crypto 2018) and Saito, Xagawa and Yamakawa (Eurocrypt 2018). However, these improvements only apply to the KEM submissions with implicit rejection and the techniques do not seem to carry over to KEMs with explicit rejection. In this paper, we provide three generic constructions of an IND-CCA-secure KEM with explicit rejection, under the same assumptions and with the same tightness in the security reductions as the aforementioned KEM constructions with implicit rejection (Crypto 2018, Eurocrypt 2018). Specifically, we develop a novel approach to verify the validity of a ciphertext in the QROM and use it to extend the proof techniques for KEM constructions with implicit rejection (Crypto 2018, Eurocrypt 2018) to our KEM constructions with explicit rejection. Moreover, using an improved version of one-way to hiding lemma by Ambainis, Hamburg and Unruh (ePrint 2018/904), for two of our constructions, we present tighter reductions to the standard IND-CPA assumption. Our results directly apply to 9 KEM submissions with explicit rejection, and provide tighter reductions than previously known (TCC 2017)

Tighter QCCA-Secure Key Encapsulation Mechanism with Explicit Rejection in the Quantum Random Oracle Model

Hofheinz et al. (TCC 2017) proposed several key encapsulation mechanism (KEM) variants of Fujisaki-Okamoto (\textsf{FO}) transformation, including \textsf{FO}^{\slashed{\bot}}, \textsf{FO}_m^{\slashed{\bot}}, \textsf{QFO}_m^{\slashed{\bot}}, $\textsf{FO}^{\bot}$, $\textsf{FO}_m^\bot$ and $\textsf{QFO}_m^\bot$, and they are widely used in the post-quantum cryptography standardization launched by NIST. These transformations are divided into two types, the implicit and explicit rejection type, including \{\textsf{FO}^{\slashed{\bot}}, \textsf{FO}_m^{\slashed{\bot}}, \textsf{QFO}_m^{\slashed{\bot}}\} and $\textsf{FO}^{\bot}, \textsf{FO}_m^\bot, \textsf{QFO}_m^\bot$, respectively. The decapsulation algorithm of the implicit (resp. explicit) rejection type returns a pseudorandom value (resp. an abort symbol $\bot$) for an invalid ciphertext. For the implicit rejection type, the \textsf{IND-CCA} security reduction of \textsf{FO}^{\slashed{\bot}} in the quantum random oracle model (QROM) can avoid the quadratic security loss, as shown by Kuchta et al. (EUROCRYPT 2020). However, for the explicit rejection type, the best known \textsf{IND-CCA} security reduction in the QROM presented by Hövelmanns et al. (ASIACRYPT 2022) for $\textsf{FO}_m^\bot$ still suffers from a quadratic security loss. Moreover, it is not clear until now whether the implicit rejection type is more secure than the explicit rejection type. In this paper, a QROM security reduction of $\textsf{FO}_m^\bot$ without incurring a quadratic security loss is provided. Furthermore, our reduction achieves \textsf{IND-qCCA} security, which is stronger than the \textsf{IND-CCA} security. To achieve our result, two steps are taken: The first step is to prove that the \textsf{IND-qCCA} security of $\textsf{FO}_m^\bot$ can be tightly reduced to the \textsf{IND-CPA} security of $\textsf{FO}_m^\bot$ by using the online extraction technique proposed by Don et al. (EUROCRYPT 2022). The second step is to prove that the \textsf{IND-CPA} security of $\textsf{FO}_m^\bot$ can be reduced to the \textsf{IND-CPA} security of the underlying public key encryption (PKE) scheme without incurring quadratic security loss by using the Measure-Rewind-Measure One-Way to Hiding Lemma (EUROCRYPT 2020). In addition, we prove that (at least from a theoretic point of view), security is independent of whether the rejection type is explicit ($\textsf{FO}_m^\bot$) or implicit (\textsf{FO}_m^{\slashed{\bot}}) if the underlying PKE scheme is weakly $\gamma$-spread

Tighter Post-quantum Secure Encryption Schemes Using Semi-classical Oracles

Krüpteerimisprotokollide analüüsimiseks kasutatakse tihti juhusliku oraakli mudelit (JOM), aga postkvant turvaliste protokollide analüüs tuleb läbi viiakvant juhusliku oraakli mudelis (KJOM). Kuna paljudel tõestamise tehnikatel ei ole kvant juhusliku oraakli mudelis analoogi, on KJOMis raske töötada. Seda probleemi aitab lahendada One-Way to Hiding (O2H) Teoreem, mille Unruh tõestas 2015. aastal.Ambainis, Hamburg ja Unruh esitasid teoreemi täiustatud versiooni 2018. aastal. See kasutab poolklassikalisi oraakleid, millel on suurem paindlikkus ja tihedamad piirid. Täiustatud versioon võimaldab tugevdada kõigi protokollide turvalisust, mis kasutasid vana versiooni. Me võtame ühe artikli, kus kasutati vana O2H Teoreemi versiooni, ja tõestame protokollide turvalisuse uuesti kasutades poolklassikalisi oraakleid.The random oracle model (ROM) has been widely used for analyzing cryptographic schemes. In the real world, a quantum adversary equipped with a quantum computer can execute hash functions on an arbitrary superposition of inputs. Therefore, one needs to analyze the post-quantum security in the quantum random oracle model (QROM). Unfortunately, working in the QROM is quite difficult because many proof techniques in the ROM have no analogue in the QROM. A technique that can help solve this problem is the One-Way to Hiding (O2H) Theorem, which was first proven in 2015 by Unruh. In 2018, Ambainis, Hamburg and Unruh presented an improved version of the O2H Theorem which uses so called semi-classical oracles and has higher flexibilityand tighter bounds. This improvement of the O2H Theorem should allow us to derive better security bounds for most schemes that used the old version. We take one paper that used the old version of the O2H Theorem to prove the security of different schemes in the QROM and give new proofs using semi-classical oracles

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digital-signature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of post-quantum security

Quantum Attacks on Mersenne Number Cryptosystems

Mersenne number based cryptography was introduced by Aggarwal et al. as a potential post- quantum cryptosystem in 2017. Shortly after the publication Beunardeau et al. propose a lattice based attack significantly reducing the security margins. During the NIST post-quantum project Aggarwal et al. and Szepieniec introduced a new form of Mersenne number based cryptosystems which remain secure in the presence of the lattice reduction attack. The cryptoschemes make use of error correcting codes and have a low but non-zero probability of failure during the decoding phase. In the event of a decoding failure information about the secret key may be leaked and may allow for new attacks. In the first part of this work, we analyze the Mersenne number cryptosystem and NIST submission Ramstake and identify approaches to exploit the information leaked by decoding failures. We describe different attacks on a weakened variant of Ramstake. Furthermore we pair the decoding failures with a timing attack on the code from the submission package. Both our attacks significantly reduce the security margins compared to the best known generic attack. However, our results on the weakened variant do not seem to carry over to the unweakened cryptosystem. It remains an open question whether the information flow from decoding failures can be exploited to break Ramstake. In the second part of this work we analyze the Groverization of the lattice reduction attack by Beunardeau et al.. The incorporation of classical search problem into a quantum framework promises a quadratic speedup potentially reducing the security margin by half. We give an explicit description of the quantum circuits resulting from the translation of the classical attack. This description contains, to the best of our knowledge, the first in depth description and analysis of a quantum variant of the LLL algorithm. We show that the Groverized attack requires a large (but polynomial) overhead of quantum memory

Kleptographic Attacks against Implicit Rejection

Given its integral role in modern encryption systems such as CRYSTALS-Kyber, the Fujisaki-Okamoto (FO) transform will soon be at the center of our secure communications infrastructure. An enduring debate surrounding the FO transform is whether to use explicit or implicit rejection when decapsulation fails. Presently, implicit rejection, as implemented in CRYSTALS-Kyber, is supported by a strong set of arguments. Therefore, understanding its security implications in different attacker models is essential. In this work, we study implicit rejection through a novel lens, namely, from the perspective of kleptography. Concretely, we consider an attacker model in which the attacker can subvert the user\u27s code to compromise security while remaining undetectable. In this scenario, we present three attacks that significantly reduce the security level of the FO transform with implicit rejection. Notably, our attacks apply to CRYSTALS-Kyber

A Modular Analysis of the Fujisaki-Okamoto Transformation

The Fujisaki-Okamoto (FO) transformation (CRYPTO 1999 and Journal of Cryptology 2013) turns any weakly secure public-key encryption scheme into a strongly (i.e., IND-CCA) secure one in the random oracle model. Unfortunately, the FO analysis suffers from several drawbacks, such as a non-tight security reduction, and the need for a perfectly correct scheme. While several alternatives to the FO transformation have been proposed, they have stronger requirements, or do not obtain all desired properties. In this work, we provide a fine-grained and modular toolkit of transformations for turning weakly secure into strongly secure public-key encryption schemes. All of our transformations are robust against schemes with correctness errors, and their combination leads to several tradeoffs among tightness of the reduction, efficiency, and the required security level of the used encryption scheme. For instance, one variant of the FO transformation constructs an IND-CCA secure scheme from an IND-CPA secure one with a tight reduction and very small efficiency overhead. Another variant assumes only an OW-CPA secure scheme, but leads to an IND-CCA secure scheme with larger ciphertexts. We note that we also analyze our transformations in the quantum random oracle model, which yields security guarantees in a post-quantum setting

Online-Extractability in the Quantum Random-Oracle Model

We show the following generic result. Whenever a quantum query algorithm in the quantum random-oracle model outputs a classical value $t$ that is promised to be in some tight relation with $H(x)$ for some $x$, then $x$ can be efficiently extracted with almost certainty. The extraction is by means of a suitable simulation of the random oracle and works online, meaning that it is straightline, i.e., without rewinding, and on-the-fly, i.e., during the protocol execution and without disturbing it. The technical core of our result is a new commutator bound that bounds the operator norm of the commutator of the unitary operator that describes the evolution of the compressed oracle (which is used to simulate the random oracle above) and of the measurement that extracts $x$. We show two applications of our generic online extractability result. We show tight online extractability of commit-and-open $\Sigma$-protocols in the quantum setting, and we offer the first non-asymptotic post-quantum security proof of the textbook Fujisaki-Okamoto transformation, i.e, without adjustments to facilitate the proof

IND-CCA-secure Key Encapsulation Mechanism in the Quantum Random Oracle Model, Revisited

With the gradual progress of NIST\u27s post-quantum cryptography standardization, the Round-1 KEM proposals have been posted for public to discuss and evaluate. Among the IND-CCA-secure KEM constructions, mostly, an IND-CPA-secure (or OW-CPA-secure) public-key encryption (PKE) scheme is first introduced, then some generic transformations are applied to it. All these generic transformations are constructed in the random oracle model (ROM). To fully assess the post-quantum security, security analysis in the quantum random oracle model (QROM) is preferred. However, current works either lacked a QROM security proof or just followed Targhi and Unruh\u27s proof technique (TCC-B 2016) and modified the original transformations by adding an additional hash to the ciphertext to achieve the QROM security. In this paper, by using a novel proof technique, we present QROM security reductions for two widely used generic transformations without suffering any ciphertext overhead. Meanwhile, the security bounds are much tighter than the ones derived by utilizing Targhi and Unruh\u27s proof technique. Thus, our QROM security proofs not only provide a solid post-quantum security guarantee for NIST Round-1 KEM schemes, but also simplify the constructions and reduce the ciphertext sizes. We also provide QROM security reductions for Hofheinz-Hoevelmanns-Kiltz modular transformations (TCC 2017), which can help to obtain a variety of combined transformations with different requirements and properties

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security