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