The One-Way to Hiding (O2H) theorem, first given by Unruh (J ACM 2015) and then restated by Ambainis et al. (CRYPTO 2019), is a crucial technique for solving the reprogramming problem in the quantum random oracle model (QROM). It provides an upper bound $d\cdot\sqrt{\epsilon}$ for the distinguisher's advantage, where $d$ is the query depth and $\epsilon$ denotes the advantage of a one-wayness attacker. Later, in order to obtain a tighter upper bound, Kuchta et al. (EUROCRYPT 2020) proposed...

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...

We prove that two variants of the Fujisaki-Okamoto (FO) transformations are selective opening secure (SO) against chosen-ciphertext attacks in the quantum random oracle model (QROM), assuming that the underlying public-key encryption scheme is one-way secure against chosen-plaintext attacks (OW-CPA). The two variants we consider are $\mathsf{FO}^{\not{\bot}}$ (Hofheinz, Hövelmanns, and Kiltz, TCC 2017) and $\mathsf{U}^{\not{\bot}}_\mathsf{m}$ (Jiang et al., CRYPTO 2018). This is the first...

Public key encryption with equality test, proposed by Yang et al. (CT-RSA 2010), allows anyone to check whether two ciphertexts of distinct public keys are encryptions of the same plaintext or not using trapdoors, and identity-based encryption with equality test (IBEET) is its identity-based variant. As a variant of IBEET, IBEET against insider attacks (IBEETIA) was proposed by Wu et al. (ACISP 2017), where a token is defined for each identity and is used for encryption. Lee et al. (ACISP...

Combining several primitives together to offer greater security is an old idea in cryptography. Recently, this concept has resurfaced as it could be used to improve trust in new Post-Quantum (PQ) schemes and smooth the transition to PQ cryptography. In particular, several ways to combine key exchange mechanisms (KEMs) into a secure hybrid KEM have been proposed. In this work, we observe that most PQ KEMs are built using a variant of the Fujisaki-Okamoto (FO) transform. Thus, we propose...

This paper proves, for two examples of a randomized ROM PKE C, that derandomizing C degrades ROM OW-CPA security by a factor close to the number of hash queries. The first example can be explained by the size of the message space of C but the second cannot. This paper also gives a concrete example of a randomized non-ROM PKE C that appears to have the same properties regarding known attacks.

Several recent proposals of efficient public-key encryption are based on variants of the polynomial learning with errors problem ($\mathsf{PLWE}^f$) in which the underlying polynomial ring $\mathbb{Z}_q[x]/f$ \ is replaced with the (related) modular integer ring $\mathbb{Z}_{f(q)}$; the corresponding problem is known as Integer Polynomial Learning with Errors ($\mathsf{I-PLWE}^f$). Cryptosystems based on $\mathsf{I-PLWE}^f$ and its variants can exploit optimised big-integer arithmetic to...

Xagawa and Yamakawa (PQCrypto 2019) proved the transformation SXY can tightly turn DS secure PKEs into IND-qCCA secure KEMs in the quantum random oracle model (QROM). But transformations such as KC, TPunc that turn PKEs with standard security (OW-CPA or IND-CPA) into DS secure PKEs still suffer from quadratic security loss in the QROM. In this paper, we give a tighter security reduction for the transformation KC that turns OW-CPA secure deterministic PKEs into modified DS secure PKEs in the...

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct the first universally composable (UC) protocol for oblivious transfer secure against active static adversaries based on the Computational Diffie-Hellman (CDH) assumption. Our protocol is proven secure in the observable Global Random Oracle model. We start by constructing a protocol that...

We present Séta, a new family of public-key encryption schemes with post-quantum security based on isogenies of supersingular elliptic curves. It is constructed from a new family of trapdoor one-way functions, where the inversion algorithm uses Petit's so called torsion attacks on SIDH to compute an isogeny between supersingular elliptic curves given an endomorphism of the starting curve and images of torsion points. We prove the OW-CPA security of Séta and present an IND-CCA variant using...

[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...

Key encapsulation mechanism (KEM) variants of the Fujisaki-Okamoto (FO) transformation (TCC 2017) that turn a weakly-secure public-key encryption (PKE) into an IND-CCA-secure KEM, were widely used among the KEM submissions to the NIST Post-Quantum Cryptography Standardization Project. Under the standard CPA security assumptions, i.e., OW-CPA and IND-CPA, the security of these variants in the quantum random oracle model (QROM) has been proved by black-box reductions, e.g., Jiang et al....

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...

We present NTTRU -- an IND-CCA2 secure NTRU-based key encapsulation scheme that uses the number theoretic transform (NTT) over the cyclotomic ring $Z_{7681}[X]/(X^{768}-X^{384}+1)$ and produces public keys and ciphertexts of approximately $1.25$ KB at the $128$-bit security level. The number of cycles on a Skylake CPU of our constant-time AVX2 implementation of the scheme for key generation, encapsulation and decapsulation is approximately $6.4$K, $6.1$K, and $7.9$K, which is more than...

This paper aims to address the open problem, namely, to find new techniques to design and prove security of supersingular isogeny-based authenticated key exchange (AKE) protocols against the widest possible adversarial attacks, raised by Galbraith in 2018. Concretely, we present two AKEs based on a double-key PKE in the supersingular isogeny setting secure in the sense of CK$^+$, one of the strongest security models for AKE. Our contributions are summarised as follows. Firstly, we propose...

This paper highlights a particular construction of a correct KEM without failures and without ciphertext expansion from any correct deterministic PKE, and presents a simple tight proof of ROM IND-CCA2 security for the KEM assuming merely OW-CPA security for the PKE. Compared to previous proofs, this proof is simpler, and is also factored into smaller pieces that can be audited independently. In particular, this paper introduces the notion of ``IND-Hash'' security and shows that this allows a...

With the gradual progress of NIST's 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...

Key-encapsulation mechanisms secure against chosen ciphertext attacks (IND-CCA-secure KEMs) in the quantum random oracle model have been proposed by Boneh, Dagdelen, Fischlin, Lehmann, Schafner, and Zhandry (CRYPTO 2012), Targhi and Unruh (TCC 2016-B), and Hofheinz, Hövelmanns, and Kiltz (TCC 2017). However, all are non-tight and, in particular, security levels of the schemes obtained by these constructions are less than half of original security levels of their building blocks. In this...

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a...

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...

A framework of noise-free symmetric fully homomorphic encryption (FHE) is proposed in this work. Dierent from the frameworks that are dened over non-commutative groups, our framework is constructed from matrices over noncommutative rings. The scheme is one-way secure against chosen plaintext attacks (OW-CPA) based on the factorization problem of matrices over noncommutative rings as well as the hardness of an overdened system of multivariate polynomial equations over the given...

Consider a scenario in which an adversary, attacking a certain public key encryption scheme, gains knowledge of several ciphertexts which underlying plaintext are meaningfully related with a given target ciphertext. This kind of related message attack has been proved successful against several public key encryption schemes; widely known is the Franklin-Reiter attack to RSA with low exponent and its subsequent improvement by Coppersmith. However, to the best of our knowledge no formal...

Firstly, we demonstrate a pathological hash function choice that makes RSA-OAEP insecure. This shows that at least some security property is necessary for the hash functions used in RSA-OAEP. Nevertheless, we conjecture that only some very minimal security properties of the hash functions are actually necessary for the security of RSA-OAEP. Secondly, we consider certain types of reductions that could be used to prove the OW-CPA (i.e., the bare minimum) security of RSA-OAEP. We apply...

We prove in the random oracle model that OAEP++, which was proposed by us at the rump session of Asiacrypt 2000, can generate IND-CCA2 ciphers using deterministic OW-CPA cryptographic primitives. Note that OAEP++ differs from OAEP$^{++}$ proposed by Jonsson in \cite{Jon02}. While OAEP$^{++}$ requires a non-malleable block cipher, OAEP++ does not require such additional functions. The security reduction of OAEP++ is as tight as that of OAEP$^{++}$.