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IEEE Access

Chosen-Ciphertext Secure Key Encapsulation Mechanism in the Standard Model

Shengfeng Xu, Xiangxue Li

Published Jan 1, 2021• 7 citations
Publisher

Abstract

Key Encapsulation Mechanism (KEM) is a foundational cryptography primitive, which can provide secure symmetric cryptographic key material for transmission by using public key algorithms. Until now, many Chosen-Ciphertext (IND-CCA) secure KEM schemes are constructed from Chosen-Plaintext (IND-CPA) or One-Way (OW-CPA) secure PKE via the generic Fujisaki-Okamoto (FO) transformations (TCC 2017). However, the security relies on the Random Oracle Model (ROM). To the best of our knowledge, there are no IND-CCA secure KEM schemes based on Learning Parity with Noise (LPN) assumption that can against post quantum attacks in the standard model. In this work, we propose the first direct construction of LPN-based KEM, which is secure in the standard model. In particular, we use double-trapdoor technique to answer adversary’s decryption queries correctly and a Target Collision Resistant (TCR) hash function to check the validity of the ciphertext. The encapsulated key is determined by a special LPN problem (with no random oracle required). The scheme is IND-CCA secure against post-quantum attacks under the low-noise LPN assumptions by a series of games and the security reduction is tight. Compared with previous schemes on 128-bit security level, our CCA-secure scheme only holds 50.78MB public keys, 62.50MB secret keys and 4.54KB ciphertexts, which is more efficient than the schemes of Döttlinget al.(ASIACRYPT 2012), Kiltzet al.(PKC 2014) and Yuet al.(CRYPTO 2016) ((7.27GB, 7.24GB, 7.03KB), (80.89MB, 46.23MB, 6.80KB) and (70.95MB, 70.65MB, 86.50KB) respectively).

DOI
10.1109/access.2021.3051047

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IACR Communications in Cryptology•Oct 6, 2025•1 citation
Key Encapsulation Mechanism (KEM) is a foundational cryptography primitive, which can provide secure symmetric cryptographic key material for transmission by using public key algorithms. Until now, many Chosen-Ciphertext (IND-CCA) secure KEM schemes are constructed from Chosen-Plaintext (IND-CPA) or One-Way (OW-CPA) secure PKE via the generic Fujisaki-Okamoto (FO) transformations (TCC 2017). However, the security relies on the Random Oracle Model (ROM). To the best of our knowledge, there are no IND-CCA secure KEM schemes based on Learning Parity with Noise (LPN) assumption that can against post quantum attacks in the standard model. In this work, we propose the first direct construction of LPN-based KEM, which is secure in the standard model. In particular, we use double-trapdoor technique to answer adversary’s decryption queries correctly and a Target Collision Resistant (TCR) hash function to check the validity of the ciphertext. The encapsulated key is determined by a special LPN problem (with no random oracle required). The scheme is IND-CCA secure against post-quantum attacks under the low-noise LPN assumptions by a series of games and the security reduction is tight. Compared with previous schemes on 128-bit security level, our CCA-secure scheme only holds 50.78MB public keys, 62.50MB secret keys and 4.54KB ciphertexts, which is more efficient than the schemes of Döttlinget al.(ASIACRYPT 2012), Kiltzet al.(PKC 2014) and Yuet al.(CRYPTO 2016) ((7.27GB, 7.24GB, 7.03KB), (80.89MB, 46.23MB, 6.80KB) and (70.95MB, 70.65MB, 86.50KB) respectively).
Key encapsulation mechanism (KEM) is an important key distribution mechanism that not only allows both sender and receiver to safely share a random session key, but also can be mainly applied to construct a hybrid public key encryption scheme. In this paper, we give an positive answer to the question of if it is possible to build an efficient KEM over lattices. More precisely, we design an efficient KEM scheme in standard model based on ideal lattices. We prove that the proposed scheme captures indistinguishability against active chosen ciphertext attacks (IND-CCA) under the ring learning with errors problem, or more formally, IND-CCA security. Compared with the current CCA secure KEM schemes based on lattices in the standard model, our scheme has shorter public key, secret key and encapsulation ciphertext. In addition, our KEM scheme realizes IND-CCA security in the standard model.
This paper proposes a new generic Encrypt-thenMAC (EtM) transformation for constructing IND-CCA secure Key Encapsulation Mechanisms (KEMs) in the post-quantum setting. The transformation builds on a public-key encryption scheme satisfying one-wayness under plaintext-checking attacks (OW-PCA) and an existentially unforgeable MAC, and formally achieves tight IND-CCA security in the random oracle model via a rigorous security reduction. Unlike the widely used FujisakiOkamoto (FO) transformation, our approach eliminates the need for ciphertext re-encryption during decapsulation-a major source of computational overhead and side-channel vulnerability in lattice-based implementations. We instantiate the transformation using the ML-KEM (FIPS 203) subroutine, yielding the ML-KEM-EtM variant. Experimental results show that ML-KEMEtM reduces decapsulation cycle counts by72−79%72-79 {\%}72−79%across security levels, with only a modest increase in encapsulation cost(1.8−7.3%)(1.8-7.3 {\%})(1.8−7.3%)and ciphertext size(1.0−2.1%)(1.0-2.1 {\%})(1.0−2.1%). The scheme thus offers a practical and efficient a lternative to F O-based KEMs, especially in performance-critical scenarios such as post-quantum TLS handshakes, where decapsulation efficiency is paramount.
In this paper, we present a novel multi-receiver identity-based key encapsulation mechanism (mID-KEM) scheme which is provably secure against chosen ciphertext attacks in the standard model and has several advantages over previous constructions without random oracles, including short public parameters, short private keys, computational efficiency in decapsulation algorithm and tight security reduction. To our best knowledge, our construction is the first in the literature to achieve such a high security level (CCA-security in the full security model).
Abstract. We use hybrid encryption with Fuzzy Identity-Based Encryption (Fuzzy-IBE) schemes, and present the first and efficient fuzzy identity-based key encapsulation mechanism (Fuzzy-IB-KEM) schemes which are chosen-ciphertext secure (CCA) without random oracle in the selective-ID model. To achieve these goals, we consider Fuzzy-IBE schemes as consisting of separate key and data encapsulation mechanisms (KEM-DEM), and then give the definition of Fuzzy-IB-KEM. Our main idea is to enhance Sahai and Waters ' "large universe " construction, chosen-plaintext secure (CPA) Fuzzy-IBE, by adding some redundant information to the ciphertext to make it CCA-secure.
Practical deployments of key encapsulation mechanisms (KEMs) may entail large servers each using their public keys to communicate with potentially millions of clients simultaneously. While the standard IND-CCA security definition for KEMs considers only a single challenge public key and single challenge ciphertext, it can be relevant to consider multi-target scenarios where the adversary aims to break one of many challenge ciphertexts, for one of many challenge public keys. Many post-quantum KEMs have been built by applying the Fujisaki-Okamoto (FO) transform to a public key encryption (PKE) scheme. Although the FO transform incurs only a few bits of security loss for the standard, single-challenge IND-CCA property, this does not hold in the multi-target setting. Attacks have been identified against standards-track FO-based KEMs with 128-bit message spaces (FrodoKEM-640 and HQC-128) which become feasible if the adversary is given many challenge ciphertexts (say, 2^64). These attacks exploit the deterministic encryption induced by the FO transform which allows the IND-CCA experiment to be reduced to a search problem on the message space, which in some cases may not be large enough to avoid collisions between pre-computation and challenge values. A cost effective way to amplify the hardness of this search problem is to add a random but public salt during encapsulation. While revised versions of FrodoKEM and HQC have used salts, there has been no proof showing that salting provides multi-ciphertext security. In this work, we formally analyze a salted variant of the Fujisaki-Okamoto transform, in the classical and quantum random oracle model (ROM); for the classical ROM, we show that multi-target IND-CCA security of the resulting KEM tightly reduces to the multi-target IND-CPA security of the underlying PKE. Our results imply that, for FrodoKEM and HQC at the 128-bit security level, replacing the FO transform with the salted variant can recover 62 bits of multi-target security, at the cost of a very small overhead increase.
Combiners for cryptographic schemes are a common way to increase security using redundancy. The security notions for public key encryption (PKE) combiners can be extended beyond the standard IND-CCA security to achieve even stronger security notions. In the indistinguishability under adaptive strong multiple chosen-ciphertext attack (IND-sMCCA) security notion, the adversary has additional oracle access to the underlying cipher components of the combiner. Recently, combiners have received more attention because of the possibility of combining classical and post-quantum (PQ) cryptography. This allows for the use of novel PQ algorithms while still having the security guarantees of the classical algorithms. In order to examine the security against quantum adversaries, the quantum random oracle model (QROM) has become the most relevant security model. However, there are no PKE combiners that achieve IND-sMCCA security in the QROM, even though this security notion describes much better the current state where classical, PQ, and combined schemes are deployed at the same time. In this paper, we close this gap by providing a new PKE combiner that is IND-sMCCA secure in the QROM. Our construction is more efficient and lean than the existing PKE combiners, considering the primitives used and the ciphertext size. We accomplish this by applying the Fujisaki-Okamoto (FO) transformation to a PKE combiner of Asmuth and Blakley. To achieve IND-sMCCA security for the combiner, the PKE components must be OW-CCA secure. However, when using weaker (OW-CPA secure) PKE components, we still achieve standard IND-CCA security for the combiner. The security reductions are given in the ROM and the QROM, achieving bounds of different tightness.