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.
We present BAT – an IND-CCA secure key encapsulation mechanism (KEM) that is based on NTRU but follows an encryption/decryption paradigm distinct from classical NTRU KEMs. It demonstrates a new approach of decrypting NTRU ciphertext since its introduction 25 years ago. Instead of introducing an artificial masking parameter p to decrypt the ciphertext, we use 2 linear equations in 2 unknowns to recover the message and the error. The encryption process is therefore close to the GGH scheme. However, since the secret key is now a short basis (not a vector), we need to modify the decryption algorithm and we present a new NTRU decoder. Thanks to the improved decoder, our scheme works with a smaller modulus and yields shorter ciphertexts, smaller than RSA-4096 for 128-bit classical security with comparable public-key size and much faster than RSA or even ECC. Meanwhile, the encryption and decryption are still simple and fast in spite of the complicated key generation. Overall, our KEM has more compact parameters than all current lattice-based schemes and a practical efficiency. Moreover, due to the similar key pair structure, BAT can be of special interest in some applications using Falcon signature that is also the most compact signature in the round 3 of the NIST post-quantum cryptography standardization. However, different from Falcon, our KEM does not rely on floating-point arithmetic and can be fully implemented over the integers.
In IEEE TIFS 2023, NTRU+ has been proposed, an efficient lattice-based post-quantum Key Encapsulation Mechanism (KEM), which has also been submitted to the KpqC competition. In this paper, we propose an effective classical chosen ciphertext attack to recover the transmitted session key for NTRU+ with all but negligible probability for the first time. With the proposed attacks, we show that all the suggested parameters of NTRU+ do not satisfy the claimed IND-CCA security. Moreover, we elaborate on some flaws in the security proof, a part of which introduces our attack. We also suggest a way to modify the NTRU+ scheme to defend our attack while maintaining its practical performance.
Abstract The rapid progress of quantum computing threatens widely deployed public-key cryptosystems such as RSA and Diffie–Hellman, accelerating the transition toward post-quantum cryptography (PQC). During this migration, hybrid key encapsulation mechanisms (KEMs) that combine classical and post-quantum primitives are strongly recommended by standardization bodies and cybersecurity agencies. However, existing hybrid designs mainly focus on combining post-quantum KEMs with Diffie–Hellman–style constructions, while the systematic integration of standardized classical public-key encryption (PKE) schemes with post-quantum KEMs remains largely unexplored. In this work, we introduce two generic hybrid constructions, and , that combine a classical PKE scheme with a post-quantum KEM satisfying ciphertext second-preimage resistance (C2PRI). We prove that both constructions achieve IND-CCA security in the standard model. The refined construction additionally relies on a new security notion of the classical PKE scheme, termed partial ciphertext second-preimage resistance (PC2PRI), which captures second-preimage resistance when a designated ciphertext component is fixed. This new property enables shared-key derivation from only a designated PKE ciphertext component in . Finally, we provide a systematic analysis of the PC2PRI property for several standardized classical encryption schemes, including ECIES, PSEC, and SM2.
The NTRU lattice is a promising candidate to construct practical cryptosystems, in particular key encapsulation mechanism (KEM), resistant to quantum computing attacks. Nevertheless, there are still some inherent obstacles to NTRU-based KEM schemes in having integrated performance, taking security, bandwidth, error probability, and computational efficiency \emph{as a whole}, that is as good as and even better than their \{R,M\}LWE-based counterparts. In this work, we solve this problem by presenting a new family of NTRU-based KEM schemes, referred to as CTRU and CNTR. By bridging low-dimensional lattice codes and high-dimensional NTRU-lattice-based cryptography with careful design and analysis, to the best of our knowledge CTRU and CNTR are the first NTRU-based KEM schemes with scalable ciphertext compression via only one \emph{single} ciphertext polynomial, and are the first that could outperform \{R,M\}LWE-based KEM schemes in integrated performance. For instance, compared to Kyber that is currently the only standardized KEM by NIST, on the recommended parameter set CNTR-768 has about
12% smaller ciphertext size while encapsulating 384-bit keys compared to the fixed 256-bit key size of Kyber, security strengthened by
(8,7) bits for classical and quantum security respectively, and significantly lower error probability (
2−230 of CNTR-768 vs.
2−164 of Kyber-768). In comparison with the state-of-the-art AVX2 implementation of Kyber-768, CNTR-768 is faster by 1.9X in KeyGen, 2.6X in Encaps, and 1.2X in Decaps, respectively. When compared to the NIST Round 3 finalist NTRU-HRSS, our CNTR-768 has about
15% smaller ciphertext size, and the security is strengthened by
(55,49) bits for classical and quantum security respectively. As for the AVX2 implementation, CNTR-768 is faster than NTRU-HRSS by 19X in KeyGen, 2.3X in Encaps, and 1.6X in Decaps, respectively.