ISO/IEC standardizes several chosen ciphertext-secure key encapsulation mechanism (KEM) schemes in ISO/IEC 18033-2. However, all ISO/IEC KEM schemes are not quantum resilient. In this paper, we introduce new isogeny-based KEM schemes (i.e., CSIDH-ECIES-KEM and CSIDH-PSEC-KEM) by modifying Diffie-Hellman-based KEM schemes in ISO/IEC standards. The main advantage of our schemes are compactness. The key size and the ciphertext overhead of our schemes are smaller than these of SIKE, which is submitted to NIST's post-quantum cryptosystems standardization, for current security analyses. Moreover, though SIKE is proved in the classical random oracle model, CSIDH-PSEC-KEM is proved in the quantum random oracle model. Finally, we discuss difficulty to construct isogeny-based KEM from ISO/IEC KEM schemes in the standard model (i.e., ACE-KEM and FACE-KEM).
ISO/IEC standardizes several chosen ciphertext-secure key encapsulation mechanism (KEM) schemes in ISO/IEC 18033-2. However, all ISO/IEC KEM schemes are not quantum resilient. In this paper, we introduce new isogeny-based KEM schemes (i.e., CSIDH-ECIES-KEM and CSIDH-PSEC-KEM) by modifying Diffie-Hellman-based KEM schemes in ISO/IEC standards. The main advantage of our schemes are compactness. The key size and the ciphertext overhead of our schemes are smaller than these of SIKE, which is submitted to NIST's post-quantum cryptosystems standardization, for current security analyses. Moreover, though SIKE is proved in the classical random oracle model, CSIDH-PSEC-KEM is proved in the quantum random oracle model. Finally, we discuss difficulty to construct isogeny-based KEM from ISO/IEC KEM schemes in the standard model (i.e., ACE-KEM and FACE-KEM).
ISO/IEC standardizes several chosen ciphertext-secure key encapsulation mechanism (KEM) schemes in ISO/IEC 18033-2. However, all ISO/IEC KEM schemes are not quantum resilient. In this paper, we introduce new isogeny-based KEM schemes (i.e., CSIDH-ECIES-KEM and CSIDH-PSEC-KEM) by modifying Diffie-Hellman-based KEM schemes in ISO/IEC standards. The main advantage of our schemes are compactness. The key size and the ciphertext overhead of our schemes are about five times smaller than these of SIKE-KEM which is submitted to NIST's post-quantum cryptosystems standardization.
Abstract The SIDH and CSIDH are now the two most well-known post-quantum key exchange protocols from the supersingular isogeny-based cryptography, which have attracted much attention in recent years and served as the building blocks of other supersingular isogeny-based cryptographic schemes. The famous SIKE is a post-quantum key encapsulation mechanism (KEM) constructed on the SIDH, motivated by which, this article presents a new post-quantum KEM-based on the CSIDH, which is thereby named as CSIKE. The presented CSIKE has much higher computation efficiency in the decapsulation part by involving an additional tag in the encapsulation results. The new CSIKE is formally proved to be IND-CCA secure under the standard isogeny-based quantum resistant security assumption. Moreover, by comparing the new CSIKE with the only two existing CSIDH-based KEM schemes, i.e., CSIDH-PSEC-KEM and CSIDH-ECIES-KEM, it can be easily found that the new CSIKE has a slightly longer encapsulation size than CSIDH-PSEC-KEM and CSIDH-ECIES-KEM, but (i) it beats the CSIDH-PSEC-KEM by the improvement of approximately 50% in decapsulation speed, and (ii) it has a certain advantage over the CSIDH-ECIES-KEM in security since in the random oracle model, the security proof for CSIDH-ECIES-KEM needs to rely on the stronger CSI-GDH assumption, while the new CSIKE just needs to rely on the basic CSI-CDH assumption.
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.
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).
The emergence of quantum computing poses a significant threat to the security of currently deployed public-key cryptosystems, including those based on elliptic curves (ECC). Shor's algorithm can solve the underlying integer factorization and discrete logarithm problems in polynomial time, rendering established cryptographic standards obsolete. This has catalyzed the development of post-quantum cryptography (PQC), a new generation of algorithms resistant to attacks by both classical and quantum computers. Among the most promising PQC candidates are systems based on supersingular isogeny graphs. This paper provides a comprehensive analysis of the supersingular isogeny paradigm as a quantum-secure evolution of elliptic curve cryptography. It begins by introducing the mathematical foundations of elliptic curves and isogenies, which are structure-preserving maps between them. The core of isogeny-based cryptography lies in the conjectured hardness of finding an isogeny path between two given supersingular elliptic curves in the vast isogeny graph. This is fundamentally different from the discrete logarithm problem that underpins traditional ECC. We review the foundational Supersingular Isogeny Diffie-Hellman (SIDH) key exchange protocol and its subsequent realization as the Supersingular Isogeny Key Encapsulation (SIKE) mechanism, which was a candidate in the NIST PQC standardization process. We discuss its advantages, such as small key sizes and perfect forward secrecy, which made it an attractive alternative. However, the paper also presents a balanced view by thoroughly examining the devastating cryptanalytic breakthroughs of 2022 that rendered the original SIDH/SIKE schemes insecure. These attacks, which exploit auxiliary point information, underscore the dynamic nature of PQC research. Despite this setback, the isogeny-based field remains active, with ongoing research into alternative constructions like CSIDH and other variants that are not vulnerable to the known attacks. We conclude that while the initial promise of SIDH/SIKE was broken, the underlying mathematical problem of finding isogenies remains a compelling basis for quantum-secure cryptography, representing a paradigm of active research rather than a discarded concept.
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.