Secure Key Encapsulation Mechanism Research Articles

Side-channel attacks on CRYSTALS-KYBER, countermeasures and comparison with SKELYA (DSTU 8961-2019)

Although the mathematical problems used in post-quantum cryptography algorithms appear to be mathematically secure, a class of attacks known as side-channel attacks may prove to be a threat to the security of such algorithms. Side-channel attacks affect the hardware on which the cryptographic algorithm runs, they are not attacks on the algorithm itself.
 The good news is that side-channel analysis on new post-quantum cryptographic algorithms started early, even before the algorithms were standardized, given that older algorithms still face side-channel problems.
 Kyber is a lattice-based post-quantum algorithm based on the complexity of the M-LWE problem. Kyber offers a secure public key encryption (PKE) scheme against a chosen plaintext attack (CPA) and a secure key encapsulation mechanism against a chosen ciphertext attack (CCA).
 This paper provides a study of side-channel and fault-injection attacks on lattice-based schemes, with focus on the Kyber (KEM).
 Considering the wide range of known attacks, the protection of the algorithm requires the implementation of individual countermeasures. The paper presents and tests a number of countermeasures capable of providing/improving protection against existing SCA/FIA for Kyber KEM.
 The obtained results show that the presented countermeasures incur a reasonable performance cost. Therefore, the use of special countermeasures in real implementations of lattice-based schemes, either alone or as an augmentation of general countermeasures, is necessary.

High Throughput Implementation of Post-Quantum Key Encapsulation and Decapsulation on GPU for Internet of Things Applications

Internet of Things (IoT) sensor nodes are placed ubiquitously to collect information, which is then vulnerable to malicious attacks. For instance, adversaries can perform side channel attack on the sensor nodes to recover the symmetric key for encrypting IoT data. Refreshing the symmetric key frequently can reduce the risk of compromised keys. However, the number of sensor nodes connected to the gateway and cloud server is massive. Refreshed symmetric keys need to be sent to gateway devices and cloud server frequently with a secure key encapsulation mechanism (KEM), which is time-consuming. In this article, novel and efficient implementation techniques are proposed to accelerate Kyber, a post-quantum KEM, on a Graphics Processing Unit (GPU). Fully parallel implementation of number theoretic transform (NTT) with combined levels is presented, which is 2.65× faster than state-of-the-art result on a GPU. Other proposed techniques include parallel rejection sampling, central binomial distribution with coalesced memory access and parallel fine-grain AES-256. These techniques enable high throughput performance with 162760 encapsulations/second and 107631 decapsulations/second on an RTX2060 GPU. This is also the first fine grain implementation of post-quantum KEM (Kyber) on a GPU, which can be used to offer key encapsulation/decapsulation as a service to reduce the burden on IoT systems.

Analysis of the FO Transformation in the Lattice-Based Post-Quantum Algorithms

Newer variants of the Fujisaki–Okamoto transformation are used in most candidates of the third round of the NIST Post-Quantum Cryptography standardization call in the category of public key encryption schemes. These transformations are applied to obtain a highly secure key encapsulation mechanism from a less secure public key encryption scheme. Furthermore, there are five candidates (three finalists and two alternatives) that passed to the third round of the process and whose security is based in lattice problems. This work analyzes the different ways in which the lattice-based candidates of the NIST call apply the Fujisaki–Okamoto transformation and the particularities of each application. The study of such differences and their repercussion in the design of the proposals will allow a better understanding of the algorithms. Moreover, we propose a modification of the Kyber algorithm—the only public key encryption candidate established as a PQC standard by NIST in its more recent publication—in order to avoid the re-encryption in the decapsulation algorithm and, in this way, to reduce the side channel attacks vulnerability.

BAT: Small and Fast KEM over NTRU Lattices

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.

Masking Kyber: First- and Higher-Order Implementations

In the final phase of the post-quantum cryptography standardization effort, the focus has been extended to include the side-channel resistance of the candidates. While some schemes have been already extensively analyzed in this regard, there is no such study yet of the finalist Kyber.In this work, we demonstrate the first completely masked implementation of Kyber which is protected against first- and higher-order attacks. To the best of our knowledge, this results in the first higher-order masked implementation of any post-quantum secure key encapsulation mechanism algorithm. This is realized by introducing two new techniques. First, we propose a higher-order algorithm for the one-bit compression operation. This is based on a masked bit-sliced binary-search that can be applied to prime moduli. Second, we propose a technique which enables one to compare uncompressed masked polynomials with compressed public polynomials. This avoids the costly masking of the ciphertext compression while being able to be instantiated at arbitrary orders.We show performance results for first-, second- and third-order protected implementations on the Arm Cortex-M0+ and Cortex-M4F. Notably, our implementation of first-order masked Kyber decapsulation requires 3.1 million cycles on the Cortex-M4F. This is a factor 3.5 overhead compared to the unprotected optimized implementationin pqm4. We experimentally show that the first-order implementation of our new modules on the Cortex-M0+ is hardened against attacks using 100 000 traces and mechanically verify the security in a fine-grained leakage model using the verification tool scVerif.

Revisiting NIZK-Based Technique for Chosen-Ciphertext Security: Security Analysis and Corrected Proofs

Non-interactive zero-knowledge (NIZK) proofs for chosen-ciphertext security are generally considered to give an impractical construction. An interesting recent work by Seo, Abdalla, Lee, and Park (Information Sciences, July 2019) proposed an efficient semi-generic conversion method for achieving chosen-ciphertext security based on NIZK proofs in the random oracle model. The recent work by Seo et al. demonstrated that the semi-generic conversion method transforms a one-way (OW)-secure key encapsulation mechanism (KEM) into a chosen-ciphertext secure KEM while preserving tight security reduction. This paper shows that the security analysis of the semi-generic conversion method has a flaw, which comes from the OW security condition of the underlying KEM. Without changing the conversion method, this paper presents a revised security proof under the changed conditions that (1) the underlying KEM must be chosen-plaintext secure in terms of indistinguishability and (2) an NIZK proof derived from the underlying KEM via the Fiat–Shamir transform must have the properties of zero-knowledge and simulation soundness. This work extended the security proof strategy to the case of identity-based KEM (IBKEM) and also revise the security proof for IBKEM of previous method by Seo et al. Finally, this work gives a corrected security proof by applying the new proofs to several existing (IB)KEMs.

Chosen-Ciphertext Secure Key Encapsulation Mechanism in the Standard Model

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 Döttling <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (ASIACRYPT 2012), Kiltz <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (PKC 2014) and Yu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (CRYPTO 2016) ((7.27GB, 7.24GB, 7.03KB), (80.89MB, 46.23MB, 6.80KB) and (70.95MB, 70.65MB, 86.50KB) respectively).

Optimized IoT Cryptoprocessor Based on QC-MPDC Key Encapsulation Mechanism

The key encapsulation mechanism (KEM) is an important cryptographic tool to protect communication in the Internet of Things (IoT). In the near future, classical algorithms used to construct KEMs, such as RSA and elliptic curve cryptography, will be vulnerable to attacks from quantum computers. Recently, Yamada et al. proposed the quasicyclic medium density parity check (QC-MDPC) KEM, which is considered one of the most advanced code-based cryptosystems to resist quantum attacks. In this article, an optimized implementation of QC-MDPC KEM for IoT applications is presented. Our main contributions are threefold: 1) the fastest QC-MDPC McEliece decryption in field-programmable gate array (FPGA); 2) the first QC-MDPC KEM implementation in FPGA; and 3) the first iteration count attack-resistant QC-MDPC decoder in FPGA. To improve the decryption speed, we introduce a novel customized rotation engine (CRE) and incorporated several recent techniques reported in the literature, including adaptive threshold and Hamming weight estimation. The best-achieved throughput in our implementation on Xilinx Virtex 7 FPGA is 12.7% faster than the state-of-the-art result reported by Heyse et al. The proposed CRE was then integrated with QC-MDPC KEM to produce a fast and secure KEM. Furthermore, to prevent timing attacks demonstrated recently, a constant-time implementation of the QC-MDPC McEliece decoder was presented.

Breaking the hardness assumption and IND‐CPA security of HQC submitted to NIST PQC project

Hamming quasi-cyclic (HQC) cryptosystem, proposed by Aguilar Melchor et al. , is a code-based key encapsulation mechanism (KEM) submitted for the NIST standardisation process of post-quantum cryptography (PQC). Under the assumption that the s -decision quasi-cyclic syndrome decoding ( s -DQCSD) problem is hard for s = 2 and 3, HQC, viewed as a public-key encryption scheme, is proven to be indistinguishability under chosen plaintext attack (IND-CPA) secure, and can be transformed into an IND-Adaptive chosen ciphertext attack secure KEM. However, the authors will show that the s -DQCSD problem is actually not intractable and HQC cannot attain IND-CPA security with all the proposed parameter sets. As HQC was selected as one of the second-round candidates by NIST, it was also updated to resist attack. The underlying s -DQCSD problem was replaced by the s -DQCSD with a parity problem and they claimed that the updated HQC could attain IND-CPA security under the hardness of the new problem. However, they find that there is some flaw in their security proof and the updated HQC is still vulnerable to attack. To fix it, they define a new problem called s -DQCSD with variable weight and present revised scheme HQC- β , which finally attains the IND-CPA security under the hardness assumption of the new problem.

Analysis of Error Dependencies on Newhope

Among many submissions to the NIST post-quantum cryptography (PQC) project, NewHope is a promising key encapsulation mechanism (KEM) based on the Ring-Learning with errors (Ring-LWE) problem. Since NewHope is an indistinguishability (IND)-chosen ciphertext attack secure KEM by applying the Fujisaki-Okamoto transform to an IND-chosen plaintext attack secure public key encryption, accurate calculation of decryption failure rate (DFR) is required to guarantee resilience against attacks that exploit decryption failures. However, the current upper bound of DFR on NewHope is rather loose because the compression noise, the effect of encoding/decoding of NewHope, and the approximation effect of centered binomial distribution are not fully considered. Furthermore, since NewHope is a Ring-LWE based cryptosystem, there is a problem of error dependency among error coefficients, which makes accurate DFR calculation difficult. In this paper, we derive much tighter upper bound on DFR than the current upper bound using constraint relaxation and union bound. Especially, the above-mentioned factors are all considered in derivation of new upper bound and the centered binomial distribution is not approximated to subgaussian distribution. In addition, since the error dependency is considered, the new upper bound is much closer to the real DFR than the previous upper bound. Furthermore, the new upper bound is parameterized by using Chernoff-Cramer bound in order to facilitate calculation of new upper bound for the parameters of NewHope. Since the new upper bound is much lower than the DFR requirement of PQC, this DFR margin is used to improve the security and bandwidth efficiency of NewHope. As a result, the security level of NewHope is improved by 7.2 % or bandwidth efficiency is improved by 5.9 %.

New technique for chosen-ciphertext security based on non-interactive zero-knowledge

In this study, we propose a new method for conversion from a one-way (OW)-secure key encapsulation mechanism (KEM) into a chosen-ciphertext (CCA) secure KEM in the random oracle model. Our conversion method is based on the non-interactive zero-knowledge (NIZK) proof system for proving the relationships (e.g., equality or linearity) of discrete logarithms, where the security analysis of our conversion method depends on the NIZK properties of soundness and zero-knowledge. Our conversion method achieves tight security reduction and it is semi-generic in the sense that other than OW-security, a KEM should be NIZK-compatible. From a theoretical viewpoint, our conversion method can be considered as the corresponding approach for obtaining an efficient signature by applying the Fiat–Shamir transform to the NIZK system. We applied our conversion method to several OW-secure (identity-based) KEMs and compared the results with those obtained by previous methods for achieving CCA security.

New efficient chosen ciphertext secure Elgamal encryption schemes for secure Cloud storage service

Nowadays Cloud computation has become a commonplace information service paradigm for all actors in ICT field, from individuals to big corporates. In particular, Cloud platforms and data centres are being used each time more for outsourcing data. However, data owners often worry about their data security and privacy before outsourcing the data to the Cloud, thus it is often a practice to first encrypt the data sets and then outsource them to the Cloud. The drawback of this approach is that, if the encryption scheme can only achieve chosen plaintext security, it cannot be assured to achieve strong security against many kinds of malicious adversaries in the Cloud setting. The chosen ciphertext security is essential for outsourcing ciphertexts to the Cloud, on the other hand, in most cases the data owners prefer to choose high-efficient encryption schemes for saving computation and communication costs. In this paper, we propose a new way to achieve chosen ciphertext security for Elgamal encryption scheme, which is a very basic and usual primitive for encapsulating block data encryption keys. We propose two new chosen ciphertext attack (CCA) secure schemes. The first one, which is a public key encryption proved secure in the random oracle based on the computational Diffie-Hellman (CDH) assumption, has almost no additional overhead compared with the traditional (indistinguishable under chosen plaintext attack secure Elgamal scheme, except one additional modular exponentiation for the decryption. The second scheme, which is a key encapsulation mechanism (KEM) proved secure in the standard model based on a new non-interactive assumption, has only two group elements as the encapsulations. Thus we solve the open problem left by Hanaoka et al. in Crypto'12, which consists in how to construct anindistinguishable under chosen ciphertext attack secure KEM without pairings based on a non-interactive assumption and with two group element encapsulations. To prove the scheme's security, we develop a new assumption called verifiable CDH assumption. We also generalise our technique to several existing well-known CCA secure KEMs, including the Boneh-Mei-Waters (BMW) KEM and the Hofheinz-Kiltz (HK) KEM, and show that our new schemes are even more efficient than these well-known schemes. Finally, we propose a new framework for efficient and secure data outsourcing to the Cloud based on our new schemes and present a rough analysis of its security.

New efficient chosen ciphertext secure Elgamal encryption schemes for secure Cloud storage service

Nowadays Cloud computation has become a commonplace information service paradigm for all actors in ICT field, from individuals to big corporates. In particular, Cloud platforms and data centres are being used each time more for outsourcing data. However, data owners often worry about their data security and privacy before outsourcing the data to the Cloud, thus it is often a practice to first encrypt the data sets and then outsource them to the Cloud. The drawback of this approach is that, if the encryption scheme can only achieve chosen plaintext security, it cannot be assured to achieve strong security against many kinds of malicious adversaries in the Cloud setting. The chosen ciphertext security is essential for outsourcing ciphertexts to the Cloud, on the other hand, in most cases the data owners prefer to choose high-efficient encryption schemes for saving computation and communication costs. In this paper, we propose a new way to achieve chosen ciphertext security for Elgamal encryption scheme, which is a very basic and usual primitive for encapsulating block data encryption keys. We propose two new chosen ciphertext attack (CCA) secure schemes. The first one, which is a public key encryption proved secure in the random oracle based on the computational Diffie-Hellman (CDH) assumption, has almost no additional overhead compared with the traditional (indistinguishable under chosen plaintext attack secure Elgamal scheme, except one additional modular exponentiation for the decryption. The second scheme, which is a key encapsulation mechanism (KEM) proved secure in the standard model based on a new non-interactive assumption, has only two group elements as the encapsulations. Thus we solve the open problem left by Hanaoka et al. in Crypto'12, which consists in how to construct anindistinguishable under chosen ciphertext attack secure KEM without pairings based on a non-interactive assumption and with two group element encapsulations. To prove the scheme's security, we develop a new assumption called verifiable CDH assumption. We also generalise our technique to several existing well-known CCA secure KEMs, including the Boneh-Mei-Waters (BMW) KEM and the Hofheinz-Kiltz (HK) KEM, and show that our new schemes are even more efficient than these well-known schemes. Finally, we propose a new framework for efficient and secure data outsourcing to the Cloud based on our new schemes and present a rough analysis of its security.

Efficient chosen ciphertext secure key encapsulation mechanism in standard model over ideal lattices

ABSTRACTKey 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.

Strongly secure authenticated key exchange from factoring, codes, and lattices

An unresolved problem in research on authenticated key exchange (AKE) in the public-key setting is to construct a secure protocol against advanced attacks such as key compromise impersonation and maximal exposure attacks without relying on random oracles. HMQV, a state of the art AKE protocol, achieves both efficiency and the strong security proposed by Krawczyk (we call it the $${\mathrm {CK}}^+$$CK+ model), which includes resistance to advanced attacks. However, the security proof is given under the random oracle model. We propose a generic construction of AKE from a key encapsulation mechanism (KEM). The construction is based on a chosen-ciphertext secure KEM, and the resultant AKE protocol is $${\mathrm {CK}}^+$$CK+ secure in the standard model. The construction gives the first $${\mathrm {CK}}^+$$CK+ secure AKE protocols based on the hardness of integer factorization problem, code-based problems, or learning problems with errors. In addition, instantiations under the Diffie---Hellman assumption or its variant can be proved to have strong security without non-standard assumptions such as $$\pi $$?PRF and KEA1. Furthermore, we extend the $${\mathrm {CK}}^+$$CK+ model to identity-based (called the $${\hbox {id-CK}^+}$$id-CK+ model), and propose a generic construction of identity-based AKE (ID-AKE) based on identity-based KEM, which satisfies $${\hbox {id-CK}^+}$$id-CK+ security. The construction leads first strongly secure ID-AKE protocols under the hardness of integer factorization problem, or learning problems with errors.

Identification Schemes from Key Encapsulation Mechanisms

We propose a generic way for deriving an identification (ID) scheme secure against concurrent man-in-the-middle attacks from a key encapsulation mechanism (KEM) secure against chosen ciphertext attacks on one-wayness (oneway-CCA). Then we give a concrete one-way-CCA secure KEM based on the Computational Diffie-Hellman (CDH) assumption. In that construction, the Twin Diffie-Hellman technique of Cash, Kiltz and Shoup is essentially employed. We compare efficiency of the ID scheme derived from our KEM with previously known ID schemes and KEMs. It turns out that our KEM-based ID scheme reduces the computation by one exponentiation than the currently most efficient one derived from the Hanaoka-Kurosawa one-way-CCA secure KEM, whose security is based on the same (CDH) assumption.

How to Shorten a Ciphertext of Reproducible Key Encapsulation Mechanisms in the Random Oracle Model

This paper shows a simple methodology for shortening a ciphertext of reproducible key encapsulation mechanisms. Specifically, it transforms a key encapsulation mechanism having OW-CCCA security and reproducibility into that of IND-CCA secure in the random oracle model whose ciphertext is shorter. Various existing chosen-ciphertext secure key encapsulation mechanisms (in the standard model) are reproducible, and thus their ciphertext can be shortened by the proposed transformation. The transformed scheme requires only one additional hashing for encryption. This property enables us to implement both the original scheme and the transformed scheme into a single chip simultaneously with small gate-size overhead. Using this chip, a sender can flexibly switch schemes to encrypt a message in a message-by-message manner. Such a use of schemes is also analyzed.