Secure Public Key Encryption Research Articles

The Perils of Limited Key Reuse: Adaptive and Parallel Mismatch Attacks with Post-processing Against Kyber

The Module Learning With Errors (MLWE)-based Key Encapsulation Mechanism (KEM) Kyber is NIST's new standard scheme for post-quantum encryption. As a building block, Kyber uses a Chosen Plaintext Attack (CPA)-secure Public Key Encryption (PKE) scheme, referred to as Kyber.CPAPKE. In this paper we study the robustness of Kyber.CPAPKE against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised if having access to a few mismatch queries of Kyber.CPAPKE, by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in Kyber.CPAPKE. We further propose an adaptive method to enhance parallel mismatch attacks, initially proposed by Shao et al. at AsiaCCS 2024, thereby significantly reducing query complexity. This method combines the adaptive attack with post-processing via lattice reduction to retrieve the final secret key entries. Our method proves its efficacy by reducing query complexity by 14.6 % for Kyber512 and 7.5 % for Kyber768/Kyber1024. Furthermore, this approach has the potential to improve multi-value Plaintext-Checking (PC) oracle-based side-channel attacks and fault-injection attacks against Kyber itself.

Verifiable Encryption from MPC-in-the-Head

Verifiable encryption (VE) is a protocol where one can provide assurance that an encrypted plaintext satisfies certain properties, or relations. It is an important building block in cryptography with many useful applications, such as key escrow, group signatures, optimistic fair exchange, and others. However, the majority of previous VE schemes are restricted to instantiation with specific public-key encryption schemes or relations. In this work, we propose a novel framework that realizes VE protocols using zero-knowledge proof systems based on the MPC-in-the-head paradigm (Ishai et al. STOC 2007). Our generic compiler can turn a large class of zero-knowledge proofs into secure VE protocols for any secure public-key encryption scheme with the undeniability property, a notion that essentially guarantees binding of encryption when used as a commitment scheme. Our framework is versatile: because the circuit proven by the MPC-in-the-head prover is decoupled from a complex encryption function, the work of the prover is focused on proving the encrypted data satisfies the relation, not the proof of plaintext knowledge. Hence, our approach allows for instantiation with various combinations of properties about the encrypted data and encryption functions. We then consider concrete applications, to demonstrate the efficiency of our framework, by first giving a new approach and implementation to verifiably encrypt discrete logarithms in any prime order group more efficiently than was previously known. Then we give the first practical verifiable encryption scheme for AES keys with post-quantum security, along with an implementation and benchmarks.

Tightly Secure Public Key Encryption With Equality Test in Setting With Adaptive Corruptions

Tightly Secure Public Key Encryption With Equality Test in Setting With Adaptive Corruptions

Possibility of decryption speed-up by parallel processing in CCA secure hashed ElGamal.

In order to prove the ElGamal CCA(Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group where ICDH(Interactive Computational Diffie Hellman) assumption holds. Until now, only bilinear group with complex algebraic structure has been known as the ICDH group. In this paper, we introduce the ICDH group with simple algebraic structure. In other words, we prove that ICDH assumption holds in the integer group with composite modulus. On the basis of this, we propose the CCA secure hashed ElGamal and its fast variant to speed up decryption by parallel processing. Our parallel scheme has the fastest decryption among all CCA secure PKE(Public Key Encryption) schemes implemented in integer group and gives the possibility that ElGamal protocol could be practical when the big modulus numbers are used to resist the quantum attack.

Provably secure public key encryption with keyword search for data outsourcing in cloud environments

In recent days, the application of cloud computing has been gaining significant popularity among people. A considerable amount of data are being stored in the cloud server. However, data owners outsource their encrypted data to the cloud for various security reasons. Unfortunately, encrypted data cannot be searched, like plaintext data. So how to search encrypted data is an interesting problem in this era. Many public key encryption with keyword search (PEKS) schemes have been designed in the literature. However, most of them cannot prevent keyword-guessing attacks. In this paper, we develop a provably secure PEKS scheme in the random oracle model. This scheme may be used for secure email access from an email server containing a list of encrypted keywords. The proposed scheme can resist keyword-guessing attacks, and offer ciphertext and trapdoor indistinguishability properties. We use the data owner’s private key during encryption to prevent keyword-guessing attacks. Using the data owner’s public key in the verification phase ensures the resilience of keyword-guessing attacks. Finally, the proposed scheme has been tested on a real testbed, and the results show that it can be used in the cloud computing scenario to search for keywords on encrypted data.

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.

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.

Forward Secure Public Key Encryption with Keyword Search for Outsourced Cloud Storage

Cloud storage has become a primary industry in remote data management service but also attracts security concerns, where the best available approach for preventing data disclosure is encryption. Among them the public key encryption with keyword search (PKSE) is considered to be a promising technique, since clients can efficiently search over encrypted data files. That is, a client first generates a search token when to query data files, the cloud server uses the search token to proceed the query over encrypted data files. However, a serious attack is raised when PKSE meets cloud. Formally speaking, the cloud server can learn the information of a newly added encrypted data file containing the keyword that previously queried by using the search tokens it has received, and can further discover the privacy information. To address this issue, we propose a forward secure public key searchable encryption scheme, in which a cloud server cannot learn any information about a newly added encrypted data file containing the keyword that previously queried. To better understand the design principle, we introduce a framework for constructing forward secure public key searchable encryption schemes based on attribute-based searchable encryption. Finally, the experiments show our scheme is efficient.

Curse of Re-encryption: A Generic Power/EM Analysis on Post-Quantum KEMs

This paper presents a side-channel analysis (SCA) on key encapsulation mechanism (KEM) based on the Fujisaki–Okamoto (FO) transformation and its variants. The FO transformation has been widely used in actively securing KEMs from passively secure public key encryption (PKE), as it is employed in most of NIST post-quantum cryptography (PQC) candidates for KEM. The proposed attack exploits side-channel leakage during execution of a pseudorandom function (PRF) or pseudorandom number generator (PRG) in the re-encryption of KEM decapsulation as a plaintext-checking oracle that tells whether the PKE decryption result is equivalent to the reference plaintext. The generality and practicality of the plaintext-checking oracle allow the proposed attack to attain a full-key recovery of various KEMs when an active attack on the underlying PKE is known. This paper demonstrates that the proposed attack can be applied to most NIST PQC third-round KEM candidates, namely, Kyber, Saber, FrodoKEM, NTRU, NTRU Prime, HQC, BIKE, and SIKE (for BIKE, the proposed attack achieves a partial key recovery). The applicability to Classic McEliece is unclear because there is no known active attack on this cryptosystem. This paper also presents a side-channel distinguisher design based on deep learning (DL) for mounting the proposed attack on practical implementation without the use of a profiling device. The feasibility of the proposed attack is evaluated through experimental attacks on various PRF implementations (a SHAKE software, an AES software, an AES hardware, a bit-sliced masked AES software, and a masked AES hardware based on threshold implementation). Although it is difficult to implement the oracle using the leakage from the TI-based masked hardware, the success of the proposed attack against these implementations (even except for the masked hardware), which include masked software, confirms its practicality.

CPA/CCA2-secure PKE with squared-exponential DFR from low-noise LPN

LPN (learning parity with noise) problem is a good candidate for post-quantum cryptography which enjoys simplicity and suitability for weak-power devices. Döttling et al. (ASIACRYPT 2012) initiated the first secure public key encryption (PKE) under the low-noise LPN assumption. Kiltz et al. (PKC 2014) proposed a simpler and more efficient scheme using double-trapdoor technique from the same assumption. Both schemes abide the decoding failure rate (DFR) 2−Θ(k) (k is the security parameter) and there exists CPA/CCA2-secure PKE with squared-exponential DFR 2−Θ(k2) from constant-noise LPN (Yu and Zhang, CRYPTO 2016). In this work, we give a positive answer with squared-exponential DFR in the low-noise setting.More precisely, we first introduce a variant (VxLPN) of the low-noise Exact LPN (xLPN, proposed by Jain et al. at ASIACRYPT 2012 and used as building block in commitments and zero-knowledge proofs), where the coefficient matrix A follows the uniform distribution over {0,1}q×n (n=Θ(k2),q=Θ(n)), the secret x is sampled from Bμn (Bμ is the Bernoulli distribution with noise rate μ=Θ(1q)), and the noise e follows a column vector distribution uniform over {z∈{0,1}q:|z|=qμ}. A series of reductions show that VxLPN is at least as hard as the standard LPN for the same noise rate μ. We then construct from the VxLPN CPA/CCA2 secure PKE schemes with squared-exponential DFR 2−Θ(k2) which share the common structure extrinsically with Kiltz et al. and Yu-Zhang schemes. The secret key(s) in our schemes are simply sampled from the Bernoulli distribution, and comparatively, the secret key(s) in Yu-Zhang schemes must be chosen from a tailored version of Bernoulli distribution (along with the coefficient matrix A that follows a distribution Dλn×n=Un×λ⋅Uλ×n induced by multiplying two random matrices in the public key, λ=Θ(log2⁡n)) in order to guarantee the correctness of their schemes. Consider the performance on 128-bit security level, our CCA2-secure scheme only holds 117.79 MB public keys, 67.31 MB secret keys and 10.15 KB ciphertexts, and thus is more efficient than the schemes of Döttling et al. and Kiltz et al. ((14.53 GB, 14.48 GB, 14.06 KB) and (161.78 MB, 92.45 MB, 13.60 KB) respectively).

A CCA secure public key encryption scheme based on finite groups of Lie type

A CCA secure public key encryption scheme based on finite groups of Lie type

Receiver Selective Opening CCA Secure Public Key Encryption from Various Assumptions

Receiver Selective Opening CCA Secure Public Key Encryption from Various Assumptions

Two-Round Password-Based Authenticated Key Exchange from Lattices

Password-based authenticated key exchange (PAKE) allows participants sharing low-entropy passwords to agree on cryptographically strong session keys over insecure networks. In this paper, we present two PAKE protocols from lattices in the two-party and three-party settings, respectively, which can resist quantum attacks and achieve mutual authentication. The protocols in this paper achieve two rounds of communication by carefully utilizing the splittable properties of the underlying primitive, a CCA (Chosen-Ciphertext Attack)-secure public key encryption (PKE) scheme with associated nonadaptive approximate smooth projection hash (NA-ASPH) system. Compared with other related protocols, the proposed two-round PAKE protocols have relatively less communication and computation overhead. In particular, the two-round 3PAKE is more practical in large-scale communication systems.

A fast and secure public-key image encryption scheme based on Mordell elliptic curves

Encryption schemes based on elliptic curves (ECs) have shown high resistance against modern cryptanalysis. However, these schemes involve heavy computation for the generation of points over ECs, and therefore they are not suitable for communication systems such as sensor networks and Internet of Things. Thus, we propose a fast and secure public-key image encryption scheme. In this scheme, the sender and receiver agree on a public EC. Then the scheme performs pixel-masking and pixel-scrambling procedures using random numbers and a dynamic substitution box over ECs that are isomorphic to the public EC. For a fixed public EC, we prove that our scheme has a computational complexity that is a polylogarithmic function of the size of the plain text. In other words, the computational complexity of our scheme is independent of the point generation over ECs. We tested the security of our scheme against modern attacks by encrypting all standard images in the USC-SIPI image database. Compared to some state-of-the-art cryptosystems, our scheme is fast and has high security.

New approach to practical leakage-resilient public-key cryptography

AbstractWe present a new approach to construct several leakage-resilient cryptographic primitives, including leakage-resilient public-key encryption (PKE) schemes, authenticated key exchange (AKE) protocols and low-latency key exchange (LLKE) protocols. To this end, we introduce a new primitive called leakage-resilient non-interactive key exchange (LR-NIKE) protocol. We introduce an appropriate security model for LR-NIKE protocols in the bounded memory leakage (BML) settings. We then show a secure construction of the LR-NIKE protocol in the BML setting that achieves an optimal leakage rate, i.e., 1 – o(1). Our construction of LR-NIKE requires a minimal use of a leak-free hardware component. We argue that the use of such a leak-free hardware component seems to be unavoidable in any construction of an LR-NIKE protocol, even in the BML setting. Finally, we show how to construct the aforementioned leakage-resilient primitives from such an LR-NIKE protocol as summarized below. All these primitives also achieve the same (optimal) leakage rate as the underlying LR-NIKE protocol. We show how to construct a leakage-resilient (LR) IND-CCA-2-secure PKE scheme in the BML model generically from a bounded LR-NIKE (BLR-NIKE) protocol. Our construction of LR-IND-CCA-2 secure PKE differs significantly from the state-of-the-art constructions of these primitives, which mainly use hash proof techniques to achieve leakage resilience. Moreover, our transformation preserves the leakage-rate of the underlying BLR-NIKE protocol. We introduce a new leakage model for AKE protocols, in the BML setting, and present a leakage-resilient AKE protocol construction from the LR-NIKE protocol. We introduce the first-ever leakage model for LLKE protocols in the BML setting and the first construction of such a leakage-resilient LLKE from the LR-NIKE protocol.

A New Framework of IND-CCA Secure Public Key Encryption with Keyword Search

AbstractIn the era of cloud computing, public key encryption with keyword search (PEKS) is an extremely useful cryptographic tool for searching on encryption data, whose strongest security notion is indistinguishability encryption against chosen ciphertext attack (ind-cca). Adballa et al. presented a transformation from identity based encryption (IBE) to PEKS in the Theory of Cryptography Conference 2010. This paper proposes a new framework of ind-cca secure PEKS in the standard model. Our main technical tool is a newly introduced notion of smooth projective hash function with key mapping, in which the hash key hk is mapped into another mapping projection key mhp besides the classical projection key hp. Finally, we provide an instantiation of our framework based on symmetric eXternal Diffie–Hellman assumption.

Tightly secure inner product functional encryption: Multi-input and function-hiding constructions

Tightly secure cryptographic schemes have been extensively studied in the fields of chosen-ciphertext secure public-key encryption (CCA-secure PKE), identity-based encryption (IBE), signatures and more. We extend tightly secure cryptography to inner product functional encryption (IPFE) and present the first tightly secure schemes related to IPFE. We first construct a new IPFE schemes that are tightly secure in the multi-user and multi-challenge setting. In other words, the security of our schemes do not degrade even if an adversary obtains many ciphertexts generated by many users. Our schemes are constructible on a pairing-free group and secure under the matrix decisional Diffie-Hellman (MDDH) assumption, which is the generalization of the decisional Diffie-Hellman (DDH) assumption. Applying the known conversions by Lin (CRYPTO 2017) and Abdalla et al. (CRYPTO 2018) to our schemes, we can obtain the first tightly secure function-hiding IPFE schemes and multi-input IPFE (MIPFE) schemes respectively. Our second main contribution is the proposal of a new generic conversion from function-hiding IPFE to function-hiding MIPFE, which was left as an open problem by Abdalla et al. (CRYPTO 2018). We can obtain the first tightly secure function-hiding MIPFE schemes by applying our conversion to the tightly secure function-hiding IPFE schemes described above.

Public-Key Encryption Secure Against Related Randomness Attacks for Improved End-to-End Security of Cloud/Edge Computing

Public-key encryption is often used to protect data security/privacy and secure communication in scenarios of cloud computing and edge computing. Related randomness attacks model (RRA) for public-key encryption was motivated by randomness failures. This paper proposes some methods of constructing secure public-key encryption scheme against related randomness attacks, i.e. RRA-CPA secure public-key encryption scheme with efficient decryption algorithm and short ciphertexts size obtained from one-way function with weak RKA-security and indistinguishability obfuscation, RRA-CPA secure public-key encryption scheme against arbitrarily function from any publicly deniable encryption and RRA-CCA secure public-key encryption scheme against arbitrarily function from standard IND-CCA public-key encryption scheme with a hardcore function for arbitrarily correlated inputs.

CCA Secure Public Key Encryption against After-the-Fact Leakage without NIZK Proofs

In leakage resilient cryptography, there is a seemingly inherent restraint on the ability of the adversary that it cannot get access to the leakage oracle after the challenge. Recently, a series of works made a breakthrough to consider a postchallenge leakage. They presented achievable public key encryption (PKE) schemes which are semantically secure against after-the-fact leakage in the split-state model. This model puts a more acceptable constraint on adversary’s ability that the adversary cannot query the leakage of secret states as a whole but the functions of several parts separately instead of prechallenge query only. To obtain security against chosen ciphertext attack (CCA) for PKE schemes against after-the-fact leakage attack (AFL), existing works followed the paradigm of “double encryption” which needs noninteractive zero knowledge (NIZK) proofs in the encryption algorithm. We present an alternative way to achieve AFL-CCA security via lossy trapdoor functions (LTFs) without NIZK proofs. First, we formalize the definition of LTFs secure against AFL (AFLR-LTFs) and all-but-one variants (ABO). Then, we show how to realize this primitive in the split-state model. This primitive can be used to construct AFLR-CCA secure PKE scheme in the same way as the method of “CCA from LTFs” in traditional sense.

Simulation-based receiver selective opening CCA secure PKE from standard computational assumptions

In the situation where there are one sender and multiple receivers and the sender transmits ciphertexts of correlated plaintexts, a receiver selective opening (RSO) attack for a public key encryption (PKE) scheme considers adversaries that can corrupt some of the receivers and get their secret keys and plaintexts. Security against RSO attacks for a PKE scheme ensures confidentiality of ciphertexts of uncorrupted receivers. Simulation-based RSO security against chosen ciphertext attacks (SIM-RSO-CCA) is the strongest security notion in all RSO attack scenarios. Jia, Lu, and Li (2016) [19] proposed the first SIM-RSO-CCA secure PKE scheme. However, their scheme used indistinguishability obfuscation, which is not known to be constructed from any standard computational assumption. In this paper, we give two contributions for constructing SIM-RSO-CCA secure PKE from standard computational assumptions. Firstly, we propose a generic construction of SIM-RSO-CCA secure PKE using an IND-CPA secure PKE scheme and a non-interactive zero-knowledge proof system satisfying one-time simulation soundness. Secondly, we propose an efficient and concrete construction of SIM-RSO-CCA secure PKE based on the decisional Diffie-Hellman (DDH) assumption. Moreover, we give a method for efficiently expanding the plaintext space of the DDH-based construction. By applying this method to the construction, we obtain the first DDH-based SIM-RSO-CCA secure PKE scheme supporting a super-polynomially large plaintext space with compact ciphertexts.