Post-Quantum Secure Inner Product Functional Encryption Using Multivariate Public Key Cryptography

Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE) family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose a new variant of the HFE scheme by considering the special equation x2=x defined over the finite field F3 when x=0,1. We observe that the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. It is shown that the proposed public key encryption scheme is secure against known attacks including the MinRank attack, the algebraic attacks, and the linearization equations attacks. The proposal gains some advantages over the original HFE scheme with respect to the encryption speed and public key size.

Authentication of public keys in asymmetric cryptography is an important objective to fulfil. Identity-based schemes are an efficient solution for this scenario. There are various identity-based schemes that are based on either factoring problem or DLP problem, but these problems can be solved in polynomial time using quantum computers. Multivariate cryptography is one of the main alternatives for the construction of post-quantum digital signature schemes. Digital signature construction needs modest computations in multivariate public key cryptography, so these schemes are considered quite efficient. In this paper, we present a new identity-based signature scheme in which the signature size and user key size are relatively small. The design of our proposed signature scheme is based on MQDSS construction.KeywordsMultivariate public key cryptographyMQ problemIdentity-based signature scheme

Multivariate Public Key Cryptography(MPKC) has become one of a few options for security in the quantum model of computing. Though a few multivariate systems have resisted years of effort from the cryptanalytic community, many such systems have fallen to a surprisingly small pool of techniques. There have been several recent attempts at formalizing more robust security arguments in this venue with varying degrees of applicability. We present an extension of one such recent measure of security against a differential adversary which has the benefit of being immediately applicable in a general setting on unmodified multivariate schemes.

Multivariate public key cryptography is one of the main candidates for post‐quantum cryptography. Rainbow, an improved (multi‐layer) version of unbalanced oil and vinegar (UOV), is one of the most famous multivariate signature schemes that is a promising candidate for NIST standardisation. At INDOCRYPT 2017, Beullens and Preneel introduced a new variant LUOV of UOV. Their idea is to generate a UOV scheme over the binary field and then lift it into a bigger field and hence dramatically reduce the public key size. In this study, the authors first theoretically deduce the choice for the subfield L (which is different from ) which results in smaller signature sizes (up to 40%). Moreover, they extend the idea to Rainbow and theoretically yield the optimal choice for the subfield L over which a Rainbow is generated before being lifted to K . As a result, they can reduce the public key size of the obtained Rainbow scheme up to at least 36%.

Pairing-based cryptography (PBC), a variant of elliptic curve cryptography (ECC), uses bilinear maps between elliptic curves and finite fields to enable several novel applications beyond traditional key exchange and signatures [1]. Fig. 1 shows two such applications - (a) signature aggregation, where arbitrarily large number of signatures are aggregated into one to resolve communication bottleneck in mesh networks such as blockchain [9], and (b) functional encryption, which allows computation on encrypted data with a function embedded in the decryption key [7]. In particular, pairing-based function-hiding inner product functional encryption [10] can be used for privacy-preserving data classification, thus enabling a new paradigm in the field of secure computation.

Practical reusable garbled circuits with parallel updates

Access control schemes in predicate encryption can effectively reduce the risk of information leakage in the inner product function encryption (IPFE). However, when we try to transition from identity-based IPFE to attribute-based IPFE, the fine-grained nature of attributes induces some unprecedented access control problems. These problems not only lead to incorrect inner product computation results from attribute-based IPFE but also inevitable passive information leakage induced by large attribute set secret key. At the same time, since the above problems are not common in identity-based IPFE and traditional ABEs, they cannot be properly addressed by existing schemes. To address the above problems, we introduce a new scheme - Ciphertext Policy Based Inner Product Function Encryption (CP-IPFE). In this scheme, we propose to use a "label vector" to label the attributes of n-dimensional vectors and encode them onto the relevant information, so as to ensure that the attribute-based IPFE will not output incorrect inner-product computation results; establishing a leaf node set-based "reverse access control policy" to realize reverse access control on "risky ciphertext", ensures that "risky ciphertext" will not be leaked encrypted-information by the secret key of large attribute sets. In addition, CP-IPFE also has the characteristics of traditional attribute encryption and supports more fine-grained access control. Finally, we prove the CPA security of the CP-IPFE in the GGM model and show a detailed application of the CP-IPFE on a general-purpose platform.

Multi-Client Attribute-Based Unbounded Inner Product Functional Encryption, and More

Function-Hiding Zero Predicate Inner Product Functional Encryption from Pairings

There is no quantum election protocol that can fulfil the eight requirements of an electronic election protocol, i.e., completeness, robustness, privacy, legality, unreusability, fairness, verifiability, and receipt-freeness. To address this issue, we employ the general construction of quantum digital signature and quantum public key encryption, in conjunction with classic public key encryption, to develop and instantiate a general construction of quantum election protocol. The proposed protocol exhibits the following advantages: (i) no pre-shared key between any two participants is required, and no trusted third party or anonymous channels are required. The protocol is suitable for large-scale elections with numerous candidates and voters and accommodates the situation in which multiple voters vote simultaneously. (ii) It is the first protocol that dismantles the contradiction between verifiability and receipt-freeness in a quantum election protocol. It satisfies all eight requirements stated earlier under the physical assumptions that there exists a one-way untappable channel from the administrator to the voter and that there is no collusion between any of the three parties in the protocol. Compared with current election protocols with verifiability and receipt-freeness, this protocol relies upon fewer physical assumptions. (iii) This construction is flexible and can be instantiated into an election scheme having post-quantum security by applying cryptographic algorithms conveying post-quantum security. Moreover, utilizing quantum digital signature and public key encryption yields a good result: the transmitted ballots are in quantum states, so owing to the no-cloning theorem, ballot privacy is less likely to be compromised, even if private keys of the signature and public key encryption are leaked after the election. However, in existing election protocols employing classic digital signatures and public key encryption, ballot privacy can be easily violated if attackers obtain private keys. Thus, our construction enhances privacy.

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.

Introduction Digital identity infrastructures used in electronic passports, national eID schemes, and federated authentication systems rely predominantly on centralised registries and classical public key cryptography. These architectures enable large-scale identity correlation, mass data aggregation, and single points of compromise, while remaining vulnerable to quantum attacks against RSA and elliptic-curve cryptography. There is no deployed identity framework that simultaneously provides post-quantum security, cryptographic privacy guarantees, and decentralised trust. Methods This study proposes a quantum-proof digital passport architecture combining lattice-based post-quantum cryptography, decentralised blockchain identifiers, and transformer-based decentralised artificial intelligence. The framework employs NIST-aligned post-quantum key encapsulation and digital signatures, zero-knowledge proofs for selective disclosure of identity attributes, and homomorphic encryption for encrypted identity verification. Blockchain oracles and decentralised identifiers enforce credential integrity and auditability without reliance on central identity providers. Transformer attention mechanisms support adaptive identity validation while preventing persistent identity profiling. Results Architectural analysis shows that the proposed system prevents quantum-enabled credential forgery, retrospective decryption, and cross-service identity linkability. Zero-knowledge verification removes plaintext exposure of personal data, and decentralised credential control eliminates central compromise vectors. The design remains interoperable with existing passport and eID infrastructures. Discussion The results demonstrate that secure post-quantum digital identity requires the combined application of quantum-resistant cryptography, decentralised governance, and cryptographic privacy enforcement.

The post-quantum security of cryptographic schemes assumes that the quantum adversary only receives the classical result of computations with the secret key. Further, it is unknown whether the post-quantum secure schemes still remain secure if the adversary can obtain a superposition state of the results. In this paper, we formalize one class of public-key encryption schemes named oracle-masked schemes. Then we define the plaintext extraction procedure for those schemes and this procedure simulates the quantum-accessible decryption oracle with a certain loss. The construction of the plaintext extraction procedure does not need to take the secret key as input. Based on this property, we prove the IND-qCCA security of the Fujisaki-Okamoto (FO) transformation in the quantum random oracle model (QROM) and our security proof is tighter than the proof given by Zhandry (Crypto 2019). We also give the first IND-qCCA security proof of the REACT transformation in the QROM. Furthermore, our formalization can be applied to prove the IND-qCCA security of key encapsulation mechanisms with explicit rejection. As an example, we present the IND-qCCA security proof of $$\textsf {T}_{\textsf {CH}}$$ transformation, proposed by Huguenin-Dumittan and Vaudenay (Eurocrypt 2022), in the QROM.

The invention of public-key cryptography was of central importance to the field of cryptography and provided answers to many key management problems for large scale networks. For all its benefits, however, public-key cryptography did not provide a comprehensive solution to the key management problem. Indeed, the possibilities brought forth by public-key cryptography heightened the need for sophisticated key management systems to answer questions such as the following:"How can I easily encrypt a file once for a number of different people using public-key cryptography?""If I lose my keys, how can I decrypt all of my files that were encrypted with those keys?""How do I know that I really have Alice’s public key and not the public key of someone pretending to be Alice?""How can I know that a public key is still trustworthy?"The paper discusses public key cryptography and its use in applications such as Key Agreement, Data Encryption and Digital Signature. The paper discusses some public key algorithms such as DH, RSA, and DSA and also gives working explanations of these algorithms.KeywordsShared SecretCertificate AuthorityCipher TextHash CodeDigital CertificateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Code-based public key encryption (PKE) is a popular choice to achieve post-quantum security, partly due to its capability to achieve fast encryption/decryption. However, code-based PKE has larger ciphertext and public key sizes in comparison to conventional PKE schemes (e.g., those based on RSA). In 2018, Lau and Tan proposed a new rank metric code-based PKE scheme, which has smaller public key and ciphertext sizes compared to other code-based PKE schemes. They also proved that their scheme achieves IND-CPA security, assuming the intractability of the decisional rank syndrome decoding problem. It is known that IND-CCA2 security is the strongest and most popular security assurance for PKE schemes. Therefore, in this paper, we obtain a new code-based PKE scheme from Lau and Tan’s scheme, in order to inherit the underlying small public key and ciphertext sizes. However, our new scheme is shown to achieve IND-CCA2 security, instead of the weaker IND-CPA security. Specifically, the respective public key size and ciphertext size in our new scheme are 15.06 KB and 1.37 KB under 141-bit security level, and 16.76 KB and 1.76 KB under 154-bit security level. We then present a use case for the proposed scheme, that is for secure cloud storage.