Quantum key distribution (QKD) allows Alice and Bob to share a secret key over an insecure channel with proven information-theoretic security against an adversary whose strategy is bounded only by the laws of physics. Composability-based security proofs of QKD ensure that using the established key with a one-time-pad encryption scheme provides information theoretic secrecy for the message. In this paper, we consider the problem of using the QKD established key with a secure symmetric key-based encryption algorithm and use an approach based on hybrid encryption to provide a proof of security for the composition. Hybrid encryption was first proposed as a public key cryptographic algorithm with proven security for messages of unrestricted length. We use an extension of this framework to correlated randomness setting (Sharifian et al. in ISIT 2021) to propose a quantum-enabled Key Encapsulation Mechanism (qKEM) and quantum-enabled hybrid encryption (qHE), and prove a composition theorem for the security of the qHE. We construct a qKEM with proven security using an existing QKD (Portmann et al. in Rev. of Mod. Physics 2022). Using this qKEM with a secure Data Encapsulation Mechanism (DEM), that can be constructed using a one-time symmetric key encryption scheme, results in an efficient encryption system for unrestricted length messages with proved security against an adversary with access to efficient computations on a quantum computer (i.e. post-quantum secure encryption without using any computational assumptions.)

In the context of digital signatures, the proxy signature holds a significant role of enabling an original signer to delegate its signing ability to another party (ie, proxy signer). It has significant practical applications. Particularly it is useful in distributed systems, where delegation of authentication rights is quite common. For example, key sharing protocol, grid computing, and mobile communications. Currently, a large portion of existing proxy signature schemes are based on the hardness of problems like integer factoring, discrete logarithms, and/or elliptic curve discrete logarithms. However, with the rising of quantum computers, the problem of prime factorization and discrete logarithm will be solvable in polynomial-time, due to Shor’s algorithm, which dilutes the security features of existing ElGamal, RSA, ECC, and the proxy signature schemes based on these problems. As a consequence, construction of secure and efficient post-quantum proxy signature becomes necessary. In this work, we develop a post-quantum proxy signature scheme Mult-proxy, relying on multivariate public key cryptography (MPKC), which is one of the most promising candidates of post-quantum cryptography. We employ a 5-pass identification protocol to design our proxy signature scheme. Our work attains the usual proxy criterion and a one-more-unforgeability criterion under the hardness of the Multivariate Quadratic polynomial (MQ) problem. It produces optimal size proxy signatures and optimal size proxy shares in the field of MPKC.

Signcryption is an important cryptographic scheme which is used for both confidentiality and unforgeability. It has many interesting practical applications. Enormous growth of quantum computers makes a warning to the existing classical signcryption schemes due to Shor’s algorithm. As a result, designing signcryption schemes, which can withstand quantum attack, is an interesting direction of research. Isogeny based cryptography (IBC) is an ideal post-quantum candidate that can be employed to build a quantum computer immune signcryption scheme. Less communication cost and a smaller public key is the main advantage of IBC compared to other post quantum cryptographic branches. In this paper, we design the first signcryption employing IBC. Our scheme is relying on three hard problems: Commutative Supersingular Isogeny Decisional Diffie–Hellman (𝖢𝖲𝖲𝖨𝖣𝖣𝖧), Group Action Inverse Problem (𝖦𝖠𝖨𝖯) and Commutative Supersingular Isogeny Knowledge of Exponent (𝖢𝖲𝖲𝖨𝖪𝖮𝖤). It achieves 𝖨𝖭𝖣 − 𝖢𝖢𝖠 and 𝖤𝖴𝖥 − 𝖢𝖬𝖠 security. Ciphertext size in this scheme turns out to be 16622.05 bytes for 𝑝128 and 12757.45 bytes for 𝑝256 to achieve NIST-1 level of security.

Functional encryption (FE) is an exciting new public key paradigm that provides solutions to most of the security challenges of cloud computing in a non-interactive manner. In the context of FE, inner product functional encryption (IPFE) is a widely useful cryptographic primitive. It enables a user with secret key usky associated to a vector y to retrieve only <_x0002_x, y>_x0003_ from a ciphertext encrypting a vector x, not beyond that. In the last few decades, several constructions of IPFE have been designed based on traditional classical cryptosystems, which are vulnerable to large enough quantum computers. However, there are few quantum computer resistants i.e., post-quantum IPFE. Multivariate cryptography is one of the promising candidates of post-quantum cryptography. In this paper, we propose for the first-time multivariate cryptography-based IPFE. Our work achieves non-adaptive simulationbased security under the hardness of the MQ problem.

In many realistic scenarios, participants wish to perform some secret set operations such as intersection, union, cardinality of intersection, etc. on their private data sets. Private Set Intersection (PSI) plays a major role in addressing such problems. PSI is one of the widely used secure multi-party computation technique that allows the participants to securely compute the intersection of their private input sets and nothing beyond that. It is generally executed between two parties. When the number of entities is more than two, it is known as multi-party PSI (MPSI). Today, the security of all the existing MPSI protocols are based on number theoretic assumptions. However, these will become insecure once large enough quantum computers are built. As a consequence, designing of quantum computer resistant MPSI becomes an interesting direction of research work. This paper addresses the issue by presenting the first post-quantum MPSI protocol in the so-called star network topology, using lattice-based public key encryption scheme. We utilize space-efficient probabilistic data structure (Bloom filter) as building blocks of our design. It attains security in standard model (without random oracles) under the decisional learning with errors (DLWE) assumption.

In this paper, we develop an identity-based encryption (IBE) scheme, namely , that achieves post-quantum security. Our scheme relies on multivariate public key cryptography, which is one of the most promising candidates of post-quantum cryptography. The proposed IBE is efficient as it incurs low communication and computation costs. Our design is proven to be IND-ID-CCA (believed to be the right security model for IBE) secure in the random oracle model under the hardness of the MQ problem. Moreover, the proposed is resistant to the collusion attack. In particular, our scheme is the first to achieve IND-ID-CCA in the context of multivariate identity-based encryption systems.

In the context of privacy preserving protocols, Private Set Intersection (PSI) plays an important role due to their wide applications in recent research community. In general, PSI involves two participants to securely determine the intersection of their respective input sets, not beyond that. These days, in the context of PSI, it is become a common practice to store datasets in the cloud and delegate PSI computation to the cloud on outsourced datasets, similar to secure cloud computing. We call this outsourced PSI as OPSI. In this paper, we design a new construction of OPSI in malicious setting under the Decisional Diffie-Hellman (DDH) assumption without using any random oracle. In particular, our OPSI is the first that incurs linear complexity in malicious environment with not-interactive setup. Further, we employ a random permutation to extend our OPSI to its cardinality variant OPSI-CA. In this case, all the properties remain unchanged except that the adversarial model is semi-honest instead of malicious.

In the context of secure multi-party computation, private set intersection (PSI) is an important cryptographic primitive for performing joint operations on datasets in a privacy preserving manner. In particular, it allows the participants to privately determine the intersection of their private datasets. Most of the existing PSI protocols are based on traditional classical cryptosystems, which are proven to be vulnerable in quantum domain. This makes the requirement of quantum computer resistant PSI. Applying quantum cryptography in the design of PSI is an ideal approach to address these issues. In this paper, we present a quantum PSI (QPSI) relying on the basic quantum mechanics principles, which are resistant against well-known quantum attacks. Quantum resources in our QPSI are considered as single photons and we require to perform only simple single-particle projective measurements. These features make our QPSI more feasible to implement with the present technology, compared to the existing QPSI protocols, which adopt multi-particle entangled states and complicated quantum operators. On a more positive note, in our QPSI, only one time quantum communication and quantum computation allows execution of set intersection functionality multiple number of times, provided the client’s set size remains same, while the existing QPSI protocols do not achieve this property.