Discrete Logarithm Research Articles

Performance comparison of quantum-safe multivariate polynomial public key encapsulation algorithm

A novel quantum-safe key encapsulation algorithm, called Multivariate Polynomial Public Key (MPPK), was recently proposed by Kuang, Perepechaenko, and Barbeau. Security of the MPPK key encapsulation mechanism does not rely on the prime factorization or discrete logarithm problems. It builds upon the NP-completeness of the modular Diophantine equation problem, for which there are no known efficient classical or quantum algorithms. Hence, it is resistant to known quantum computing attacks. The private key of MPPK comprises a pair of multivariate polynomials. In a companion paper, we analyzed the performance of MPPK when these polynomials are quadratic. The analysis highlighted the MPPK high decapsulation time. We found that, while maintaining the security strength, the polynomials can be linear. Considerable performance gains are obtained for the decapsulation process. In this article, we benchmark the linear case and compare the results with the previous quadratic case.

Improving efficiency and security of Camenisch–Lysyanskaya signatures for anonymous credential systems

Camenisch–Lysyanskaya signature scheme with randomizability, namely CL signatures, at CRYPTO’04 has been well adopted for many privacy-preserving constructions, especially in the context of anonymous credential systems. Unfortunately, CL signatures suffer from linear size drawbacks. The signature size grows linearly based on the signing messages, which decreases the interest in practice, as each user may have multiple attributes (messages). Its standard EUF-CMA security was first proven under an interactive assumption. While the interactive assumption is not desirable in cryptography, Fuchsbauer et al. revisited its security at CRYPTO’18 by proving the scheme under the discrete logarithm (Dlog) assumption in the algebraic group model (AGM) that idealizes the adversary’s computation to be algebraic, yet the reduction loss is non-tight. In this work, we propose a new variant of CL signatures, namely CL+ signatures, that improves efficiency and security. The proposed CL+ signatures possess randomizability without the linear size drawback, such that signature size is a constant of three group elements. Besides, we prove the security of CL+ signatures can be tightly reduced to the DLog problem in AGM with only a loss factor of 3. Lastly, we show how CL+ signatures can also be instantiated to anonymous credential systems.

An Explicit High-Moment Forking Lemma and its Applications to the Concrete Security of Multi-Signatures

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized model. The key difference between our lemma and previous ones is that instead of focusing on the tradeoff between the worst-case or expected running time of the resulting forking algorithm and its success probability, we focus on the tradeoff between higher moments of its running time and its success probability. Equipped with our lemma, we then establish concrete security bounds for the BN and BLS multi-signature schemes that are significantly tighter than the concrete security bounds established by Bellare and Neven (CCS '06) and Boneh, Drijvers and Neven (ASIACRYPT '18), respectively. Our analysis does not limit adversaries to any idealized algebraic model, such as the algebraic group model in which all algorithms are assumed to provide an algebraic justification for each group element they produce. Our bounds are derived in the random-oracle model based on the standard-model second-moment hardness of the discrete logarithm problem (for the BN scheme) and the computational co-Diffie-Hellman problem (for the BLS scheme). Such second-moment assumptions, asking that the success probability of any algorithm in solving the underlying computational problems is dominated by the second moment of the algorithm's running time, are particularly plausible in any group where no better-than-generic algorithms are currently known.

Optimizing and Implementing Fischlin's Transform for UC-Secure Zero Knowledge

Fischlin's transform (CRYPTO 2005) is an alternative to the Fiat-Shamir transform that enables straight-line extraction when proving knowledge. In this work we focus on the problem of using the Fischlin transform to construct UC-secure zero-knowledge from Sigma protocols, since UC security – that guarantees security under general concurrent composition – requires straight-line (non-rewinding) simulators. We provide a slightly simplified transform that is much easier to understand, and present algorithmic and implementation optimizations that significantly improve the running time. It appears that the main obstacles to the use of Fischlin in practice is its computational cost and implementation complexity (with multiple parameters that need to be chosen). We provide clear guidelines and a simple methodology for choosing parameters, and show that with our optimizations the running-time is far lower than expected. For just one example, on a 2023 MacBook, the cost of proving the knowledge of discrete log with Fischlin is only 0.41ms (on a single core). This is 15 times slower than plain Fiat-Shamir on the same machine, which is a significant multiple but objectively not significant in many applications. We also extend the transform so that it can be applied to batch proofs, and show how this can be much more efficient than individually proving each statement. We hope that this paper will both encourage and help practitioners implement the Fischlin transform where relevant.

Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem

In this paper, we will solve an important form of hidden discrete logarithm problem (HDLP) and a generalized form of HDLP (GHDLP) over non-commutative associative algebras (FNAAs). We will reduce them to discrete logarithm problem (DLP) in a finite field through analyzing the eigenvalues of the representation matrix. Through the analysis of computational complexity, we will show that HDLP and GHDLP are not good improvements of DLP. With all the instruments in hand, we will break a series of corresponding schemes. Thus, we can conclude that all ideas of constructing cryptographic schemes based on the two solved problems are of no practical significance.

FlashSwift: A Configurable and More Efficient Range Proof With Transparent Setup

Bit-decomposition-based zero-knowledge range proofs in the discrete logarithm (DLOG) setting with a transparent setup, e.g., Bulletproof (IEEE S&P 18), Flashproof (ASIACRYPT 22), and SwiftRange (IEEE S&P 24), have garnered widespread popularity across various privacy-enhancing applications. These proofs aim to prove that a committed value falls within the non-negative range [0, 2^N-1] without revealing it, where N represents the bit length of the range. Despite their prevalence, the current implementations still suffer from suboptimal performance. Some exhibit reduced communication costs at the expense of increased computational costs while others experience the opposite. Presently, users are compelled to utilize these proofs in scenarios demanding stringent requirements for both communication and computation efficiency. In this paper, we introduce, FlashSwift, a stronger DLOG-based logarithmic-sized alternative. It stands out for its greater shortness and significantly enhanced computational efficiency compared with the cutting-edge logarithmic-sized ones for the most common ranges where N is no more than 64. It is developed by integrating the techniques from Flashproof and SwiftRange without using a trusted setup. The substantial efficiency gains stem from our dedicated efforts in overcoming the inherent incompatibility barrier between the two techniques. Specifically, when N=64, our proof achieves the same size as Bulletproof and exhibits 1.1 times communication efficiency of SwiftRange. More importantly, compared with the two, it achieves 2.3 times and 1.65 times proving efficiency, and 3.2 times and 1.7 times verification efficiency, respectively. At the time of writing, our proof also creates two new records of the smallest proof sizes, 289 bytes and 417 bytes, for 8-bit and 16-bit ranges among all the bit-decomposition-based ones without requiring trusted setups. Moreover, to the best of our knowledge, it is the first configurable range proof that is adaptable to various scenarios with different specifications, where the configurability allows to trade off communication efficiency for computational efficiency. In addition, we offer a bonus feature: FlashSwift supports the aggregation of multiple single proofs for efficiency improvement. Finally, we provide comprehensive performance benchmarks against the state-of-the-art ones to demonstrate its practicality.

Revealing the Correlation Between Lyapunov Exponent and Modulus of an n-Dimensional Nondegenerate Hyperchaotic Map

For their good randomness and long iteration periods, chaotic maps have been widely used in cryptography. Recently, we have revealed the correlation between Lyapunov exponent and sequence randomness of multidimensional chaotic maps based on modular operation. Since the modular operation can realize the boundedness of chaotic state points, it is important to further reveal the deterministic correlation between Lyapunov exponent and modulus. First, we constructed an [Formula: see text]-dimensional nondegenerate hyperchaotic map model with the desired Lyapunov exponents. Then, we gave the existence and uniqueness proof of quadrature rectangle decomposition theorem and revealed the correlation between Lyapunov exponent and modulus. The novelty lies in that (1) in order to realize the irreversibility of the iterative processes of chaotic maps, we constructed a chaotic map based on modular exponentiation, and its inverse function is the discrete logarithm problem; and (2) we reveal for the first time the correlation between Lyapunov exponent and modulus, and give the lower bound of the modulus of the nondegenerate chaotic map. In addition, to verify the effectiveness of the scheme, we constructed four-dimensional and five-dimensional chaotic maps, respectively, and analyzed their dynamical behaviors, and the results revealed that there exist linear or nonlinear correlation between Lyapunov exponent and modulus.

Atomic cross-chain swap based on private key exchange

Atomic Cross-Chain Swap (ACCS) is one important topic in cryptocurrency, where users can securely and trustlessly exchange assets between two different blockchains. However, most known ACCS schemes assume specific scripting functionalities of the underlying blockchains, such as Hash Time Locked Contracts (HTLC). In addition, these schemes are typically only applicable to certain digital signature schemes, like Schnorr or Elliptic Curve Digital Signature Algorithm (ECDSA) signatures. In this paper, we propose a generic ACCS scheme, independent from the underlying blockchains. To the best of our knowledge, this is the first solution of this kind. Our results are as follows. First, we define a formal system model of ACCS. Next, we present a generic ACCS scheme meets our model. This scheme admits atomicity in cross-chain swaps without the need for a Trusted Third Party (TTP) and protects users’ privacy. Finally, by using the Non-Interactive Zero-Knowledge (NIZK) proof protocol as a tool, we instantiate our generic scheme for Elliptic Curve Discrete Logarithm Problem-based (ECDLP-based) signatures. In addition, we implement our scheme, and the experimental results show that our protocol outperforms the existing ACCS schemes, such as the HTLC-based schemes.

Base of exponent representation matters -- more efficient reduction of discrete logarithm problem and elliptic curve discrete logarithm problem to the QUBO problem

This paper presents further improvements in the transformation of the Discrete Logarithm Problem (DLP) and Elliptic Curve Discrete Logarithm Problem (ECDLP) over prime fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem. This is significant from a cryptanalysis standpoint, as QUBO problems may be solved using quantum annealers, and the fewer variables the resulting QUBO problem has, the less time is expected to obtain a solution.The main idea presented in the paper is allowing the representation of the exponent in different bases than the typically used base 2 (binary representation). It is shown that in such cases, the reduction of the discrete logarithm problem over the prime field \(\mathbb{F}_p\) to the QUBO problem may be obtained using approximately \(1.89n^2\) logical variables for \(n\) being the bitlength of prime \(p\), instead of the \(2n^2\) which was previously the best-known reduction method. The paper provides a practical example using the given method to solve the discrete logarithm problem over the prime field \(\mathbb{F}_{47}\). Similarly, for the elliptic curve discrete logarithm problem over the prime field \(\mathbb{F}_p\), allowing the representation of the exponent in different bases than typically used base two results in a lower number of required logical variables for \(n\) being the bitlength of prime \(p\), from \(3n^3\) to \(\frac{6n^3}{\log_{2}\left(\frac{3}{4}n\right)}\) logical variables, in the case of Edwards curves.

Efficient Authentication Steps for Vehicle Transmission in Ad-Hoc Networks

Vehicular ad-hoc networks (VANETs) are underactive development, thanks in part to recent advances in wireless communication and networking technologies. The most fundamental part of VANET is to enable message authentications between vehicles and roadside units. Message authentication using proxy vehicles has been proposed to reduce the computational overhead of roadside units significantly. In this message authentication scheme, a proxy vehicle that verifies multiple messages at the same time improves roadside units’ efficiency. In this paper first, we show that the only proxy-based authentication scheme (PBAS) presented for this goal by Liu et al. cannot guarantee message authenticity and also it is not resistant to impersonation and modification attacks and false acceptance of batched invalid signatures. Next, we propose a new identity-based message authentication scheme using proxy vehicles (ID-MAP). Then guarantee that it can satisfy the message authentication requirements, existential unforgeability of underlying signatures against adaptability chosen message, and identity attack is proved under the Elliptic Curve discrete logarithm problem (ECDLP) in the random oracle model. It should be highlighted that ID MAP not only is more efficient than PBAS since it is pairing-free and identity based and also it does not use map-to-point hash functions, also, it satisfies the security and privacy requirements of VANETs. Furthermore, analysis shows that the required time to verify 3000 messages in ID-MAP is reduced by 76% compared to that PBAS.

Constrained Device Performance Benchmarking with the Implementation of Post-Quantum Cryptography

Advances in quantum computers may pose a significant threat to existing public-key encryption methods, which are crucial to the current infrastructure of cyber security. Both RSA and ECDSA, the two most widely used security algorithms today, may be (in principle) solved by the Shor algorithm in polynomial time due to its ability to efficiently solve the discrete logarithm problem, potentially making present infrastructures insecure against a quantum attack. The National Institute of Standards and Technology (NIST) reacted with the post-quantum cryptography (PQC) standardization process to develop and optimize a series of post-quantum algorithms (PQAs) based on difficult mathematical problems that are not susceptible to being solved by Shor’s algorithm. Whilst high-powered computers can run these PQAs efficiently, further work is needed to investigate and benchmark the performance of these algorithms on lower-powered (constrained) devices and the ease with which they may be integrated into existing protocols such as TLS. This paper provides quantitative benchmark and handshake performance data for the most recently selected PQAs from NIST, tested on a Raspberry Pi 4 device to simulate today’s IoT (Internet of Things) devices, and provides quantitative comparisons with previous benchmarking data on a range of constrained systems. CRYSTALS-Kyber and CRYSTALS-Dilithium are shown to be the most efficient PQAs in the key encapsulation and signature algorithms, respectively, with Falcon providing the optimal TLS handshake size.

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

Diffie-Hellman (DH) is the reason for the existence of a solution to the key distribution problem, where two parties can mutually set up a shared secret key over an insecure channel without any previous communication. In this study, a novel key exchange protocol based on the difficulty of the Discrete Logarithm Problem with Factor Problem (DLPFP) utilizing matrices in non-commutative semigroup over semiring is proposed. The security and complexity analyses of the protocol are discussed. Also, an ElGamal cryptosystem based on a group of invertible matrices and DLPFP over a semiring to encrypt the Sensitive Health Information (SHI) in healthcare systems is suggested.

Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup G⋊End(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G\\rtimes {{\\,\ extrm{End}\\,}}(G)$$\\end{document} for a finite semigroup G. Given g∈G,σ∈End(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g\\in G, \\sigma \\in {{\\,\ extrm{End}\\,}}(G)$$\\end{document}, and h=∏i=0t-1σi(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h=\\prod _{i=0}^{t-1}\\sigma ^i(g)$$\\end{document} for some integer t, the SDLP(G,σ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G,\\sigma )$$\\end{document}, for g and h, asks to determine t. As Shor’s algorithm crucially depends on commutativity, it is believed not to be applicable to the SDLP. For generic semigroups, the best known algorithm for the SDLP is based on Kuperberg’s subexponential time quantum algorithm. Still, the problem plays a central role in the security of certain proposed cryptosystems in the family of semidirect product key exchange. This includes a recently proposed signature protocol called SPDH-Sign. In this paper, we show that the SDLP is even easier in some important special cases. Specifically, for a finite group G, we describe quantum algorithms for the SDLP in G⋊Aut(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G\\rtimes {\ extrm{Aut}}(G)$$\\end{document} for the following two classes of instances: the first one is when G is solvable and the second is when G is a matrix group and a power of σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} with a polynomially small exponent is an inner automorphism of G. We further extend the results to groups composed of factors from these classes. A consequence is that SPDH-Sign and similar cryptosystems whose security assumption is based on the presumed hardness of the SDLP in the cases described above are insecure against quantum attacks. The quantum ingredients we rely on are not new: these are Shor’s factoring and discrete logarithm algorithms and well-known generalizations.

Root extraction in finite Abelian groups

We formulate the Root Extraction problem in finite Abelian p-groups and then extend it to generic finite Abelian groups. We provide algorithms to solve them. We also give the bounds on the number of group operations required for these algorithms. We observe that once a basis is computed and the discrete logarithm relative to the basis is solved, root extraction takes relatively fewer “bookkeeping” steps. Thus, we conclude that root extraction in finite Abelian groups is no harder than solving discrete logarithms and computing basis.

Efficient attribute-based strong designated verifier signature scheme based on elliptic curve cryptography.

In an attribute-based strong designated verifier signature, a signer who satisfies the access structure signs the message and assigns it to a verifier who satisfies the access structure to verify it, which enables fine-grained access control for signers and verifiers. Such signatures are used in scenarios where the identity of the signer needs to be protected, or where the public verifiability of the signature is avoided and only the designated recipient can verify the validity of the signature. To address the problem that the overall overhead of the traditional attribute-based strong designated verifier signature scheme is relatively large, an efficient attribute-based strong designated verifier signature scheme based on elliptic curve cryptography is proposed, as well as a security analysis of the new scheme given in the standard model under the difficulty of the elliptic curve discrete logarithm problem (ECDLP). On the one hand, the proposed scheme is based on elliptic curve cryptography and uses scalar multiplication on elliptic curves, which is computationally lighter, instead of bilinear pairing, which has a higher computational overhead in traditional attribute-based signature schemes. This reduces the computational overhead of signing and verification in the system, improves the efficiency of the system, and makes the scheme more suitable for resource-constrained cloud end-user scenarios. On the other hand, the proposed scheme uses LSSS (Linear Secret Sharing Schemes) access structure with stronger access policy expression, which is more efficient than the "And" gate or access tree access structure, making the computational efficiency of the proposed scheme meet the needs of resource-constrained cloud end-users.

Twisted Hessian curve over a local ring

In this paper, we study the twisted Hessian curve denoted $H^{n}_{a,d}$ over the ring $\mathbb{F}_{q} [X] / (X^{n})$, where $\mathbb{F}_{q}$ is a finite field of q elements, with q is a power of a prime number $p \geq 5$ and $n \geq 5$. In a first time, we describe these curves over this ring. In addition, we prove that when $p$ doesn't divide $\# ( H_{\pi(a), \ \pi(d)})$, then $H^{n}_{a,d}$ is a direct sum of $ H_{\pi(a), \ \pi(d)}$ and $\mathbb{F}_{q}^{n-1}$, where $ H_{\pi(a), \ \pi(d)}$ is the twisted Hessian curve over $\mathbb{F}_{q}$. Other results are deduced from, we cite the equivalence of the discrete logarithm problem on the twisted Hessian curves $H^{n}_{a,d}$ and $ H_{\pi (a), \ \pi (d)}$, which is beneficial for cryptography and cryptanalysis as well.

Improved RSA dynamic cryptographic accumulator-based anonymous batch authentication scheme for Internet of Vehicles

The Internet of Vehicles (IoV) provides various services to vehicles through information sharing to ensure road safety and improve traffic efficiency. However, malicious attackers can challenge the privacy and security systems of the IoV by conducting security attacks. Currently, many schemes use bilinear pairing or elliptic curves to construct authentication systems, ensuring anonymity of vehicle identities and message security. However, these schemes suffer drawbacks such as low computational efficiency and high communication overhead in highly dynamic IoV. Therefore, we propose a new efficient certificateless message authentication scheme. The proposed scheme constructs a lightweight security authentication protocol by improving the RSA dynamic accumulator and combining it with non-interactive discrete logarithm zero-knowledge proofs. In addition, our scheme eliminates the need for bilinear pairing operations, thereby reducing computational overhead. Simultaneously, it enables real-time tracking and revocation of malicious vehicle identities. Security analysis shows that our scheme can be reduced to a secure S-RSA assumption under the random oracle model, meeting various security requirements of the IoV. Performance analysis shows that our scheme diminishes not only the computational overhead but also the communication overhead.

Efficient and quantum‐secure authenticated key exchange scheme for mobile satellite communication networks

SummaryThe mobile satellite communication (MSC) system is a vital communication method in which mobile users and network control centers connect via satellites. Since the satellite's communication is wireless, communication security is a critical factor to ensure accountable communication. Key exchange and authentication (KEA) mechanism is widely used to achieve data security for data transmitted in an insecure or open channel. Different authentication systems are suggested in the last many years to establish safe communication, whereas most existing security protocols are based on factorization or discrete logarithm. However, these systems are no longer reliable by Shor's algorithm as any discrete logarithm and factorization can be resolved in polynomial time on quantum computers. Thus, developing a quantum secure KEA protocol for MSC systems is necessary. In this direction, recently a ring learning with an error‐based KEA technique is proposed to ensure a quantum‐safe environment. This scheme is quantum‐safe and satisfies desirable security attributes but has low efficiency in computation and communication. Moreover, establishing a secure session requires six communications among involved entities. As a result, replay attack detection at an early stage is not possible for the central authority (server), which could delay the server response, and the adversary gets the advantage of drawing a denial of service scenario for authorized entities. We propose a lattice‐based KEA protocol for the MSC system to improve computation, communication efficiency, and early‐stage replay attack detection. The security analysis of the proposed scheme is presented in the random oracle model. Calculation of performance is also presented to observe advantages in computation and communication overhead.

Cryptographic Signature Scheme for Mobile Edge Computing Using DLFP Over Semiring

The Undeniable Signature Scheme (USS) was first introduced by chaum and van in 1989. The advantage of the (USS) scheme is the signer’s co-operation during the verification process. In this paper, the Discrete Logarithm Problem with Factor Problem (DLFP) is introduced. It’s security and complexity is analyzed. Then, based on (DLFP), a key exchange protocol is given. An undeniable signature scheme based on DLFP over semiring is proposed along with illustration we have also given application of the proposed USS in Mobile Edge Computing (MEC). Then the proposed scheme’s security and complexity is examined.

A post-quantum secure PUF based cross-domain authentication mechanism for Internet of drones

With the increasing prevalence of drones, guaranteeing their authentication and secure communication has become paramount in drone networks to mitigate unauthorized access and malicious attacks. Cross-domain authentication is crucial in the context of the Internet of Drones (IoD) for safely verifying and establishing trust between diverse drones and their respective control stations, which may belong to different regions or organizations. Effectively accessing resources or services in another domain while maintaining security and efficiency poses a significant challenge. Conventional authentication mechanisms relying on challenging problems like discrete logarithm and integer factorization might not be sufficient to guarantee the security and effectiveness of drone-based systems in the post-quantum era. To address this, we propose a distributed post-quantum cryptography and Physical Unclonable Function (PUF) based cross-domain authentication protocol for IoD. Key contributions of this work include the elimination of secret key storage on drones, mutual authentication, emphasis on hardware security, incorporation of post-quantum security measures, efficient cross-domain authentication and resilience against cyber attacks such as eavesdropping, impersonation, replay attack, untraceability, and PUF-modeling attack. The performance of the proposed protocol is assessed utilizing metrics like processing time, communication cost and storage utilization. In operations associated to the blockchain ledger, variables such as latency, throughput, CPU utilization, and memory utilization are also examined. The protocol shows a reduced computation time and zero sensitive data storage in drone memory, despite a slightly higher communication cost that is manageable with 5G-enabled drones. Comparative analysis against existing solutions in the domain highlights the superior security of the proposed protocol, positioning it as a promising solution for the evolving quantum landscape.