MicroCloud Hologram Inc. Strong Designated Verifier Signature Protocol Based on High-Order Multivariate Algebraic Equations

SHENZHEN, China, May 06, 2026 (GLOBE NEWSWIRE) -- MicroCloud Hologram Inc. (NASDAQ: HOLO), (“HOLO” or the "Company"), a technology service provider, is committed to post-quantum cryptography innovation and has announced a forward-looking technological achievement: a Strong Designated Verifier Signature (SDVS) scheme that takes the computational difficulty of solving high-order multivariate algebraic equations as its security foundation. This scheme is also built upon post-quantum key agreement protocols. For the first time, it fully implements the core design principles of SDVS within the multivariate polynomial framework and plans to deeply participate in the quantum-resistant transformation of the Bitcoin protocol. This technology not only effectively addresses the threat posed by quantum computers to traditional cryptographic primitives, but also provides an entirely new implementation path for Bitcoin transaction signatures and privacy protocols.

The core of the high-order multivariate algebraic equation problem lies in solving a system of multivariate polynomial equations composed of multiple variables. These polynomials usually contain high-degree terms (such as cubic or higher order) and are defined over finite fields. Solving such systems has been proven to be an NP-complete problem. Even with the help of quantum algorithms such as Grover’s search, only quadratic acceleration can be provided, without achieving exponential breakthroughs, making it an ideal candidate for post-quantum cryptography. HOLO’s SDVS scheme cleverly transforms this hard problem into the cornerstone of key agreement. In the key generation phase, the signer and the designated verifier each construct a public polynomial system as the public key. The signer’s public key consists of a set of random high-order polynomials, which are bound to the private key through secret linear or affine transformations. The verifier’s public key is also a set of multivariate polynomials, but is designed to allow the signer to use its structure to generate a shared secret during the agreement process without directly solving the equations.

The implementation logic of the signing process highly relies on the non-interactive variant of the key agreement protocol. The signer first uses its own private key (i.e., the trapdoor information for solving the polynomial system) and the verifier’s public key to construct a temporary instance of a multivariate equation system, where the solution of this instance corresponds to a shared secret. Subsequently, the signer embeds the message hash value into this equation system and efficiently computes a solution vector that satisfies the equation through the trapdoor. This solution vector constitutes the core part of the signature. The entire signature output includes commitment values related to the public key and a masked proof, ensuring that external observers cannot extract useful information from the signature. After receiving the signature, the verifier uses its own private key (another trapdoor) to attempt to solve or verify the consistency of the equation system. Verification only passes when the shared secret matches and the message is intact. This design ensures that only the designated verifier has exclusive verification capability, because third parties lack the verifier’s private key trapdoor and cannot efficiently solve the corresponding multivariate equations, thus being unable to confirm the validity of the signature.

The essential characteristics of strong designated verifier signatures are perfectly embodied in this scheme. Although the verifier can verify the signature, since he himself can also use the private key to simulate the generation of an equivalent signature (by generating a fake equation system instance), he cannot provide transferable evidence to third parties. This simulation indistinguishability stems from the randomness of the multivariate polynomial system: any two legitimate equation systems are difficult to distinguish in distribution, and even with quantum computing assistance, they cannot be cracked by polynomial-time algorithms. This logic stands in sharp contrast to traditional SDVS based on discrete logarithms, which are vulnerable to quantum attacks, whereas the multivariate scheme naturally possesses quantum resistance.

In terms of technical implementation, HOLO’s scheme emphasizes parameter optimization to achieve practicality. The public key consists of dozens of variables and dozens of high-order equations. Through carefully chosen finite fields (such as GF(2^8) or larger) and polynomial degrees, the key size is controlled within a few thousand bits, which is much smaller than some lattice-based schemes. Signature generation involves efficient multivariate evaluation and trapdoor solving. These operations can be accelerated through approximate Groebner basis algorithms or specialized linearization techniques, and can be completed in sub-second time on standard CPUs. The verification process is lighter, requiring only the substitution of the verifier’s trapdoor parameters and checking whether the equation residuals are zero. Security analysis shows that the unforgeability of the scheme directly reduces to the difficulty of solving multivariate equations, meaning that any successful forgery attack can be transformed into a solver problem. This has been proven secure under the post-quantum random oracle model. The team has also considered various attack vectors, such as linearization attacks or differential attacks, and countered them by increasing polynomial nonlinearity and adding random salt values.

When applied to the Bitcoin protocol, HOLO’s multivariate SDVS scheme provides a flexible quantum upgrade path. The main risk currently facing Bitcoin is that public keys can be cracked by quantum algorithms, whereas this scheme allows designated verifier logic to be embedded in transaction outputs—for example, designating miner nodes or specific wallets as verifiers to ensure that transactions are confirmed only by authorized parties. This is particularly suitable for privacy-enhanced transactions or multi-party protocols, such as using SDVS to prevent fraud when closing Lightning Network channels. At the same time, the scheme supports hybrid use with existing ECDSA by introducing new script opcodes through a soft fork to support multivariate polynomial evaluation, thereby enabling gradual migration. HOLO points out that this design not only maintains Bitcoin’s decentralized characteristics but also significantly improves the overall privacy level, because signatures are no longer publicly verifiable but are controlled by designated entities.

From the implementation details perspective, the integration of the key agreement protocol is the core innovation of the scheme. The signer can directly generate a shared secret through the public key without any additional interaction with the verifier. This non-interactivity greatly reduces network overhead. In polynomial construction, HOLO adopted hidden trapdoor technology—for example, representing the private key as a linear combination of a low-degree polynomial and the high-degree part of the public key, making solving efficient only when the trapdoor is possessed. Security is further strengthened through a multi-round challenge-response mechanism, ensuring that signatures cannot be forged even under an adaptive adversary model. Performance benchmarks show that at the 128-bit post-quantum security level, the signature size is approximately several times that of traditional ECDSA, but can be further optimized through compression techniques, making it suitable for Bitcoin’s block space constraints.

Compared with other post-quantum schemes, this multivariate SDVS demonstrates advantages in key generation speed and verification efficiency. Although lattice-based schemes are mature, their keys are larger; hash-based schemes have excessively long signatures. The multivariate method, relying on its NP-complete assumption, provides a more compact implementation and is easy to accelerate in hardware, such as implementing parallel polynomial multiplication on FPGA. HOLO plans to submit the scheme to the Bitcoin Improvement Process and cooperate with the community for security audits to ensure robustness before deployment. Potential challenges include the impact of parameter selection on performance and possible future improvements in multivariate solving by quantum algorithms, but these risks can be effectively controlled through dynamic parameter adjustment.

HOLO’s SDVS scheme based on high-order multivariate algebraic equations marks an important step in the development of Bitcoin’s post-quantum protocol. It not only achieves a seamless integration of post-quantum key agreement and signature design at the technical level, but also provides a scalable security solution for the entire blockchain ecosystem. As the practical application of quantum computers approaches, the implementation of this technology will help Bitcoin maintain its core position as digital gold and continue to play a key role in the global financial system.

MicroCloud Hologram Inc. focuses on the development of quantum computing and quantum holography, and enhancing Bitcoin’s resistance to quantum attacks is a key development plan. HOLO’s cash reserves exceed 390 million U.S. dollars, and it plans to invest more than 400 million U.S. dollars in Bitcoin blockchain quantum security development, quantum computing technology research and development, quantum holography technology research and development, and derivative products and technology development in other cutting-edge technology fields. With the support of several hundred million U.S. dollars in funding, HOLO’s goal is to become the world’s leading company in quantum-resistant Bitcoin security blockchain technology.

About MicroCloud Hologram Inc.

MicroCloud Hologram Inc. (NASDAQ: HOLO) is committed to the research and development and application of holographic technology. Its holographic technology services include holographic light detection and ranging (LiDAR) solutions based on holographic technology, holographic LiDAR point cloud algorithm architecture design, technical holographic imaging solutions, holographic LiDAR sensor chip design, and holographic vehicle intelligent vision technology, providing services to customers offering holographic advanced driving assistance systems (ADAS). MicroCloud Hologram Inc. provides holographic technology services to global customers. MicroCloud Hologram Inc. also provides holographic digital twin technology services and owns proprietary holographic digital twin technology resource libraries. Its holographic digital twin technology resource library utilizes a combination of holographic digital twin software, digital content, space data-driven data science, holographic digital cloud algorithms, and holographic 3D capture technology to capture shapes and objects in 3D holographic form.

MicroCloud Hologram Inc. focuses on the development of quantum computing and quantum holography. With cash reserves exceeding 390 million USD, the company plans to invest over 400 million USD in blockchain development, quantum computing R&D, quantum holography technology, as well as in the development of derivatives and technologies in cutting-edge fields such as AI, AR, and more. MicroCloud Hologram Inc.'s goal is to become a global leader in quantum holography and quantum computing technologies.

Safe Harbor Statement

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