Speeding Up Post-Quantum Signatures with GPU Power

Author: Denis Avetisyan

A new framework dramatically accelerates the generation of SPHINCS+ digital signatures by harnessing the parallel processing capabilities of modern GPUs.

Performance metrics-specifically, Kernel Operations Per Second (KOPS) and kernel launch latency measured in microseconds-demonstrate that fully optimized HERO-Sign achieves substantial gains over the baseline, further amplified by the integration of CUDA Graphs, excluding graph instantiation time.

HERO-Sign leverages compiler-time optimizations and efficient memory access to achieve significant performance gains for hash-based signature schemes.

Despite the promise of post-quantum cryptography, stateless hash-based signature schemes like SPHINCS+ suffer from performance bottlenecks due to intensive hash computations. This paper introduces HERO-Sign: Hierarchical Tuning and Efficient Compiler-Time GPU Optimizations for SPHINCS+ Signature Generation, a GPU-accelerated framework that overcomes these limitations through a novel combination of hierarchical tuning and adaptive compiler optimizations. HERO-Sign achieves significant speedups across diverse GPU architectures by intelligently fusing parallelizable operations and dynamically selecting optimal compilation strategies. Will this approach pave the way for practical, high-throughput deployments of post-quantum digital signatures?

Unveiling the Quantum Threat: A System Under Scrutiny

The backbone of contemporary digital security, public-key cryptography systems like RSA and Elliptic Curve Cryptography (ECC), safeguard online transactions, secure communications, and protect sensitive data worldwide. These systems operate on the mathematical difficulty of certain problems – factoring large numbers for RSA and solving the elliptic curve discrete logarithm problem for ECC – problems considered intractable for classical computers. However, the emergence of quantum computing presents a fundamental challenge to this security. Unlike classical bits representing 0 or 1, quantum bits, or qubits, leverage superposition and entanglement, enabling quantum computers to perform calculations exponentially faster than their classical counterparts. This enhanced computational power renders the mathematical problems underpinning RSA and ECC solvable, effectively breaking the encryption and exposing previously secure information to potential adversaries. The widespread reliance on these vulnerable algorithms highlights the urgent need to transition to more robust cryptographic methods.

Shor’s algorithm, developed by mathematician Peter Shor in 1994, presents a fundamental challenge to the security of widely used public-key cryptosystems. These systems, like RSA and Elliptic Curve Cryptography (ECC), depend on the practical difficulty of factoring large numbers or solving the discrete logarithm problem – computations considered intractable for classical computers. However, Shor’s algorithm leverages the principles of quantum mechanics, specifically quantum superposition and quantum Fourier transforms, to solve these problems with exponential speedup. While classical algorithms require time that grows exponentially with the size of the key, Shor’s algorithm reduces this to a polynomial time complexity. This means that a sufficiently powerful quantum computer could break these cryptographic systems in a feasible timeframe, compromising secure communications and data protection as currently practiced. The algorithm efficiently finds the period of a mathematical function, a crucial step in both integer factorization and discrete logarithm calculations – effectively dismantling the mathematical foundations upon which these security protocols rest.

The acknowledged vulnerability of current encryption standards to quantum computing power is driving substantial research and development in the field of post-quantum cryptography (PQC). This isn’t simply a matter of strengthening existing algorithms; it requires entirely new mathematical approaches. PQC focuses on developing cryptographic systems that are believed to be secure against both classical computers and future quantum computers. These algorithms are typically based on different mathematical problems, such as lattice-based cryptography, code-based cryptography, multivariate cryptography, and hash-based signatures, which are thought to be inherently resistant to attacks from Shor’s algorithm and other quantum threats. The National Institute of Standards and Technology (NIST) is currently leading a global effort to standardize a new generation of PQC algorithms, aiming to proactively secure digital infrastructure before quantum computers become powerful enough to break widely used encryption. This transition to PQC represents a fundamental shift in cryptographic thinking and is crucial for maintaining data security in the quantum era.

A tree-based reduction process efficiently computes Merkle tree signatures by selecting leaf nodes <span class="katex-eq" data-katex-display="false">\l_e_a_f\_\idx</span> to guide authentication and leveraging fast on-chip SRAM access with an even-odd pattern to achieve near register-level performance. — A tree-based reduction process efficiently computes Merkle tree signatures by selecting leaf nodes $\l_e_a_f\_\idx$ to guide authentication and leveraging fast on-chip SRAM access with an even-odd pattern to achieve near register-level performance.

SPHINCS+: Forging Resilience from Hash Functions

SPHINCS+ operates as a stateless hash-based signature scheme, meaning it does not require the maintenance of secret long-term keys, mitigating risks associated with key compromise or state exposure. Its security is based on the assumed hardness of the hash function used; specifically, it relies on the collision and preimage resistance of the underlying hash function, offering resistance against both classical and quantum cryptanalytic attacks. This resistance stems from the fact that breaking SPHINCS+ would require finding collisions in the hash function, a computationally intensive task even with the advent of quantum computers. The scheme’s design ensures that even with a fully functional quantum computer, forging a valid signature without knowledge of the private key remains computationally infeasible, providing a post-quantum security guarantee.

SPHINCS+ achieves its security through a layered approach utilizing three primary components: FORS (Few-OT-RSA Signature), WOTS+ (Winternitz One-Time Signature+), and MSS (Merkle Signature Scheme). FORS mitigates forgery attempts by requiring a sufficient number of one-time signatures to be valid, increasing the computational effort for an attacker. WOTS+ provides a standardized method for generating one-time signatures from hash functions, ensuring each signature is unique and non-reusable. MSS builds upon WOTS+ by using a Merkle tree to compress multiple WOTS+ signatures into a single, verifiable root hash; this compression reduces signature size while maintaining security. The combination of these components, carefully parameterized to resist known attacks, forms the foundation of SPHINCS+’s post-quantum security.

The Hypertree structure in SPHINCS+ organizes the FORS, WOTS+, and MSS components into a multi-layered tree to facilitate efficient signature generation and verification. This structure comprises multiple layers of hash trees, where each node hashes the data from its child nodes. The height of the hypertree, and thus the number of layers, is a configurable parameter affecting both security and performance. Signature generation involves computing and concatenating leaf hashes and hashes along the paths from the leaves to the root, while verification involves recomputing these hashes and comparing the final result to the provided signature. This hierarchical structure allows for parallel computation of hashes at each layer, significantly reducing the time required for both signing and verification compared to a simple, flat structure. The specific arrangement and parameters of the hypertree are crucial for balancing signature size, computational cost, and security against potential attacks.

SPHINCS+ employs a hypertree structure comprising FORS, WOTS+, and MSS components to compute and store signatures from left to right, leveraging parallelizable regions and a Tree Tuning algorithm for efficient compile-time path selection.

HERO-Sign: Unleashing GPU Power for Post-Quantum Speed

HERO-Sign is a signature scheme implementation built upon the stateless hash-based signature scheme SPHINCS+. It utilizes the Compute Unified Device Architecture (CUDA) framework to offload computational tasks to Graphics Processing Units (GPUs). This parallel processing approach is specifically designed to accelerate the signature generation process, a computationally intensive operation in hash-based cryptography. By leveraging the inherent parallelism of GPUs, HERO-Sign aims to provide substantially improved performance compared to CPU-based implementations of SPHINCS+.

HERO-Sign’s performance is directly linked to its utilization of the CUDA Single Instruction, Multiple Threads (SIMT) architecture. This allows for parallel execution of the same instruction across multiple data elements, accelerating cryptographic operations inherent in SPHINCS+. Crucially, the implementation employs a tiered memory access strategy: frequently accessed data is stored in Shared Memory for rapid access by threads within a block; larger datasets reside in Global Memory, and constant parameters are cached in Constant Memory. This optimized memory hierarchy minimizes data transfer latency and maximizes throughput by exploiting the distinct access characteristics and bandwidth capabilities of each memory type within the GPU architecture.

The HERO-Sign implementation of SPHINCS+ achieves a throughput of 33.88 Kilobytes per Second (KOPS) when executed on an NVIDIA RTX 4090 GPU. This performance represents a substantial improvement over baseline SPHINCS+ implementations; HERO-Sign delivers a 2.14x speedup across a range of tested GPU architectures. This speedup is indicative of the effectiveness of the GPU acceleration and optimization techniques employed, providing a considerable increase in signature generation rates.

Tree Tuning is an automated algorithm integrated into the HERO-Sign implementation to optimize the performance of the FORS (Forest of Random Subsets) component of SPHINCS+. This process dynamically searches for the most efficient configuration of parameters within the FORS structure, specifically focusing on the height of the trees and the size of the subsets. By systematically evaluating different configurations, Tree Tuning minimizes computational overhead associated with FORS signature generation and verification, leading to improved overall performance without requiring manual parameter adjustments. The algorithm aims to identify configurations that balance the trade-off between computational cost and security level, ensuring an optimized implementation for a given hardware platform.

HERO-Sign consistently outperforms the baseline across various GPU architectures when processing blocks of size 1024.

Decoding Optimization: How HERO-Sign Achieves Acceleration

HERO-Sign leverages a Task Graph to model the relationships between individual computational tasks involved in signature generation and verification. This graph explicitly defines dependencies, allowing the system to identify tasks that can be executed in parallel on the GPU. By representing these dependencies, the scheduler can optimize task allocation and minimize idle time, thereby maximizing GPU utilization and overall throughput. The Task Graph facilitates efficient parallel execution by enabling the system to launch and manage concurrent tasks without the overhead associated with traditional sequential processing.

The HERO-Sign implementation leverages PTX (Parallel Thread Execution), NVIDIA’s intermediate representation for GPU-accelerated computing. PTX allows for architecture-specific optimizations to be applied during compilation, maximizing performance on NVIDIA GPUs. This includes instruction selection, register allocation, and memory access patterns tailored to the target GPU’s streaming multiprocessors. By utilizing PTX, HERO-Sign avoids limitations imposed by higher-level languages and directly addresses the parallel processing capabilities of the GPU, resulting in substantial speed and efficiency gains compared to implementations targeting alternative hardware like FPGAs or ASICs.

HERO-Sign employs the SHA-256 cryptographic hash function as a core component of its signature generation process. SHA-256 generates a fixed-size 256-bit (32-byte) hash value from any input data. This hash serves as a digital fingerprint, enabling verification of data integrity; any modification to the input data will result in a different hash value. Within HERO-Sign, SHA-256 is utilized to hash the data being signed, and this hash is then incorporated into the signature generation process, ensuring that any tampering with the data will invalidate the signature and be detectable during verification. The algorithm’s collision resistance is critical for the security of the signature scheme, preventing the creation of fraudulent signatures.

HERO-Sign significantly reduces operational overhead by leveraging CUDA Graphs to minimize kernel launch latency, achieving a 221.3x reduction. This optimization, coupled with efficient memory access patterns, results in substantial power savings; per-signature power consumption (PPS) is reduced by a factor of 133x when compared to implementations utilizing Field Programmable Gate Arrays (FPGAs). Furthermore, HERO-Sign demonstrates even greater efficiency, achieving a 158x reduction in PPS relative to FPGA-based signature generation.

Performance evaluations demonstrate that HERO-Sign achieves significant speedups compared to ASIC implementations of the SPHINCSLET signature scheme. Specifically, HERO-Sign exhibits a 229.75x speedup with a 128f parameter set, a 327.15x speedup with a 192f parameter set, and a 338.8x speedup with a 256f parameter set. These results indicate substantial gains in signature generation speed when utilizing HERO-Sign on compatible GPU hardware instead of dedicated ASIC implementations of SPHINCSLET.

HERO-Sign consistently outperforms the Baseline across all block sizes, demonstrating improved performance in KOPS.

Beyond Acceleration: Charting the Future of Post-Quantum Security

The advent of HERO-Sign signifies a pivotal step in realizing the performance benefits of hardware acceleration within post-quantum cryptography. This implementation leverages the parallel processing capabilities of Graphics Processing Units (GPUs) to significantly enhance the speed and efficiency of PQC algorithms, traditionally constrained by computational demands. By offloading cryptographic operations to the GPU, HERO-Sign demonstrates a pathway to overcome these limitations and achieve practical performance levels necessary for widespread adoption. This successful integration not only validates the feasibility of GPU acceleration for PQC but also opens avenues for further optimization and exploration of other hardware-based acceleration techniques, promising a future where quantum-resistant cryptography is both secure and efficient.

The advent of quantum computing poses a significant threat to currently deployed cryptographic systems, necessitating sustained effort in post-quantum cryptography (PQC) implementation and optimization. While novel PQC algorithms are being developed, their practical deployment hinges on achieving performance levels comparable to existing standards; this demands continuous refinement of code, leveraging hardware acceleration, and exploring compilation techniques to minimize overhead. Further research isn’t simply about discovering new algorithms, but critically about making those algorithms efficient enough for widespread adoption, ensuring a smooth and secure transition as quantum computational capabilities mature. This includes optimizing for various platforms – from embedded systems with limited resources to high-performance servers – and addressing potential vulnerabilities that may emerge during implementation and real-world usage, guaranteeing long-term security in a post-quantum landscape.

A robust cryptographic future demands more than reliance on a single post-quantum algorithm; therefore, current efforts prioritize diversification through the exploration of multiple promising schemes. Alongside hash-based signatures – known for their strong security foundations – algorithms like CRYSTALS-Kyber and CRYSTALS-Dilithium are receiving significant attention. CRYSTALS-Kyber, a key-encapsulation mechanism, and CRYSTALS-Dilithium, a digital signature scheme, offer a compelling balance of security, performance, and implementation practicality. By actively researching and developing these varied approaches, cryptographers aim to build a resilient defense against potential attacks, ensuring that a compromise in one algorithm does not jeopardize the entire system. This multi-faceted strategy mitigates risk and establishes a more secure foundation for digital communications in the post-quantum era.

HERO-Sign significantly streamlines the development and deployment of post-quantum cryptographic solutions by achieving a 1.26x reduction in compilation time. This optimization is accomplished through the innovative use of compile-time branching, a technique that allows the compiler to resolve certain code paths during the compilation process itself, rather than at runtime. By predetermining these paths, HERO-Sign minimizes the computational burden during application execution and accelerates the overall build process. This improvement is particularly valuable for resource-constrained environments and large-scale deployments, where even incremental gains in efficiency can have a substantial impact on performance and scalability. Ultimately, this faster compilation contributes to a more agile and responsive development cycle for post-quantum cryptography.

Block-based CUDA graph construction organizes <span class="katex-eq" data-katex-display="false">FORS_{Sign}</span>, <span class="katex-eq" data-katex-display="false">TREE_{Sign}</span>, and <span class="katex-eq" data-katex-display="false">WOTS_{+Sign}</span> kernels into directed acyclic graphs (DAGs) by explicitly defining dependencies between nodes. — Block-based CUDA graph construction organizes $FORS_{Sign}$ , $TREE_{Sign}$ , and $WOTS_{+Sign}$ kernels into directed acyclic graphs (DAGs) by explicitly defining dependencies between nodes.

The pursuit of efficiency in cryptographic systems, as demonstrated by HERO-Sign’s GPU acceleration of SPHINCS+, echoes a fundamental principle of information theory. Claude Shannon observed that “Communication is the transmission of information, not the transmission of the signal.” Similarly, HERO-Sign doesn’t merely transmit data; it optimizes the process of signature generation. By focusing on compile-time branching and optimized memory access – effectively reducing redundancy in the computational ‘signal’ – the framework extracts maximum information throughput. This aligns with Shannon’s view; a secure, efficient system isn’t about complexity, but about distilling communication down to its essential elements and eliminating unnecessary overhead, even if it means testing the boundaries of existing architectures to achieve it.

What’s Next?

The presented work, in accelerating SPHINCS+ through HERO-Sign, does not so much solve a problem as expose the inherent tensions within hash-based cryptography. The speedups achieved are, predictably, constrained by memory bandwidth – a persistent bottleneck. One might argue that forcing hash functions through parallel pipelines simply highlights their sequential nature; a bug in the system confessing its design sins. Future work shouldn’t focus solely on squeezing more performance from existing architectures, but rather on fundamentally re-evaluating the computational primitives themselves.

The reliance on compile-time branching, while effective, introduces a rigidity. It’s a trade-off: speed for adaptability. What remains unexplored is a dynamic system – one capable of reconfiguring itself during signature generation to exploit transient resource availability. A truly robust post-quantum signature scheme shouldn’t merely be fast; it should be opportunistic, capable of morphing to maximize efficiency given the prevailing hardware landscape.

Ultimately, HERO-Sign serves as a useful, albeit temporary, reprieve. The true challenge lies not in optimizing the known, but in discovering the unknown. The next iteration demands a departure from incremental improvements and a willingness to dismantle – intellectually, of course – the foundational assumptions of hash-based signature schemes. The goal isn’t just a faster signature; it’s a signature that understands its own limitations and actively works to overcome them.

Original article: https://arxiv.org/pdf/2512.23969.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/