Electronics Guide

Hardware Acceleration for Post-Quantum Cryptography

Post-quantum cryptographic algorithms require substantially more computational resources than their classical counterparts, making hardware acceleration essential for practical deployment. While classical RSA and elliptic curve operations can be performed efficiently in software on modern processors, post-quantum algorithms like ML-KEM and ML-DSA involve polynomial arithmetic, matrix operations, and hash computations at scales that benefit greatly from dedicated hardware. Specialized accelerators make post-quantum cryptography practical for resource-constrained embedded systems and enable high-throughput operation in servers and network infrastructure.

Hardware acceleration for post-quantum cryptography addresses multiple challenges simultaneously. Raw performance improvements enable cryptographic operations to complete within acceptable latency bounds. Energy efficiency improvements extend battery life in portable devices and reduce power consumption in data centers. Side-channel protection can be implemented more effectively in dedicated hardware than in software running on general-purpose processors. Understanding these accelerator architectures is essential for hardware designers implementing quantum-resistant security systems.

Number Theoretic Transform Accelerators

The Number Theoretic Transform (NTT) is the computational foundation of efficient lattice-based cryptography. NTT enables polynomial multiplication in quasi-linear time rather than the quadratic time of naive multiplication, making it essential for practical performance of ML-KEM, ML-DSA, and related algorithms. NTT accelerators provide the most significant performance improvement for lattice-based post-quantum implementations.

NTT computes the discrete Fourier transform over finite fields rather than complex numbers. For a polynomial of degree n, NTT computes n evaluations at n-th roots of unity in the field. Polynomial multiplication becomes element-wise multiplication of NTT outputs, followed by inverse NTT to recover the product polynomial. The transform structure enables efficient hardware implementation through butterfly operations.

Butterfly units form the basic computational element of NTT accelerators. Each butterfly performs an addition and subtraction combined with multiplication by a twiddle factor (power of a root of unity). The Cooley-Tukey decomposition arranges butterflies in log(n) stages, with n/2 butterflies per stage. Hardware implementations may execute butterflies sequentially, in parallel, or in various pipelined configurations based on area and throughput requirements.

Modular arithmetic within butterflies requires efficient reduction operations. The prime moduli used in post-quantum standards are chosen to enable efficient reduction; ML-KEM uses q = 3329, which allows Barrett or Montgomery reduction with precomputed constants. Hardware multipliers produce double-width products that must be reduced modulo q, with the reduction method significantly affecting latency and area.

Memory architecture is critical for NTT accelerator performance. NTT accesses polynomial coefficients in patterns determined by the transform structure, with different stages accessing different stride patterns. Efficient memory interfaces minimize stalls due to bank conflicts or bandwidth limitations. On-chip memory reduces latency but limits polynomial size; off-chip memory supports larger polynomials but introduces access latency.

Polynomial Arithmetic Units

Beyond NTT, lattice-based cryptography requires additional polynomial arithmetic operations including coefficient-wise operations, polynomial addition, and sampling operations. Dedicated hardware for these operations complements NTT acceleration to provide complete lattice cryptography support.

Coefficient-wise operations include addition, subtraction, and multiplication modulo q. While individually simple, these operations occur frequently and benefit from wide datapaths that process multiple coefficients in parallel. SIMD-style processing units apply the same operation across coefficient vectors, improving throughput for operations that don't require the structural complexity of NTT.

Polynomial addition and subtraction are straightforward coefficient-wise operations that benefit primarily from memory bandwidth and parallelism. The key optimization is ensuring that polynomial storage and access patterns align with computational unit widths, avoiding partial operations that waste hardware capability.

Sampling operations generate polynomial coefficients from specified distributions. ML-KEM and ML-DSA use centered binomial distributions or rejection sampling from uniform distributions. Hardware samplers can generate coefficients in parallel, feeding polynomial storage at high rates. The sampling process should be constant-time to prevent side-channel leakage of generated values.

Compression and decompression operations prepare polynomials for transmission or storage, reducing bit widths through controlled rounding. These operations involve bit manipulation and rounding logic that can be efficiently implemented in dedicated hardware, particularly for the specific parameters of standardized algorithms.

Matrix and Vector Operations

Lattice-based cryptography operates on matrices and vectors of polynomials, requiring coordination of multiple polynomial operations. Matrix-vector multiplication, the core operation in ML-KEM key generation and encapsulation, multiplies an m-by-n matrix of polynomials by an n-element vector, producing an m-element vector result.

Matrix-vector multiplication requires n polynomial multiplications and n-1 polynomial additions for each of the m result elements. The operations can be arranged for various resource-throughput trade-offs: minimal hardware performs one polynomial operation at a time; maximum throughput hardware performs all mn multiplications in parallel. Practical designs fall between these extremes based on area and performance requirements.

Scheduling matrix operations affects memory access patterns and hardware utilization. Row-major processing completes each result element before starting the next, requiring storage for one result polynomial and one row of matrix polynomials. Column-major processing processes matrix columns in sequence, accumulating partial results for all output elements simultaneously. Hybrid schedules can optimize for specific memory architectures.

Hardware sharing between matrix operations and other algorithm phases improves resource efficiency. The same NTT units used for polynomial multiplication can handle key generation, encapsulation, and decapsulation with appropriate control logic. Careful scheduling ensures continuous hardware utilization across algorithm phases.

Hash Function Acceleration

Post-quantum algorithms use hash functions extensively for key derivation, message hashing, and in hash-based signature schemes. The hash functions specified in NIST standards, particularly SHA-3 (Keccak) and SHAKE extendable-output functions, benefit from dedicated hardware acceleration.

SHA-3 and SHAKE are based on the Keccak permutation, a 1600-bit transformation composed of five operations applied over 24 rounds. Hardware implementations range from compact iterative designs that process one round per cycle to unrolled designs that complete the entire permutation in fewer cycles. The choice depends on area budget, throughput requirements, and whether hash operations are on the critical path.

Hash-based signatures like SLH-DSA (SPHINCS+) have particularly high hash function demands, potentially requiring thousands of hash invocations per signature. Hardware acceleration is essential for practical SLH-DSA performance, with accelerator throughput directly determining signature generation time.

Hash function accelerators must support multiple modes of operation. SHAKE functions produce variable-length output needed for key derivation and sampling. SHA3-256 and SHA3-512 produce fixed-length outputs for message hashing. A unified accelerator supports all required modes through configurable parameters.

Memory interfaces between hash accelerators and the rest of the cryptographic system affect overall performance. High-bandwidth interfaces enable streaming of data through hash operations without bottlenecks. Integration with polynomial samplers that consume hash output directly reduces data movement between components.

FPGA Implementation Approaches

Field-Programmable Gate Arrays (FPGAs) provide flexible platforms for post-quantum cryptography acceleration, enabling rapid prototyping, customization, and deployment in applications requiring reconfigurability. FPGA implementations must navigate the trade-offs inherent in programmable logic while achieving acceptable performance.

DSP block utilization significantly impacts FPGA PQC performance. Modern FPGAs include hardened DSP blocks optimized for multiply-accumulate operations. Mapping NTT butterflies to DSP blocks provides substantial speedup compared to logic-only implementation. The coefficient bit widths and modular reduction requirements of specific algorithms affect DSP utilization efficiency.

Block RAM provides on-chip storage for polynomial coefficients and intermediate values. FPGA block RAM organization into fixed-width, fixed-depth blocks constrains memory architecture design. Efficient polynomial storage requires matching coefficient sizes and polynomial lengths to available block RAM configurations.

High-level synthesis (HLS) tools enable rapid development of PQC accelerators from C or C++ descriptions. While HLS-generated designs may not achieve the efficiency of hand-optimized RTL, they significantly reduce development time and enable exploration of design alternatives. Critical paths can be hand-optimized after HLS establishes baseline functionality.

Partial reconfiguration capabilities of some FPGAs enable algorithm agility, loading different accelerator configurations to support various algorithms or security levels. This is particularly valuable during the transition period when algorithm choices may evolve. Reconfiguration time and configuration storage requirements must be considered for practical deployment.

ASIC Design Considerations

Application-Specific Integrated Circuits (ASICs) provide maximum performance and efficiency for post-quantum cryptography acceleration, suitable for high-volume applications or those requiring ultimate performance. ASIC design requires larger upfront investment but amortizes across production volume.

Custom arithmetic circuits can be optimized for the specific prime moduli used in standardized algorithms. Barrett or Montgomery reduction circuits tuned for q = 3329 (ML-KEM) or q = 8380417 (ML-DSA) achieve better area and timing than general-purpose modular arithmetic. Single-cycle butterfly operations enable high NTT throughput.

Memory hierarchy design in ASICs can precisely match algorithm requirements. On-chip SRAM provides fast access to coefficient storage with size tailored to maximum polynomial dimensions. Custom memory layouts avoid the fixed configurations of FPGA block RAM. Memory bandwidth can be designed to match computational throughput, avoiding bottlenecks.

Pipeline depth optimization balances latency against throughput for specific algorithm structures. Deep pipelines maximize clock frequency and throughput but increase latency for individual operations. Shallow pipelines provide lower latency at reduced throughput. The optimal balance depends on application requirements and whether operations can be pipelined.

Power optimization through clock gating, power domains, and voltage scaling is more controllable in ASICs than FPGAs. Unused accelerator components can be clock-gated or power-gated when not needed. Voltage scaling can trade performance for power efficiency based on current workload. These optimizations extend battery life in portable devices and reduce cooling requirements in data centers.

Instruction Set Extensions

Instruction set extensions add post-quantum cryptography support to general-purpose processors, providing acceleration without requiring separate accelerator hardware. This approach is particularly valuable for systems that cannot accommodate dedicated accelerators or need flexibility to run diverse workloads.

Vector instructions accelerate coefficient-wise polynomial operations through SIMD processing. ARM SVE and RISC-V Vector extensions provide scalable vector processing that can handle multiple coefficients per instruction. Efficient utilization requires mapping polynomial operations to vector instruction sequences with minimal overhead.

Dedicated instructions for modular reduction, butterfly operations, or NTT can provide substantial speedup compared to general-purpose instruction sequences. Adding such instructions requires careful analysis of which operations provide the greatest benefit relative to instruction encoding cost and implementation complexity.

Cryptographic extensions like ARM Cryptographic Extension and Intel SHA extensions provide accelerated hash operations useful for post-quantum implementations. These existing extensions benefit hash-based signatures and hash-heavy algorithm phases without requiring new post-quantum-specific extensions.

Compiler support is essential for practical use of instruction set extensions. Intrinsics provide direct access to new instructions from C code. Automatic vectorization can exploit vector extensions for suitable code patterns. Library implementations using extensions enable application benefits without requiring application code changes.

Constant-Time Implementation in Hardware

Hardware implementations must maintain constant-time execution to prevent timing side-channel attacks. Unlike software where constant-time implementation requires careful programming discipline, hardware can enforce constant-time behavior through structural design choices that eliminate timing variation regardless of processed data.

Fixed-cycle arithmetic operations complete in the same number of cycles regardless of operand values. Early termination optimizations that might reduce cycles for certain inputs must be avoided. Modular multiplication and reduction should complete in fixed time even when inputs could allow shortcuts.

Memory access patterns must be data-independent to prevent cache-timing attacks on systems with shared cache hierarchies. When the accelerator shares cache with other system components, address-based timing variations can leak secret information. Constant-time memory access patterns or dedicated memory without cache sharing eliminate this vulnerability.

Control flow must not depend on secret values in timing-visible ways. Conditional operations should use selection circuits (multiplexers) rather than conditional branches. All paths through the hardware should take the same time, with results selected at the end based on conditions.

Pipeline behavior must be carefully designed to avoid timing variations. Pipeline stalls due to data dependencies should not reveal secret values. Instruction-level parallelism should not vary based on processed secrets. These properties are more naturally achieved in dedicated accelerators than in general-purpose processors where software runs.

Power and Electromagnetic Countermeasures

Hardware accelerators require protection against power analysis and electromagnetic analysis attacks. Dedicated hardware enables countermeasures that are difficult or impossible to implement effectively in software, providing stronger protection against these physical attacks.

Masking techniques split secret values into random shares processed separately, preventing correlation between power consumption and secrets. Hardware masking can be implemented at the gate level, ensuring that protection extends to all operations on secret data. The overhead is area and latency for additional shares and share recombination.

Dual-rail logic encodes each bit as a pair of complementary signals, maintaining constant switching activity regardless of data values. Transitions always involve one signal rising and one falling, masking the power signature of individual bit values. The area cost is roughly double that of single-rail logic plus the routing complexity of complementary signals.

Random noise injection adds uncorrelated activity to mask the power signature of cryptographic operations. Noise generators can be integrated into the accelerator, consuming power that obscures the signal from useful operations. The noise must be truly random and uncorrelated with the cryptographic computation to be effective.

Shielding and layout techniques reduce electromagnetic emanations from sensitive circuits. Metal layers above and around cryptographic logic block EM emissions. Balanced routing ensures that complementary signals travel similar paths, reducing differential emissions. These physical design techniques complement algorithmic countermeasures.

Integration Architectures

Post-quantum cryptography accelerators must integrate with host systems through appropriate interfaces and protocols. Integration architecture affects both performance and security, determining how efficiently the host can utilize accelerator capabilities and how well secrets are protected in transit.

Memory-mapped interfaces expose accelerator registers and memory to the host processor's address space. This approach provides flexible access but may expose sensitive data on shared buses. Protected memory regions and access controls limit which software can interact with the accelerator and access key storage.

DMA (Direct Memory Access) enables efficient bulk data transfer between host memory and accelerator without processor involvement. For operations on large amounts of data, DMA reduces overhead compared to processor-mediated transfers. Security considerations include ensuring DMA cannot access memory regions outside the accelerator's authorized scope.

Dedicated interconnects provide isolated communication paths between the accelerator and specific system components. This approach improves security by limiting attack surface but requires additional routing resources. High-security applications may justify dedicated interconnects for key management and cryptographic operations.

Coprocessor architectures tightly couple the accelerator with a processor core, enabling efficient instruction-level interaction. The processor issues cryptographic operations through coprocessor instructions, with results returned through coprocessor registers. This model suits applications requiring fine-grained mixing of general computation and cryptographic operations.

Resource-Constrained Implementations

Many deployment scenarios require post-quantum cryptography in severely resource-constrained devices including IoT sensors, smart cards, and other embedded systems. Hardware acceleration for these platforms must achieve acceptable performance within extreme area and power budgets.

Iterative architectures minimize area by reusing hardware across multiple operations. A single butterfly unit can compute entire NTT transforms by iterating through coefficient pairs. Memory can be reused by processing algorithm phases sequentially. The trade-off is increased latency compared to parallel architectures.

Algorithm selection affects resource requirements significantly. Among NIST-standardized algorithms, ML-KEM and ML-DSA have similar resource requirements based on lattice operations. SLH-DSA based on hash functions has different characteristics, potentially favoring different implementation approaches. Lightweight algorithms specifically designed for constrained devices may be standardized in the future.

Parameter selection within algorithms provides resource-performance trade-offs. Lower security levels (e.g., ML-KEM-512 versus ML-KEM-1024) require smaller keys and less computation, suitable for applications where the lower security margin is acceptable. Constrained implementations should support at least the minimum security level needed for their application.

Shared resources between cryptographic and application functions maximize utilization of limited hardware. A microcontroller with cryptographic extensions uses the same arithmetic units for both functions. Care must be taken to clear sensitive data between uses and prevent application code from accessing cryptographic state.

Performance Benchmarking

Meaningful performance comparison of post-quantum hardware accelerators requires consistent benchmarking methodologies. Benchmarks should capture metrics relevant to target applications while enabling fair comparison across different implementations and platforms.

Throughput measurements indicate operations completed per unit time, typically expressed as operations per second for key generation, encapsulation/decapsulation, or signing/verification. Throughput benchmarks should specify input sizes, security levels, and whether pipeline filling effects are included.

Latency measurements indicate the time from operation initiation to result availability. For interactive applications, latency may be more important than throughput. Latency should be measured from input availability through output validity, including any preprocessing and postprocessing.

Area metrics express hardware resource consumption. For FPGAs, this includes lookup tables (LUTs), flip-flops, DSP blocks, and block RAM. For ASICs, gate count or silicon area indicates resource consumption. Area-time products provide efficiency metrics for comparing implementations with different resource-performance trade-offs.

Energy measurements indicate power consumption over time, critical for battery-powered and thermally constrained applications. Energy per operation enables comparison independent of clock frequency. Power gating and voltage scaling effects should be included for implementations using these techniques.

Summary

Hardware acceleration enables practical deployment of post-quantum cryptography by addressing the increased computational requirements of quantum-resistant algorithms. NTT accelerators provide the foundation for efficient lattice-based cryptography, with polynomial arithmetic units, matrix operations, and hash acceleration completing the implementation. FPGA and ASIC platforms offer different trade-offs between flexibility and efficiency, while instruction set extensions bring acceleration to general-purpose processors.

Constant-time implementation, power analysis resistance, and electromagnetic shielding must be incorporated into accelerator designs to prevent side-channel attacks from undermining mathematical security. Integration architectures balance performance against security for connection with host systems. Resource-constrained implementations enable post-quantum security in embedded and IoT applications. Consistent benchmarking methodologies enable meaningful comparison across the diverse range of accelerator implementations being developed for the post-quantum transition.