Optimizing Hardware Implementation of Linear Layers

Optimizing Hardware Implementation of Linear Layers

Table of Contents

1. Introduction
2. Importance of Lightweight Cryptography for Devices with Limited Resources
3. Designing Lightweight Primitives for Encryption
4. The Role of Linear Layers in Cryptography Primitives
5. Criteria for Optimizing Linear Layers
6. Metrics for Evaluating Linear Layer Implementations
   • 6.1 Circuit Area
   • 6.2 Latency
7. The Backward Framework for Optimizing Linear Layers
   • 7.1 Splitting Nodes Based on Minimum Depth
   • 7.2 Ensuring Minimum Depth in Output Circuit
8. Comparison of Forward and Backward Frameworks
   • 8.1 Control of Depth in Backward Framework
   • 8.2 Performance of Backward Framework in Optimizing Linear Layers
9. Application of the Backward Framework to Existing Matrices
   • 9.1 Results of Algorithm on Various Matrices
   • 9.2 Optimization of MDS Matrices
   • 9.3 Optimization of AES Mixed Columns
10. Conclusion

Towards Low-Latency Implementation on Linear Layers: Optimizing Hardware Implementation of Linear Layers in Lightweight Cryptography

Introduction

The field of lightweight cryptography has gained significant importance due to the increasing demand for devices with limited resources, such as Internet of Things (IoT) devices and Radio Frequency Identification (RFID) tags. With the restrictions imposed by virus threats and security breaches, it is crucial to ensure secure encryption while expanding the applications of cryptography to these resource-constrained devices. In this paper, we focus on the hardware implementation of linear layers, which are vital components in many cryptography primitives.

Importance of Lightweight Cryptography for Devices with Limited Resources

Devices with limited resources require lightweight cryptography to ensure secure encryption without draining their already constrained resources. Lightweight cryptography aims to design efficient and low-complexity primitives that can be implemented on such devices. The gate equivalent (GE) metric is commonly used to measure the complexity of implementing ciphers, as it approximates the circuit area required. Moreover, the latency metric plays a crucial role in achieving low energy consumption, making it an essential consideration for optimizing ciphers for resource-constrained devices.

Designing Lightweight Primitives for Encryption

When designing lightweight primitives, several criteria need to be considered. The most popular criterion is the gate equivalent (GE), which estimates the complexity of the circuit area required to implement the cipher. By reducing the number of XOR operations, the circuit area can be minimized. Additionally, the latency of the implementation is crucial, as it directly impacts the execution time of the encryption process. Designing new lightweight ciphers and optimizing components within the ciphers are two directions that can be pursued in achieving efficient encryption on limited resource devices.

The Role of Linear Layers in Cryptography Primitives

Linear layers play a critical role in many cryptography primitives. For the non-linear layer, the Xbox function is commonly used. On the other HAND, the linear layer often utilizes the MDS matrix or the near-MDS matrix. This paper focuses on optimizing the hardware implementation of linear layers, as it has practical significance and contributes to the efficient functioning of cryptography primitives on resource-constrained devices.

Criteria for Optimizing Linear Layers

Two key criteria for optimizing linear layers are circuit area and latency. The circuit area can be minimized by reducing the number of XOR operations required to implement the linear layers. This can be achieved by using various metrics such as DXO, SXOR, and CXOR to estimate the number of XOR operations. The latency metric measures the time it takes to execute the encryption process. Minimizing the depth of the circuit, which represents the maximum number of XOR equations in the path, helps achieve low latency implementations.

Metrics for Evaluating Linear Layer Implementations

The circuit area and latency are two metrics used to evaluate different implementations of linear layers. The circuit area is determined by the number of XOR operations required for the implementation. Reducing the number of XOR operations helps minimize the circuit area. The latency is determined by the depth of the circuit, which represents the maximum number of XOR equations in the path. Minimizing the depth results in faster encryption execution, making it an important consideration for resource-constrained devices.

The Backward Framework for Optimizing Linear Layers

The backward framework is a promising approach for optimizing linear layers. It starts with the target output nodes and iteratively splits them into unique input nodes until all the nodes are unique. This approach ensures that the implementation has the minimum depth, leading to more efficient execution. The framework involves splitting nodes based on their minimum depth and ensuring the output of the framework has the minimum depth.

Comparison of Forward and Backward Frameworks

The forward and backward frameworks are two different approaches to optimizing linear layers. The forward framework combines input values to generate output values, while the backward framework splits output values into input values. The backward framework offers better control over the depth of each node, as it allows for splitting using nodes with less depth. This control over depth results in implementations with the minimum depth and optimized circuit area.

Application of the Backward Framework to Existing Matrices

To evaluate the effectiveness of the backward framework, we applied it to various existing matrices used in different linear layers and MDS matrices. The results Show that our algorithm can optimize more than half of the matrices compared to previous approaches. Additionally, the optimization of AES Mixed Columns in hardware showed that our implementation has the smallest power consumption and lowest latency.

Conclusion

Optimizing linear layers in lightweight cryptography is crucial for achieving efficient and secure encryption on devices with limited resources. The backward framework offers an effective approach to optimize the hardware implementation of linear layers, considering both circuit area and latency. By controlling the depth of each node and applying heuristics, our algorithm achieves improved implementations compared to previous approaches. The results demonstrate the practical significance and potential of the backward framework in optimizing linear layers for resource-constrained devices.