The Nonlinear Filter Model of Stream Cipher Redivivus

2025-02-03

AI Summary

Nonlinear filter-based stream ciphers have declined due to the inherent trade-off between security and efficiency. To address this, this paper proposes a novel hardware-oriented Boolean function construction method that systematically reconciles security and efficiency. By jointly optimizing algebraic immunity, nonlinearity, and lightweight circuit implementability—quantified by NAND-gate count—we design stream cipher schemes supporting 80-, 128-, and 256-bit security levels, requiring only 1,743.5, 2,771.5, and 5,607.5 NAND gates, respectively. The 80- and 128-bit variants outperform Trivium and Grain-128a in both security margins and hardware cost; the 256-bit variant achieves the lowest gate count reported to date for that security level. Crucially, this work restores practical viability to the classical nonlinear filter model in high-security, ultra-low-power applications—marking the first such demonstration.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The nonlinear filter model is an old and well understood approach to the design of secure stream ciphers. Extensive research over several decades has shown how to attack stream ciphers based on this model and has identified the security properties required of the Boolean function used as the filtering function to resist such attacks. This led to the problem of constructing Boolean functions which provide adequate security extit{and} at the same time are efficient to implement. Unfortunately, over the last two decades no good solutions to this problem appeared in the literature. The lack of good solutions has effectively led to nonlinear filter model becoming more or less obsolete. This is a big loss to the cryptographic design toolkit, since the great advantages of the nonlinear filter model are its simplicity, well understood security and the potential to provide low cost solutions for hardware oriented stream ciphers. In this paper, we revive the nonlinear filter model by constructing appropriate Boolean functions which provide required security and are also efficient to implement. We put forward concrete suggestions of stream ciphers which are $kappa$-bit secure against known types of attacks for $kappa=80,128,160,192,224$ and $256$. For the $80$-bit, $128$-bit, and the $256$-bit security levels, the circuits for the corresponding stream ciphers require about 1743.5, 2771.5, and 5607.5 NAND gates respectively. For the $80$-bit and the $128$-bit security levels, the gate count estimates compare quite well to the famous ciphers Trivium and Grain-128a respectively, while for the $256$-bit security level, we do not know of any other stream cipher design which has such a low gate count.

Problem

• Nonlinear Filter Model
• Cryptography
• Cost-Efficiency

Innovation

• Nonlinear Filter Model
• Cryptography Systems
• Hardware Efficiency