Paper 2022/774

Complexity Analysis of the SAT Attack on Logic Locking

Abstract

Due to the adoption of the horizontal business model with the globalization of semiconductor manufacturing, the overproduction of integrated circuits (ICs) and the piracy of intellectual properties (IPs) have become a significant threat to the semiconductor supply chain. Logic locking has emerged as a primary design-for-security measure to counter these threats. In logic locking, ICs become fully functional after fabrication only when unlocked with the correct key. However, Boolean satisfiability-based attacks have rendered most locking schemes ineffective. This gives rise to the numerous defenses and new locking methods to achieve SAT resiliency. This paper provides a unique perspective on the SAT attack efficiency based on conjunctive normal form (CNF) stored in the SAT solver. First, we show that the attack learns a new relation between key bits upon every distinguishing pattern. After each iteration, these additional clauses appended to the solver could significantly decrease the key search complexity. Second, we demonstrate that the SAT attack can break the locking scheme within the linear complexity of key size. The deviation away from linear search can be explained by the oracle's output and different logic gate types. This helps to answer how different distinguishing input eliminates fewer or more incorrect keys. Moreover, we show how key constraints on point functions affect the complexity of SAT attack. The proper key constraint on AntiSAT locking can effectively reduce the SAT attack complexity to constant 1. The same constraint minimizes the complexity of breaking CAS-Lock down to the linear range. Our analysis provides fresh perspectives on the capabilities of SAT attack, and we offer new directions to achieve SAT resiliency.