Synthesizing Probabilistic Saturating Counters with Differentially Private Formal Guarantees

2026-08-11

AI Summary

This work addresses the vulnerability of conventional deterministic saturating counters to side-channel attacks, wherein adversaries can infer branch directions through Prime+Probe observations. For the first time, the paper models probabilistic saturating counters as probabilistic Moore machines and formally analyzes their security within a differential privacy framework. By leveraging steady-state analysis of Markov chains and parameter synthesis, the authors derive optimal attack strategies and automatically synthesize counter parameters that satisfy pure differential privacy guarantees. The proposed approach provides provable privacy protection while maintaining branch prediction accuracy comparable to existing schemes, with theoretical misprediction rates validated on benchmark programs.

Abstract

Branch predictors improve instruction-level parallelism in modern processors and are commonly modeled using saturating counters. However, classical saturating counters are deterministic and thus vulnerable to side-channel attacks: an attacker can manipulate the counter state and infer the branch direction of a victim process. Probabilistic saturating counters (PSCs) have been proposed to mitigate this leakage by randomizing counter updates, but existing evaluations are mainly empirical. In this paper, we give a formal analysis based on differential privacy (DP): we model PSCs and the corresponding Prime+Probe attack strategies as probabilistic Moore machines, derive optimal attack strategies, and quantify the attacker's distinguishing power through DP. Our DP guarantee applies to the PSC primitive under the Prime+Probe observation model; end-to-end security for a full branch predictor under repeated or adaptive attacks is an important direction for future work. We then synthesize parameters for an enhanced PSC that satisfies a target pure DP guarantee. To evaluate utility, we derive the stationary misprediction rate and validate the theoretical predictions on benchmark programs. Compared to deterministic and existing probabilistic saturating counters, the synthesized PSCs provide formal security guarantees while preserving competitive prediction performance.

Problem

• side-channel attacks
• branch prediction
• saturating counters
• differential privacy
• information leakage

Innovation

• differential privacy
• probabilistic saturating counters
• formal security guarantees
• branch prediction
• side-channel mitigation