Paper 2026/713

How to construct even faster and indifferentiable hash functions from random permutations

Han Sui, Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences

Lei Zhang, Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences

Wenling Wu, Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences

Abstract

Designing cryptographic hash functions that simultaneously achieve high throughput and strong provable security remains a fundamental challenge in symmetric cryptography. Traditional constructions, such as the Merkle-Damg\aa rd (MD) and SPONGE paradigms, inherently suffer from structural limitations: they either expose internal chaining values to length-extension attacks or impose a rigid trade-off between security (capacity) and efficiency (rate), bounding their architectural potential. In this paper, we introduce the \textbf{Compress-then-Randomize} paradigm, a modular design principle that structurally decouples a hash function into two independent components with distinct security objectives: (1) a \emph{variable-input-length} (VIL) compression component optimized for high-speed message absorption, requiring only collision resistance and multiple-preimage resistance; and (2) a \emph{fixed-input-length} (FIL) finalization component utilizing independent random permutations to ensure indifferentiability from a random oracle. This separation enables the VIL component to maximize processing throughput (approaching the full primitive width) while the FIL component provides robust randomness extraction, effectively mitigating length-extension attacks and achieving tight security bounds. Leveraging this paradigm, we propose the \textbf{Rocket hash family}, comprising two instantiations: \emph{Rocket-JH} (based on the JH iteration structure with wide-pipe design) and \emph{Rocket-DoubleCBC} (utilizing dual parallel Cipher-Block-Chaining lanes). Both constructions employ pairwise distinct round permutations and achieve superior message processing rates compared to conventional SPONGE-based designs, with Rocket-2 delivering more than $2\times$ the throughput of SHA3-512 for large messages. For practical instantiation without requiring multiple independent cryptographic primitives, we present \textbf{CTR-Perm}, a novel domain-separation technique that derives $2^w$ effectively independent round functions from a single large permutation using a counter-based input diversification. While backward queries introduce a heuristic assumption regarding preimage multiplicity (bounded by a negligible failure probability $\leq 2^{-526}$ for counter size $w \geq 64$ and hash length 512 bits), we prove the construction remains sound for practical message lengths up to $2^{w-8}$ blocks. Finally, to formalize the security-efficiency trade-off, we propose \textbf{Hash Effectiveness} (H.E.), a scale-invariant heuristic metric defined as the product of normalized security level and normalized processing rate. We demonstrate that conventional Merkle-Damg\aa rd and SPONGE constructions exhibit H.E. values fundamentally bounded by $1/8$, whereas the Rocket constructions achieve H.E. values approaching $1/4$ (specifically, $0.227$ for Rocket-2 with Keccak-$p$[1600]), thereby establishing a new Pareto frontier in hash function design.

@misc{cryptoeprint:2026/713,
      author = {Liting Zhang and Han Sui and Lei Zhang and Wenling Wu},
      title = {How to construct even faster and indifferentiable hash functions from random permutations},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/713},
      year = {2026},
      url = {https://eprint.iacr.org/2026/713}
}