Quantifying Shannon's Work Function for Cryptanalytic Attacks

TL;DR

This paper introduces a formal framework using computability logic to quantify the computational resources needed for cryptanalytic attacks, enabling better security assessments of cryptographic systems.

Contribution

It presents a novel formalism for measuring resource use in cryptanalysis, including hardware considerations, to evaluate cryptographic security more accurately.

Findings

The approach can analyze custom hardware like FPGA in cryptanalysis.

It estimates that breaking some 90-bit cryptographic primitives could take less than two years.

Provides a theoretical basis for resource-based security evaluation.

Abstract

Attacks on cryptographic systems are limited by the available computational resources. A theoretical understanding of these resource limitations is needed to evaluate the security of cryptographic primitives and procedures. This study uses an Attacker versus Environment game formalism based on computability logic to quantify Shannon's work function and evaluate resource use in cryptanalysis. A simple cost function is defined which allows to quantify a wide range of theoretical and real computational resources. With this approach the use of custom hardware, e.g., FPGA boards, in cryptanalysis can be analyzed. Applied to real cryptanalytic problems, it raises, for instance, the expectation that the computer time needed to break some simple 90 bit strong cryptographic primitives might theoretically be less than two years.