Analysis of Solitaire

TL;DR

This paper analyzes the Solitaire cipher's keystream repetitions, models their bias, proposes modifications to reduce this bias, and discusses the cipher's cycle properties, highlighting the trade-offs between security and manual implementability.

Contribution

It provides a model for keystream repetition bias in Solitaire and suggests modifications to mitigate this bias, balancing security and manual usability.

Findings

Repetition bias accounts for most keystream repetitions.

Proposed modifications can reduce bias but increase complexity.

State update function unlikely to produce short cycles.

Abstract

The Solitaire cipher was designed by Bruce Schneier as a plot point in the novel Cryptonomicon by Neal Stephenson. The cipher is intended to fit the archetype of a modern stream cipher whilst being implementable by hand using a standard deck of cards with two jokers. We find a model for repetitions in the keystream in the stream cipher Solitaire that accounts for the large majority of the repetition bias. Other phenomena merit further investigation. We have proposed modifications to the cipher that would reduce the repetition bias, but at the cost of increasing the complexity of the cipher (probably beyond the goal of allowing manual implementation). We have argued that the state update function is unlikely to lead to cycles significantly shorter than those of a random bijection.