Quantum Key Search with Side Channel Advice

Abstract

Abstract. Recently, a number of results have been published that show how to combine classical cryptanalysis with quantum algorithms, thereby (potentially) achieving considerable speed-ups. We follow this trend but add a novel twist by considering how to utilise side channel leakage in a quantum setting. This is non-trivial because Grover's algorithm deals with unstructured data, however we are interested in searching through a key space which has structure due to the side channel information. We present a novel variation of a key enumeration algorithm that produces batches of keys that can be efficiently tested using Grover's algorithm. This results in the first quantum key search that benefits from side channel information.

A Comprehensive Study of the Key Enumeration Problem

“…Broadly speaking, optimal key enumeration algorithms [18,28] tend to consume more memory and to be less efficient while generating high-scoring key candidates, whereas nonoptimal key enumeration algorithms [12][13][14][15][16][17]26,29] are expected to run faster and to consume less memory. Table 1 shows a preliminary taxonomy of the key enumeration algorithms to be reviewed in this section.…”

“…In this subsection, we will describe a quantum key enumeration algorithm introduced in the research paper [29] for the sake of completeness. This algorithm is constructed from a nonoptimal key enumeration algorithm, which uses the key rank algorithm given by Martin et al in the research paper [16] to return a single key candidate (the r th ) with a weight in a particular range.…”

“…Equipped with the getkey algorithm, the authors of [29] introduced a nonoptimal key enumeration algorithm to enumerate and test all key candidates in the given range. This algorithm works by calling the function getKey to obtain a key candidate in the given range until there are no more key candidates in the given range.…”

“…18: Combining together the function keySearch with techniques for searching over partitions independently, the authors of the research paper [29] introduced a key search algorithm, described in Algorithm 20. The function KS works by partitioning the search space into sections of which the size follows a geometrically increasing sequence using a size parameter a = O(1).…”

“…Choose W e such that rank(0, W e ) is approx e; Having introduced the function KS, the authors of the research paper [29] transformed it into a quantum key search algorithm that heavily relies on Grover's algorithm [32]. This is a quantum algorithm to solve the following problem: Given a black box function which returns 1 on a single input x and 0 on all other inputs, find x.…”