A Comprehensive Study of the Key Enumeration Problem

Ricardo Villanueva-Polanco

doi:10.3390/e21100972

Abstract

In this paper, we will study the key enumeration problem, which is connected to the key recovery problem posed in the cold boot attack setting. In this setting, an attacker with physical access to a computer may obtain noisy data of a cryptographic secret key of a cryptographic scheme from main memory via this data remanence attack. Therefore, the attacker would need a key-recovery algorithm to reconstruct the secret key from its noisy version. We will first describe this attack setting and then pose the problem of key recovery in a general way and establish a connection between the key recovery problem and the key enumeration problem. The latter problem has already been studied in the side-channel attack literature, where, for example, the attacker might procure scoring information for each byte of an Advanced Encryption Standard (AES) key from a side-channel attack and then want to efficiently enumerate and test a large number of complete 16-byte candidates until the correct key is found. After establishing such a connection between the key recovery problem and the key enumeration problem, we will present a comprehensive review of the most outstanding key enumeration algorithms to tackle the latter problem, for example, an optimal key enumeration algorithm (OKEA) and several nonoptimal key enumeration algorithms. Also, we will propose variants to some of them and make a comparison of them, highlighting their strengths and weaknesses.

Highlights

A side-channel attack may be defined as any attack by which an attacker is able to obtain private information of a cryptographic algorithm from its implementation instead of exploiting weaknesses in the implemented algorithm itself
We present a memory-efficient, nonoptimal key enumeration algorithm that generates key candidates of which their total scores are within a given interval [ B1, B2 ] that is based on the algorithm introduced by Martin et al in the research paper [16]
Once a random instance has been generated, each key enumeration algorithm is run for a fixed number of key candidates

Summary

Introduction

A side-channel attack may be defined as any attack by which an attacker is able to obtain private information of a cryptographic algorithm from its implementation instead of exploiting weaknesses in the implemented algorithm itself Most of these attacks are based on a divide-and-conquer approach through which the attacker obtains ranking information about the chunks of the secret key and uses such information to construct key candidates for that key. Exploiting the data remanence property of dynamic random-access memories (DRAMs) , an attacker with physical access to a computer, may procure noisy data of a secret key from main memory via this attack vector After obtaining such data, the attacker’s main task is to recover the secret key from its noisy version.

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