There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

National Institute of Standards and Technology における超伝導研究及び生活

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area.

/pdf/principles-of-physical-layer-security-in-multiuser-wireless-3w4jvwpgy4.pdf

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

Im Jahre 1977 wurde der „Data Encryption Algorithm“ (DEA) vom „National Bureau of Standards“ (NBS, später „National Institute of Standards and Technology“ – NIST) zum amerikanischen Verschlüsselungsstandard für Bundesbehörden erklärt [NBS_77]. 1981 folgte die Verabschiedung der DEA-Spezifikation als ANSI-Standard „DES“ [ANSI_81]. Die Empfehlung des DES als StandardVerschlüsselungsverfahren wurde auf fünf Jahre befristet und 1983, 1988 und 1993 um jeweils weitere fünf Jahre verlängert. Derzeit liegt eine Neufassung des NISTStandards vor [NIST_99], in dem der DES für weitere fünf Jahre übergangsweise zugelassen sein soll, aber die Verwendung von Triple-DES empfohlen wird: eine dreifache Anwendung des DES mit drei verschiedenen Schlüsseln (effektive Schlüssellänge: 168 bit) [NIST_99]. Der DES basiert auf einer von Horst Feistel bei IBM entwickelten Blockchiffre („Lucipher“) mit einer Schlüssellänge von 128 bit. Da die amerikanische „National Security Agency“ (NSA) dafür gesorgt hatte, daß der DES eine Schlüssellänge von lediglich 64 bit besitzt, von denen nur 56 bit relevant sind, und spezielle Substitutionsboxen (den „kryptographischen Kern“ des Verfahrens) erhielt, deren Konstruktionskriterien von der NSA nicht veröffentlicht wurden, war das Verfahren von Beginn an umstritten. Kritiker nahmen an, daß es eine geheime „Trapdoor“ in dem Verfahren gäbe, die der NSA eine OnlineEntschlüsselung auch ohne Kenntnis des Schlüssels erlauben würde. Zwar ließ sich dieser Verdacht nicht erhärten, aber sowohl die Zunahme von Rechenleistung als auch die Parallelisierung von Suchalgorithmen machen heute eine Schlüssellänge von 56 bit zum Sicherheitsrisiko. Zuletzt konnte 1998 mit einer von der „Electronic Frontier Foundation“ (EFF) entwickelten Spezialmaschine mit 1.800 parallel arbeitenden, eigens entwickelten Krypto-Prozessoren ein DES-Schlüssel in einer Rekordzeit von 2,5 Tagen gefunden werden. Um einen Nachfolger für den DES zu finden, kündigte das NIST am 2. Januar 1997 die Suche nach einem „Advanced Encryption Standard“ (AES) an. Ziel dieser Initiative ist, in enger Kooperation mit Forschung und Industrie ein symmetrisches Verschlüsselungsverfahren zu finden, das geeignet ist, bis weit ins 21. Jahrhundert hinein amerikanische Behördendaten wirkungsvoll zu verschlüsseln. Dazu wurde am 12. September 1997 ein offizieller „Call for Algorithm“ ausgeschrieben. An die vorzuschlagenden symmetrischen Verschlüsselungsalgorithmen wurden die folgenden Anforderungen gestellt: nicht-klassifiziert und veröffentlicht, weltweit lizenzfrei verfügbar, effizient implementierbar in Hardund Software, Blockchiffren mit einer Blocklänge von 128 bit sowie Schlüssellängen von 128, 192 und 256 bit unterstützt. Auf der ersten „AES Candidate Conference“ (AES1) veröffentlichte das NIST am 20. August 1998 eine Liste von 15 vorgeschlagenen Algorithmen und forderte die Fachöffentlichkeit zu deren Analyse auf. Die Ergebnisse wurden auf der zweiten „AES Candidate Conference“ (22.-23. März 1999 in Rom, AES2) vorgestellt und unter internationalen Kryptologen diskutiert. Die Kommentierungsphase endete am 15. April 1999. Auf der Basis der eingegangenen Kommentare und Analysen wählte das NIST fünf Kandidaten aus, die es am 9. August 1999 öffentlich bekanntmachte: MARS (IBM) RC6 (RSA Lab.) Rijndael (Daemen, Rijmen) Serpent (Anderson, Biham, Knudsen) Twofish (Schneier, Kelsey, Whiting, Wagner, Hall, Ferguson).

Advanced Encryption Standard (AES).

Implementations of cryptographic algorithms continue to proliferate in consumer products due to the increasing demand for secure transmission of confidential information. Although the current standard cryptographic algorithms proved to withstand exhaustive attacks, their hardware and software implementations have exhibited vulnerabilities to side channel attacks, e.g., power analysis and fault injection attacks. This paper focuses on fault injection attacks that have been shown to require inexpensive equipment and a short amount of time. The paper provides a comprehensive description of these attacks on cryptographic devices and the countermeasures that have been developed against them. After a brief review of the widely used cryptographic algorithms, we classify the currently known fault injection attacks into low-cost ones (which a single attacker with a modest budget can mount) and high-cost ones (requiring highly skilled attackers with a large budget). We then list the attacks that have been developed for the important and commonly used ciphers and indicate which ones have been successfully used in practice. The known countermeasures against the previously described fault injection attacks are then presented, including intrusion detection and fault detection. We conclude the survey with a discussion on the interaction between fault injection attacks (and the corresponding countermeasures) and power analysis attacks.

/pdf/fault-injection-attacks-on-cryptographic-devices-theory-12qo1dda0z.pdf

Fault Injection Attacks on Cryptographic Devices: Theory, Practice, and Countermeasures

The goal of the Advanced Encryption Standard (AES) is to achieve secure communication. The use of AES does not, however, guarantee reliable communication. Prior work has shown that even a single transient error occurring during the AES encryption (or decryption) process will very likely result in a large number of errors in the encrypted/decrypted data. Such faults must be detected before sending to avoid the transmission and use of erroneous data. Concurrent fault detection is important not only to protect the encryption/decryption process from random faults. It will also protect the encryption/decryption circuitry from an attacker who may maliciously inject faults in order to find the encryption secret key. In this paper, we first describe some studies of the effects that faults may have on a hardware implementation of AES by analyzing the propagation of such faults to the outputs. We then present two fault detection schemes: The first is a redundancy-based scheme while the second uses an error detecting code. The latter is a novel scheme which leads to very efficient and high coverage fault detection. Finally, the hardware costs and detection latencies of both schemes are estimated.

/pdf/error-analysis-and-detection-procedures-for-a-hardware-m0pt3hgj31.pdf

Error analysis and detection procedures for a hardware implementation of the advanced encryption standard

Rijndael is the winner algorithm of the AES contest; therefore it should become the most used symmetric-key cryptographic algorithm. One important application of this new standard is cryptography on smart cards. In this paper we present an optimisation of the Rijndael algorithm to speed up execution on 32-bits processors with memory constraints, such as those used in smart cards. First a theoretical analysis of the Rijndael algorithm and of the proposed optimisation is discussed, and then simulation results of the optimised algorithm on different processors are presented and compared with other reference implementations, as known from the technical literature.

https://link.springer.com/content/pdf/10.1007%2F3-540-36400-5_13.pdf

Efficient Software Implementation of AES on 32-Bit Platforms

This paper presents a new attack against a software implementation of the Advanced Encryption Standard. The attack aims at flushing elements of the SBOX from the cache, thus inducing a cache miss during the encryption phase. The power trace is then used to detect when the cache miss occurs; if the miss happens in the first round of the AES then the information can be used to recover part of the secret key. The attack has been simulated using the Wattch simulation framework and a simple software implementation of AES (using a single table for the SBOX). The attack can be easily extended to more sophisticated versions of AES with more than one table. Eventually, we present a simple countermeasure which does not require randomization.

AES power attack based on induced cache miss and countermeasure

A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of ...

Luca Breveglieri

Papers

Fault Injection Attacks on Cryptographic Devices: Theory, Practice, and Countermeasures

Error analysis and detection procedures for a hardware implementation of the advanced encryption standard

Efficient Software Implementation of AES on 32-Bit Platforms

AES power attack based on induced cache miss and countermeasure

Multi-push-down languages and grammars