Topic

# Advanced Encryption Standard

About: Advanced Encryption Standard is a research topic. Over the lifetime, 4134 publications have been published within this topic receiving 71018 citations. The topic is also known as: Rijndael & AES.

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14 Feb 2002

TL;DR: The underlying mathematics and the wide trail strategy as the basic design idea are explained in detail and the basics of differential and linear cryptanalysis are reworked.

Abstract: 1. The Advanced Encryption Standard Process.- 2. Preliminaries.- 3. Specification of Rijndael.- 4. Implementation Aspects.- 5. Design Philosophy.- 6. The Data Encryption Standard.- 7. Correlation Matrices.- 8. Difference Propagation.- 9. The Wide Trail Strategy.- 10. Cryptanalysis.- 11. Related Block Ciphers.- Appendices.- A. Propagation Analysis in Galois Fields.- A.1.1 Difference Propagation.- A.l.2 Correlation.- A. 1.4 Functions that are Linear over GF(2).- A.2.1 Difference Propagation.- A.2.2 Correlation.- A.2.4 Functions that are Linear over GF(2).- A.3.3 Dual Bases.- A.4.2 Relationship Between Trace Patterns and Selection Patterns.- A.4.4 Illustration.- A.5 Rijndael-GF.- B. Trail Clustering.- B.1 Transformations with Maximum Branch Number.- B.2 Bounds for Two Rounds.- B.2.1 Difference Propagation.- B.2.2 Correlation.- B.3 Bounds for Four Rounds.- B.4 Two Case Studies.- B.4.1 Differential Trails.- B.4.2 Linear Trails.- C. Substitution Tables.- C.1 SRD.- C.2 Other Tables.- C.2.1 xtime.- C.2.2 Round Constants.- D. Test Vectors.- D.1 KeyExpansion.- D.2 Rijndael(128,128).- D.3 Other Block Lengths and Key Lengths.- E. Reference Code.

3,444 citations

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01 Jan 2002

TL;DR: This volume is the authoritative guide to the Rijndael algorithm and AES and professionals, researchers, and students active or interested in data encryption will find it a valuable source of information and reference.

Abstract: From the Publisher:
In October 2000, the US National Institute of Standards and Technology selected the block cipher Rijndael as the Advanced Encryption Standard (AES). AES is expected to gradually replace the present Data Encryption Standard (DES) as the most widely applied data encryption technology.|This book by the designers of the block cipher presents Rijndael from scratch. The underlying mathematics and the wide trail strategy as the basic design idea are explained in detail and the basics of differential and linear cryptanalysis are reworked. Subsequent chapters review all known attacks against the Rijndael structure and deal with implementation and optimization issues. Finally, other ciphers related to Rijndael are presented.|This volume is THE authoritative guide to the Rijndael algorithm and AES. Professionals, researchers, and students active or interested in data encryption will find it a valuable source of information and reference.

2,140 citations

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01 Dec 2002TL;DR: In this article, the security of S-boxes in block ciphers was studied under an additional hypothesis that the S-box can be described by an overdefined system of algebraic equations.

Abstract: Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds Nr.In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt'00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure.The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in Nr, with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.

844 citations

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19 Aug 2012

TL;DR: A working implementation of leveled homomorphic encryption without bootstrapping that can evaluate the AES-128 circuit in three different ways, and develops both AES-specific optimizations as well as several "generic" tools for FHE evaluation.

Abstract: We describe a working implementation of leveled homomorphic encryption without bootstrapping that can evaluate the AES-128 circuit in three different ways. One variant takes under over 36 hours to evaluate an entire AES encryption operation, using NTL over GMP as our underlying software platform, and running on a large-memory machine. Using SIMD techniques, we can process over 54 blocks in each evaluation, yielding an amortized rate of just under 40 minutes per block. Another implementation takes just over two and a half days to evaluate the AES operation, but can process 720 blocks in each evaluation, yielding an amortized rate of just over five minutes per block. We also detail a third implementation, which theoretically could yield even better amortized complexity, but in practice turns out to be less competitive.
For our implementations we develop both AES-specific optimizations as well as several "generic" tools for FHE evaluation. These last tools include among others a different variant of the Brakerski-Vaikuntanathan key-switching technique that does not require reducing the norm of the ciphertext vector, and a method of implementing the Brakerski-Gentry-Vaikuntanathan modulus-switching transformation on ciphertexts in CRT representation.

814 citations

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TL;DR: The Advanced Encryption Standard (AES), which has been approved after an international competition by the National Institute of Standards and Technology, is described.

Abstract: In this paper, we describe the Advanced Encryption Standard (AES), which has been approved after an international competition by the National Institute of Standards and Technology.

782 citations