UNIT4 The Advanced Encryption Standard (AES) PDF

Cryptography (CYS603) The Advanced Encryption Standard (AES)  Understanding Cryptography by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 4 – The Advanced Encryption Standard...

Cryptography (CYS603) The Advanced Encryption Standard (AES)  Understanding Cryptography by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 4 – The Advanced Encryption Standard (AES) ver. October 28, 2009 These slides were prepared by Daehyun Strobel, Christof Paar and Jan Pelzl  Some legal stuff (sorry): Terms of Use The slides can used free of charge. All copyrights for the slides remain with Christof Paar and Jan Pelzl. The title of the accompanying book “Understanding Cryptography” by Springer and the author’s names must remain on each slide. If the slides are modified, appropriate credits to the book authors and the book title must remain within the slides. It is not permitted to reproduce parts or all of the slides in printed form whatsoever without written consent by the authors. 3/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Overview of the AES algorithm Internal structure of AES Byte Substitution layer Diffusion layer Key Addition layer Key schedule Decryption Practical issues 4/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Overview of the AES algorithm Internal structure of AES Byte Substitution layer Diffusion layer Key Addition layer Key schedule Decryption Practical issues 5/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Some Basic Facts AES is the most widely used symmetric cipher today The algorithm for AES was chosen by the US National Institute of Standards and Technology (NIST) in a multi-year selection process The requirements for all AES candidate submissions were: Block cipher with 128-bit block size Three supported key lengths: 128, 192 and 256 bit Security relative to other submitted algorithms Efficiency in software and hardware 6/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Chronology of the AES Selection The need for a new block cipher announced by NIST in January, 1997 15 candidates algorithms accepted in August, 1998 5 finalists announced in August, 1999: Mars – IBM Corporation RC6 – RSA Laboratories Rijndael – J. Daemen & V. Rijmen Serpent – Eli Biham et al. Twofish – B. Schneier et al. In October 2000, Rijndael was chosen as the AES AES was formally approved as a US federal standard in November 2001 7/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   AES: Overview The number of rounds depends on the chosen key length: Key length (bits) Number of rounds 128 10 192 12 256 14 8/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   AES: Overview Iterated cipher with 10/12/14 rounds Each round consists of “Layers” 9/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Overview of the AES algorithm Internal structure of AES Byte Substitution layer Diffusion layer Key Addition layer Key schedule Decryption Practical issues 10/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Internal Structure of AES AES is a byte-oriented cipher The state A (i.e., the 128-bit data path) can be arranged in a 4x4 matrix: A0 A4 A8 A12 A1 A5 A9 A13 A2 A6 A10 A14 A3 A7 A11 A15 with A0,…, A15 denoting the 16-byte input of AES 11/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Internal Structure of AES Round function for rounds 1,2,…,nr-1: Note: In the last round, the MixColumn tansformation is omitted 12/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Byte Substitution Layer The Byte Substitution layer consists of 16 S-Boxes with the following properties: The S-Boxes are identical the only nonlinear elements of AES, i.e., ByteSub(Ai) + ByteSub(Aj) ≠ ByteSub(Ai + Aj), for i,j = 0,…,15 bijective, i.e., there exists a one-to-one mapping of input and output bytes  S-Box can be uniquely reversed In software implementations, the S-Box is usually realized as a lookup table 13/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Diffusion Layer The Diffusion layer provides diffusion over all input state bits consists of two sublayers: ShiftRows Sublayer: Permutation of the data on a byte level MixColumn Sublayer: Matrix operation which combines (“mixes”) blocks of four bytes performs a linear operation on state matrices A, B, i.e., DIFF(A) + DIFF(B) = DIFF(A + B) 14/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   ShiftRows Sublayer Rows of the state matrix are shifted cyclically: Input matrix B0 B4 B8 B12 B1 B5 B9 B13 B2 B6 B10 B14 B3 B7 B11 B15 Output matrix B0 B4 B8 B12 no shift B5 B9 B13 B1 ← one position left shift B10 B14 B2 B6 ← two positions left shift B15 B3 B7 B11 ← three positions left shift 15/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   MixColumn Sublayer Linear transformation which mixes each column of the state matrix Each 4-byte column is considered as a vector and multiplied by a fixed 4x4 matrix, e.g.,  C0   02 03 01 01   B0         C1   01 02 03 01   B5   C    01 01 02 03   B10   2       C3   03 01 01 02   B15  where 01, 02 and 03 are given in hexadecimal notation All arithmetic is done in the Galois field GF(28) (for more information see Chapter 4.3 in Understanding Cryptography) 16/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Key Addition Layer Inputs: 16-byte state matrix C 16-byte subkey ki Output: C  ki The subkeys are generated in the key schedule 17/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Key Schedule Subkeys are derived recursively from the original 128/192/256-bit input key Each round has 1 subkey, plus 1 subkey at the beginning of AES Key length (bits) Number of subkeys 128 11 192 13 256 15 Key whitening: Subkey is used both at the input and output of AES  # subkeys = # rounds + 1 There are different key schedules for the different key sizes 18/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Key Schedule Example: Key schedule for 128-bit key AES Word-oriented: 1 word = 32 bits 11 subkeys are stored in W…W, W…W, … , W…W First subkey W…W is the original AES key 19/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Key Schedule Function g rotates its four input bytes and performs a bytewise S-Box substitution  nonlinearity The round coefficient RC is only added to the leftmost i byte and varies from round to round: RC = x0 = (00000001)2 RC = x1 = (00000010)2 RC = x2 = (00000100)2... RC = x9 = (00110110)2 xi represents an element in a Galois field (again, cf. Chapter 4.3 of Understanding Cryptography) 20/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Overview of the AES algorithm Internal structure of AES Byte Substitution layer Diffusion layer Key Addition layer Key schedule Decryption Practical issues 21/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Decryption AES is not based on a Feistel network  All layers must be inverted for decryption: MixColumn layer → Inv MixColumn layer ShiftRows layer→ Inv ShiftRows layer Byte Substitution layer → Inv Byte Substitution layer Key Addition layer is its own inverse 22/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Decryption Inv MixColumn layer: The To reverse the MixColumn operation, each column of the state matrix C must be multiplied with the inverse of the 4x4 matrix, e.g.,  B0   0E 0B 0D 09   C0         B1   09 0E 0B 0D   C1   B    0D 09 0E 0B    C   2     2   B3   0B 0D 09 0E   C3  where 09, 0B, 0D and 0E are given in hexadecimal notation Again, all arithmetic is done in the Galois field GF(28) (for more information see Chapter 4.3 in Understanding Cryptography) 23/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Decryption Inv ShiftRows layer: All rows of the state matrix B are shifted to the opposite direction: Input matrix B0 B4 B8 B12 B1 B5 B9 B13 B2 B6 B10 B14 B3 B7 B11 B15 Output matrix B0 B4 B8 B12 no shift B13 B1 B5 B9 → one position right shift B10 B14 B2 B6 → two positions right shift B7 B11 B15 B3 → three positions right shift 24/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Decryption Inv Byte Substitution layer: Since the S-Box is bijective, it is possible to construct an inverse, such that Ai = S-1(Bi) = S-1(S(Ai))  The inverse S-Box is used for decryption. It is usually realized as a lookup table Decryption key schedule: Subkeys are needed in reversed order (compared to encryption) In practice, for encryption and decryption, the same key schedule is used. This requires that all subkeys must be computed before the encryption of the first block can begin 25/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Overview of the AES algorithm Internal structure of AES Byte Substitution layer Diffusion layer Key Addition layer Key schedule Decryption Practical issues 26/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Implementation in Software One requirement of AES was the possibility of an efficient software implementation Straightforward implementation is well suited for 8-bit processors (e.g., smart cards), but inefficient on 32-bit or 64-bit processors A more sophisticated approach: Merge all round functions (except the key addition) into one table look-up This results in four tables with 256 entries, where each entry is 32 bits wide One round can be computed with 16 table look-ups Typical SW speeds are more than 1.6 Gbit/s on modern 64-bit processors 27/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Security Brute-force attack: Due to the key length of 128, 192 or 256 bits, a brute-force attack is not possible Analytical attacks: There is no analytical attack known that is better than brute-force Side-channel attacks: Several side-channel attacks have been published Note that side-channel attacks do not attack the underlying algorithm but the implementation of it 28/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl   Lessons Learned AES Is modern AES is a modern block cipher which supports three key lengths of 128, 192 and 256 bit. It To provides excellent long-term security against brute-force attacks. AES has been studied intensively since the late 1990s and no attacks have been found that are better than brute-force. AES is not based on Feistel networks. Its basic operations use Galois field arithmetic and provide strong diffusion and confusion. AES is part of numerous open standards such as IPsec or TLS, in addition to being the mandatory encryption algorithm for US government applications. It seems likely that the cipher will be the dominant encryption algorithm for many years to come. AES is efficient in software and hardware. 29/28 Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl