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52-490: Twofish's distinctive features are the use of pre-computed key-dependent S-boxes , and a relatively complex key schedule . One half of an n-bit key is used as the actual encryption key and the other half of the n-bit key is used to modify the encryption algorithm (key-dependent S-boxes). Twofish borrows some elements from other designs; for example, the pseudo-Hadamard transform (PHT) from the SAFER family of ciphers. Twofish has

104-460: A Feistel structure like DES . Twofish also employs a Maximum Distance Separable matrix. When it was introduced in 1998, Twofish was slightly slower than Rijndael (the chosen algorithm for Advanced Encryption Standard ) for 128-bit keys , but somewhat faster for 256-bit keys. Since 2008, virtually all AMD and Intel processors have included hardware acceleration of the Rijndael algorithm via

156-406: A block cipher is a deterministic algorithm that operates on fixed-length groups of bits , called blocks . Block ciphers are the elementary building blocks of many cryptographic protocols . They are ubiquitous in the storage and exchange of data, where such data is secured and authenticated via encryption . A block cipher uses blocks as an unvarying transformation. Even a secure block cipher

208-457: A key stream for the emulation of a synchronous stream cipher . The newer counter (CTR) mode similarly creates a key stream, but has the advantage of only needing unique and not (pseudo-)random values as initialization vectors; the needed randomness is derived internally by using the initialization vector as a block counter and encrypting this counter for each block. From a security-theoretic point of view, modes of operation must provide what

260-413: A round . Usually, the round function R takes different round keys K i as a second input, which is derived from the original key: where M 0 {\displaystyle M_{0}} is the plaintext and M r {\displaystyle M_{r}} the ciphertext, with r being the number of rounds. Frequently, key whitening is used in addition to this. At

312-564: A substitution box implemented as a lookup table as in Data Encryption Standard and Advanced Encryption Standard , a permutation box , and multiplication as in IDEA . A block cipher by itself allows encryption only of a single data block of the cipher's block length. For a variable-length message, the data must first be partitioned into separate cipher blocks. In the simplest case, known as electronic codebook (ECB) mode,

364-511: A 2005 blog entry that this paper did not present a full cryptanalytic attack, but only some hypothesized differential characteristics: "But even from a theoretical perspective, Twofish isn't even remotely broken. There have been no extensions to these results since they were published in 2000." Substitution box In cryptography , an S-box ( substitution-box ) is a basic component of symmetric key algorithms which performs substitution. In block ciphers , they are typically used to obscure

416-402: A block cipher must be secure, in addition to being robust against brute-force attacks . Most block cipher algorithms are classified as iterated block ciphers which means that they transform fixed-size blocks of plaintext into identically sized blocks of ciphertext , via the repeated application of an invertible transformation known as the round function , with each iteration referred to as

468-548: A block size. There is a trade-off though as large block sizes can result in the algorithm becoming inefficient to operate. Earlier block ciphers such as the DES have typically selected a 64-bit block size, while newer designs such as the AES support block sizes of 128 bits or more, with some ciphers supporting a range of different block sizes. A linear cryptanalysis is a form of cryptanalysis based on finding affine approximations to

520-404: A ciphertext ( R n + 1 , L n + 1 ) {\displaystyle (R_{n+1},L_{n+1})} is accomplished by computing for i = n , n − 1 , … , 0 {\displaystyle i=n,n-1,\ldots ,0} Then ( L 0 , R 0 ) {\displaystyle (L_{0},R_{0})}

572-485: A fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about

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624-404: A good block cipher is designed to avoid side-channel attacks, such as branch prediction and input-dependent memory accesses that might leak secret data via the cache state or the execution time. In addition, the cipher should be concise, for small hardware and software implementations. One important type of iterated block cipher known as a substitution–permutation network (SPN) takes a block of

676-443: A means of effectively improving security by combining simple operations such as substitutions and permutations . Iterated product ciphers carry out encryption in multiple rounds , each of which uses a different subkey derived from the original key. One widespread implementation of such ciphers named a Feistel network after Horst Feistel is notably implemented in the DES cipher. Many other realizations of block ciphers, such as

728-679: A message is first split into separate blocks of the cipher's block size (possibly extending the last block with padding bits), and then each block is encrypted and decrypted independently. However, such a naive method is generally insecure because equal plaintext blocks will always generate equal ciphertext blocks (for the same key), so patterns in the plaintext message become evident in the ciphertext output. To overcome this limitation, several so-called block cipher modes of operation have been designed and specified in national recommendations such as NIST 800-38A and BSI TR-02102 and international standards such as ISO/IEC 10116 . The general concept

780-419: A plaintext value P , such that For example, a block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext. The exact transformation is controlled using a second input – the secret key. Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of ciphertext together with the secret key, and yields

832-427: A small block of input bits with another block of output bits. This substitution must be one-to-one , to ensure invertibility (hence decryption). A secure S-box will have the property that changing one input bit will change about half of the output bits on average, exhibiting what is known as the avalanche effect —i.e. it has the property that each output bit will depend on every input bit. A permutation box (P-box)

884-399: A tradeoff would be the precomputation of round subkeys or s-boxes, which can lead to speed increases of a factor of two or more. These come, however, at the cost of more RAM needed to store them. The estimates in the table below are all based on existing 0.35 μm CMOS technology. In 1999, Niels Ferguson published an impossible differential attack that breaks 6 rounds out of 16 of

936-456: Is a permutation of all the bits: it takes the outputs of all the S-boxes of one round, permutes the bits, and feeds them into the S-boxes of the next round. A good P-box has the property that the output bits of any S-box are distributed to as many S-box inputs as possible. At each round, the round key (obtained from the key with some simple operations, for instance, using S-boxes and P-boxes)

988-912: Is accomplished by computing for i = n , n − 1 , … , 0 {\displaystyle i=n,n-1,\ldots ,0} where T i = F ( L i + 1 ′ − R i + 1 ′ , K i ) {\displaystyle T_{i}=\mathrm {F} (L_{i+1}'-R_{i+1}',K_{i})} and ( L n + 1 ′ , R n + 1 ′ ) = H − 1 ( L n + 1 , R n + 1 ) {\displaystyle (L_{n+1}',R_{n+1}')=\mathrm {H} ^{-1}(L_{n+1},R_{n+1})} Then ( L 0 , R 0 ) = ( L 0 ′ , R 0 ′ ) {\displaystyle (L_{0},R_{0})=(L_{0}',R_{0}')}

1040-406: Is combined using some group operation, typically XOR . Decryption is done by simply reversing the process (using the inverses of the S-boxes and P-boxes and applying the round keys in reversed order). In a Feistel cipher , the block of plain text to be encrypted is split into two equal-sized halves. The round function is applied to one half, using a subkey, and then the output is XORed with

1092-498: Is known as semantic security . Informally, it means that given some ciphertext under an unknown key one cannot practically derive any information from the ciphertext (other than the length of the message) over what one would have known without seeing the ciphertext. It has been shown that all of the modes discussed above, with the exception of the ECB mode, provide this property under so-called chosen plaintext attacks . Some modes such as

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1144-511: Is suitable for the encryption of only a single block of data at a time, using a fixed key. A multitude of modes of operation have been designed to allow their repeated use in a secure way to achieve the security goals of confidentiality and authenticity . However, block ciphers may also feature as building blocks in other cryptographic protocols, such as universal hash functions and pseudorandom number generators . A block cipher consists of two paired algorithms , one for encryption, E , and

1196-472: Is termed a perfect S-box . S-boxes can be analyzed using linear cryptanalysis and differential cryptanalysis in the form of a Linear approximation table (LAT) or Walsh transform and Difference Distribution Table (DDT) or autocorrelation table and spectrum. Its strength may be summarized by the nonlinearity (bent, almost bent) and differential uniformity (perfectly nonlinear, almost perfectly nonlinear). Block cipher In cryptography ,

1248-519: Is that it also splits the input block into two equal pieces. However, the round function is applied to the difference between the two, and the result is then added to both half blocks. Let F {\displaystyle \mathrm {F} } be the round function and H {\displaystyle \mathrm {H} } a half-round function and let K 0 , K 1 , … , K n {\displaystyle K_{0},K_{1},\ldots ,K_{n}} be

1300-858: Is the plaintext again. Many modern block ciphers and hashes are ARX algorithms—their round function involves only three operations: (A) modular addition, (R) rotation with fixed rotation amounts, and (X) XOR . Examples include ChaCha20 , Speck , XXTEA , and BLAKE . Many authors draw an ARX network, a kind of data flow diagram , to illustrate such a round function. These ARX operations are popular because they are relatively fast and cheap in hardware and software, their implementation can be made extremely simple, and also because they run in constant time, and therefore are immune to timing attacks . The rotational cryptanalysis technique attempts to attack such round functions. Other operations often used in block ciphers include data-dependent rotations as in RC5 and RC6 ,

1352-601: Is the plaintext again. One advantage of the Feistel model compared to a substitution–permutation network is that the round function F {\displaystyle {\rm {F}}} does not have to be invertible. The Lai–Massey scheme offers security properties similar to those of the Feistel structure . It also shares the advantage that the round function F {\displaystyle \mathrm {F} } does not have to be invertible. Another similarity

1404-419: Is to use randomization of the plaintext data based on an additional input value, frequently called an initialization vector , to create what is termed probabilistic encryption . In the popular cipher block chaining (CBC) mode, for encryption to be secure the initialization vector passed along with the plaintext message must be a random or pseudo-random value, which is added in an exclusive-or manner to

1456-742: The AES , are classified as substitution–permutation networks . The root of all cryptographic block formats used within the Payment Card Industry Data Security Standard (PCI DSS) and American National Standards Institute (ANSI) standards lies with the Atalla Key Block (AKB), which was a key innovation of the Atalla Box , the first hardware security module (HSM). It was developed in 1972 by Mohamed M. Atalla , founder of Atalla Corporation (now Utimaco Atalla ), and released in 1973. The AKB

1508-501: The AES instruction set ; Rijndael implementations that use the instruction set are now orders of magnitude faster than (software) Twofish implementations. Twofish was designed by Bruce Schneier , John Kelsey , Doug Whiting , David Wagner , Chris Hall , and Niels Ferguson : the "extended Twofish team" met to perform further cryptanalysis of Twofish. Other AES contest entrants included Stefan Lucks , Tadayoshi Kohno , and Mike Stay . The Twofish cipher has not been patented , and

1560-570: The Data Encryption Standard (DES), but in some ciphers the tables are generated dynamically from the key (e.g. the Blowfish and the Twofish encryption algorithms). One good example of a fixed table is the S-box from DES (S 5 ), mapping 6-bit input into a 4-bit output: Given a 6-bit input, the 4-bit output is found by selecting the row using the outer two bits (the first and last bits), and

1612-426: The key size ), and a bit string P , of length n (called the block size ), and returns a string C of n bits. P is called the plaintext , and C is termed the ciphertext . For each K , the function E K ( P ) is required to be an invertible mapping on {0,1} . The inverse for E is defined as a function taking a key K and a ciphertext C to return

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1664-528: The reference implementation has been placed in the public domain . As a result, the Twofish algorithm is free for anyone to use without any restrictions whatsoever. It is one of a few ciphers included in the OpenPGP standard (RFC 9580). However, Twofish has seen less widespread usage than Blowfish , which has been available longer. During the design of Twofish, performance was always an important factor. It

1716-433: The 256-bit key version using 2 steps. As of 2000, the best published cryptanalysis of the Twofish block cipher is a truncated differential cryptanalysis of the full 16-round version. The paper claims that the probability of truncated differentials is 2 per block and that it will take roughly 2 chosen plaintexts (32  petabytes worth of data) to find a good pair of truncated differentials. Bruce Schneier responded in

1768-449: The CBC mode only operate on complete plaintext blocks. Simply extending the last block of a message with zero bits is insufficient since it does not allow a receiver to easily distinguish messages that differ only in the number of padding bits. More importantly, such a simple solution gives rise to very efficient padding oracle attacks . A suitable padding scheme is therefore needed to extend

1820-514: The United States National Bureau of Standards (subsequently the U.S. National Institute of Standards and Technology , NIST) in 1977 was fundamental in the public understanding of modern block cipher design. It also influenced the academic development of cryptanalytic attacks . Both differential and linear cryptanalysis arose out of studies on DES design. As of 2016 , there is a palette of attack techniques against which

1872-565: The action of a cipher . Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis . The discovery is attributed to Mitsuru Matsui , who first applied the technique to the FEAL cipher (Matsui and Yamagishi, 1992). Integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with

1924-522: The basic operation is as follows: Split the plaintext block into two equal pieces, ( L 0 {\displaystyle L_{0}} , R 0 {\displaystyle R_{0}} ) For each round i = 0 , 1 , … , n {\displaystyle i=0,1,\dots ,n} , compute Then the ciphertext is ( R n + 1 , L n + 1 ) {\displaystyle (R_{n+1},L_{n+1})} . The decryption of

1976-423: The beginning and the end, the data is modified with key material (often with XOR ): Given one of the standard iterated block cipher design schemes, it is fairly easy to construct a block cipher that is cryptographically secure, simply by using a large number of rounds. However, this will make the cipher inefficient. Thus, efficiency is the most important additional design criterion for professional ciphers. Further,

2028-419: The ciphertext is ( L n + 1 , R n + 1 ) = ( L n + 1 ′ , R n + 1 ′ ) {\displaystyle (L_{n+1},R_{n+1})=(L_{n+1}',R_{n+1}')} . The decryption of a ciphertext ( L n + 1 , R n + 1 ) {\displaystyle (L_{n+1},R_{n+1})}

2080-404: The column using the inner four bits. For example, an input " 0 1101 1 " has outer bits " 01 " and inner bits "1101"; the corresponding output would be "1001". When DES was first published in 1977, the design criteria of its S-boxes were kept secret to avoid compromising the technique of differential cryptanalysis (which was not yet publicly known). As a result, research in what made good S-boxes

2132-419: The first plaintext block before it is encrypted. The resultant ciphertext block is then used as the new initialization vector for the next plaintext block. In the cipher feedback (CFB) mode, which emulates a self-synchronizing stream cipher , the initialization vector is first encrypted and then added to the plaintext block. The output feedback (OFB) mode repeatedly encrypts the initialization vector to create

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2184-547: The last plaintext block to the cipher's block size. While many popular schemes described in standards and in the literature have been shown to be vulnerable to padding oracle attacks, a solution that adds a one-bit and then extends the last block with zero-bits, standardized as "padding method 2" in ISO/IEC 9797-1, has been proven secure against these attacks. This property results in the cipher's security degrading quadratically, and needs to be taken into account when selecting

2236-534: The original 128-bit block of plain text. For each key K , E K is a permutation (a bijective mapping) over the set of input blocks. Each key selects one permutation from the set of ( 2 n ) ! {\displaystyle (2^{n})!} possible permutations. The modern design of block ciphers is based on the concept of an iterated product cipher . In his seminal 1949 publication, Communication Theory of Secrecy Systems , Claude Shannon analyzed product ciphers and suggested them as

2288-438: The other for decryption, D . Both algorithms accept two inputs: an input block of size n bits and a key of size k bits; and both yield an n -bit output block. The decryption algorithm D is defined to be the inverse function of encryption, i.e., D = E . More formally, a block cipher is specified by an encryption function which takes as input a key K , of bit length k (called

2340-441: The other half. The two halves are then swapped. Let F {\displaystyle {\rm {F}}} be the round function and let K 0 , K 1 , … , K n {\displaystyle K_{0},K_{1},\ldots ,K_{n}} be the sub-keys for the rounds 0 , 1 , … , n {\displaystyle 0,1,\ldots ,n} respectively. Then

2392-436: The plaintext and the key as inputs and applies several alternating rounds consisting of a substitution stage followed by a permutation stage —to produce each block of ciphertext output. The non-linear substitution stage mixes the key bits with those of the plaintext, creating Shannon's confusion . The linear permutation stage then dissipates redundancies, creating diffusion . A substitution box (S-box) substitutes

2444-400: The public rediscovery of differential cryptanalysis, showing that they had been carefully tuned to increase resistance against this specific attack such that it was no better than brute force . Biham and Shamir found that even small modifications to an S-box could significantly weaken DES. Any S-box where any linear combination of output bits is produced by a bent function of the input bits

2496-469: The relationship between the key and the ciphertext , thus ensuring Shannon's property of confusion . Mathematically, an S-box is a nonlinear vectorial Boolean function . In general, an S-box takes some number of input bits , m , and transforms them into some number of output bits, n , where n is not necessarily equal to m . An m × n S-box can be implemented as a lookup table with 2 words of n bits each. Fixed tables are normally used, as in

2548-949: The sub-keys for the rounds 0 , 1 , … , n {\displaystyle 0,1,\ldots ,n} respectively. Then the basic operation is as follows: Split the plaintext block into two equal pieces, ( L 0 {\displaystyle L_{0}} , R 0 {\displaystyle R_{0}} ) For each round i = 0 , 1 , … , n {\displaystyle i=0,1,\dots ,n} , compute where T i = F ( L i ′ − R i ′ , K i ) {\displaystyle T_{i}=\mathrm {F} (L_{i}'-R_{i}',K_{i})} and ( L 0 ′ , R 0 ′ ) = H ( L 0 , R 0 ) {\displaystyle (L_{0}',R_{0}')=\mathrm {H} (L_{0},R_{0})} Then

2600-500: Was a key block, which is required to securely interchange symmetric keys or PINs with other actors in the banking industry . This secure interchange is performed using the AKB format. The Atalla Box protected over 90% of all ATM networks in operation as of 1998, and Atalla products still secure the majority of the world's ATM transactions as of 2014. The publication of the DES cipher by

2652-406: Was designed to allow for several layers of performance trade offs, depending on the importance of encryption speed, memory usage, hardware gate count, key setup and other parameters. This allows a highly flexible algorithm, which can be implemented in a variety of applications. There are multiple space–time tradeoffs that can be made, in software as well as in hardware for Twofish. An example of such

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2704-486: Was sparse at the time. Rather, the eight S-boxes of DES were the subject of intense study for many years out of a concern that a backdoor (a vulnerability known only to its designers) might have been planted in the cipher. As the S-boxes are the only nonlinear part of the cipher, compromising those would compromise the entire cipher. The S-box design criteria were eventually published (in Coppersmith 1994 ) after

#198801