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| In [[cryptography]], a '''Feistel cipher''' is a symmetric structure used in the construction of [[block cipher]]s, named after the [[Germany|German]]-born [[physicist]] and cryptographer [[Horst Feistel]] who did pioneering research while working for [[IBM]] (USA); it is also commonly known as a '''Feistel network'''. A large proportion of block [[cipher]]s use the scheme, including the [[Data Encryption Standard]] (DES). The Feistel structure has the advantage that [[encryption]] and [[decryption]] operations are very similar, even identical in some cases, requiring only a reversal of the [[key schedule]]. Therefore the size of the code or circuitry required to implement such a cipher is nearly halved.
| | 1) Ensure we do not inadvertently put yourself inside a starvation mode of metabolism. If you do, correct the situation as shortly because possible plus the simplest way to do this is eat 6 meals per day, graze on food throughout the course of the day.<br><br>On the other hand, overweight people who usually [http://safedietplans.com/bmr-calculator bmr calculator] try to consume just 500 calories a day may virtually probably be starving themselves. Because the body is much more employed to taking in over 2000 calories a day or more, then the abrupt drop of calorie consumption may signal the body into starvation mode. In this way, the body's metabolism might slow right down to conserve vitality.<br><br>We could be guy or female, nevertheless we nonetheless want muscle mass to raise the basal metabolic rate. This is a measure of how several calories your body burns every day. Already you recognize that too numerous unused calories are bad for a wellness, so you want to begin to pay attention to how much muscle is on the body. It is worth it.<br><br>If you're eating fewer calories than you're burning, you'll lose weight. How much? Well, look at it this technique - by burning an additional 500 calories a day, you'll lose one pound each week. Slow progress, sure, however, it's a perfect illustration of how, by keeping track of what you're doing, you can succeed at losing fat.<br><br>Body Surface Area: Your height plus fat contribute a lot in determining bmr. The better is your body surface area, the high is a BMR. Thin, tall persons have a high BMR.<br><br>Most immediate fat loss diets don't include any shape of physical workout. They motivate we to get rid of fat rapidly by eating extremely small. While that will cause a fast initial fat loss, the fat can come back whenever you start to eat normally again.<br><br>So, if you are 40-year-old female whom is 55 plus 150 lb, and we get light exercise, we want 1,959 calories to keep the weight. To lose a pound a week, we have to eat about 1,460 calories a day. If thats too difficult (and it happens to be very low), try upping your exercise. Then youll reach eat 1,700 calories a day. |
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| A Feistel network is an iterated cipher with an internal function called a round function.<ref>{{cite book |title=Handbook of Applied Cryptography |first=Alfred J. |last=Menezes |first2=Paul C. van |last2=Oorschot |first3=Scott A. |last3=Vanstone |edition=Fifth |year=2001 |page=251 |isbn=0849385237 }}</ref>
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| ==Historical==
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| Feistel networks were first seen commercially in IBM's [[Lucifer (cipher)|Lucifer]] cipher, designed by Horst Feistel and [[Don Coppersmith]] in 1973. Feistel networks gained respectability when the U.S. Federal Government adopted the [[Data Encryption Standard|DES]] (a cipher based on Lucifer, with changes made by the [[National Security Agency|NSA]]). Like other components of the DES, the iterative nature of the Feistel construction makes implementing the cryptosystem in hardware easier (particularly on the hardware available at the time of DES's design).
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| ==Theoretical work==
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| Many modern and also some old symmetric block ciphers are based on Feistel networks (e.g. [[GOST 28147-89]] block cipher), and the structure and properties of Feistel ciphers have been extensively explored by [[cryptographer]]s. Specifically, [[Michael Luby]] and [[Charles Rackoff]] analyzed the Feistel cipher construction, and proved that if the round function is a cryptographically secure [[pseudorandom function]], with K<sub>i</sub> used as the seed, then 3 rounds are sufficient to make the block cipher a [[pseudorandom permutation]], while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom even to an adversary who gets [[oracle machine|oracle]] access to its inverse permutation).<ref name=pseudorandom>{{Citation |first1=Michael |last1=Luby |first2=Charles |last2=Rackoff |title=How to Construct Pseudorandom Permutations from Pseudorandom Functions |journal=SIAM Journal on Computing |volume=17 |issue=2 |date=April 1988 |doi=10.1137/0217022 |pages=373–386 |issn=0097-5397}}</ref>
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| Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called Luby–Rackoff block ciphers. Further theoretical work has generalized the construction somewhat, and given more precise bounds for security.<ref name=7-rounds>{{Citation |first=Jacques |editor1-last=Boneh |last=Patarin |editor1-first=Dan |title=Luby-Rackoff: 7 Rounds Are Enough for 2<sup>''n''(1−ε)</sup> Security |url=http://www.iacr.org/archive/crypto2003/27290510/27290510.pdf |doi=10.1007/b11817 |journal=Advances in Cryptology—CRYPTO 2003 |series=Lecture Notes in Computer Science |volume=2729 |date=October 2003 |pages=513–529 |accessdate=2009-07-27}}</ref>
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| ==Construction details==
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| [[File:Feistel cipher diagram en.svg|right]]
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| Let <math>{\rm F}</math> be the round function and let
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| <math>K_0,K_1,\ldots,K_{n}</math> be the sub-keys for the rounds <math>0,1,\ldots,n</math> respectively.
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| Then the basic operation is as follows:
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| Split the plaintext block into two equal pieces, (<math>L_0</math>, <math>R_0</math>)
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| For each round <math>i =0,1,\dots,n</math>, compute
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| :<math>L_{i+1} = R_i\,</math>
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| :<math>R_{i+1}= L_i \oplus {\rm F}(R_i, K_i)</math>. | |
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| Then the ciphertext is <math>(R_{n+1}, L_{n+1})</math>.
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| Decryption of a ciphertext <math>(R_{n+1}, L_{n+1})</math> is accomplished by computing for <math>i=n,n-1,\ldots,0</math>
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| :<math>R_{i} = L_{i+1}\,</math>
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| :<math>L_{i} = R_{i+1} \oplus {\rm F}(L_{i+1}, K_{i})</math>.
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| Then <math>(L_0,R_0)</math> is the plaintext again.
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| One advantage of the Feistel model compared to a [[substitution-permutation network]] is that the round function <math>{\rm F}</math> does not have to be invertible.
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| The diagram illustrates both encryption and decryption. Note the reversal of the subkey order for decryption; this is the only difference between encryption and decryption.
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| ===Unbalanced Feistel cipher===
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| Unbalanced Feistel ciphers use a modified structure where <math>L_0</math> and <math>R_0</math> are not of equal lengths.<ref>http://www.schneier.com/paper-unbalanced-feistel.html</ref> The [[Skipjack (cipher)|Skipjack]] cipher is an example of such a cipher. The [[Texas Instruments]] [[Digital Signature Transponder]] uses a proprietary unbalanced Feistel cipher to perform [[challenge-response authentication]].<ref name=crypto-rfid>S. Bono, M. Green, A. Stubblefield, A. Rubin, A. Juels, M. Szydlo. "Security Analysis of a Cryptographically-Enabled RFID Device". In ''Proceedings of the USENIX Security Symposium'', August 2005. [http://www.usenix.org/events/sec05/tech/bono/bono.pdf (pdf)]</ref>
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| The [[Thorp shuffle]] is an extreme case of an unbalanced Feistel cipher in which one side is a single bit. This has better provable security than a balanced Feistel cipher but requires more rounds.<ref name=thorp>Ben Morris, Phillip Rogaway, Till Stegers. "How to Encipher Messages on a Small Domain". CRYPTO 2009. [http://www.cs.ucdavis.edu/~rogaway/papers/thorp.pdf (pdf)]</ref>
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| ===Other uses===
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| The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the [[Optimal Asymmetric Encryption Padding]] (OAEP) scheme uses a simple Feistel network to randomize ciphertexts in certain [[asymmetric key encryption]] schemes.
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| A generalized Feistel algorithm can be used to create strong permutations on small domains of size not a power of two (see [[format-preserving encryption]]).
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| ===Feistel networks as a design component===
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| Whether the entire cipher is a Feistel cipher or not, Feistel-like networks can be used as a component of a cipher's design. For example, [[MISTY1]] is a Feistel cipher using a three-round Feistel network in its round function, [[Skipjack (cipher)|Skipjack]] is a modified Feistel cipher using a Feistel network in its G permutation, and [[Threefish]] (part of [[Skein (hash function)|Skein]]) is a non-Feistel block cipher that uses a Feistel-like MIX function.
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| ==List of Feistel ciphers==
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| Feistel or modified Feistel:
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| * [[Blowfish (cipher)|Blowfish]]
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| * [[Camellia (cipher)|Camellia]]
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| * [[CAST-128]]
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| * [[Data Encryption Standard|DES]]
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| * [[FEAL]]
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| * [[GOST 28147-89]]
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| * [[Information Concealment Engine|ICE]]
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| * [[KASUMI (block cipher)|KASUMI]]
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| * [[LOKI97]]
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| * [[Lucifer (cipher)|Lucifer]]
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| * [[MARS (cryptography)|MARS]]
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| * [[MAGENTA (cipher)|MAGENTA]]
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| * [[MISTY1]]
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| * [[RC5]]
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| * [[Simon (cipher)|Simon]]
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| * [[Tiny Encryption Algorithm|TEA]]
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| * [[Triple DES]]
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| * [[Twofish]]
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| * [[XTEA]]
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| Generalised Feistel:
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| * [[CAST-256]]
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| * [[CLEFIA]]
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| * [[MacGuffin (cipher)|MacGuffin]]
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| * [[RC2]]
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| * [[RC6]]
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| * [[Skipjack (cipher)|Skipjack]]
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| * [[SMS4]]
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| ==See also==
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| * [[Cryptography]]
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| * [[Stream cipher]]
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| * [[Substitution-permutation network]]
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| * [[Lifting scheme]] for discrete wavelet transform has pretty much the same structure
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| * [[Format-preserving encryption]]
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| * [[Lai-Massey scheme]]
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| ==References==
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| {{Reflist}}
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| {{Cryptography navbox | block}}
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| <!-- To be merged with -->
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| [[Category:Feistel ciphers| ]]
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| {{Link GA|ru}}
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1) Ensure we do not inadvertently put yourself inside a starvation mode of metabolism. If you do, correct the situation as shortly because possible plus the simplest way to do this is eat 6 meals per day, graze on food throughout the course of the day.
On the other hand, overweight people who usually bmr calculator try to consume just 500 calories a day may virtually probably be starving themselves. Because the body is much more employed to taking in over 2000 calories a day or more, then the abrupt drop of calorie consumption may signal the body into starvation mode. In this way, the body's metabolism might slow right down to conserve vitality.
We could be guy or female, nevertheless we nonetheless want muscle mass to raise the basal metabolic rate. This is a measure of how several calories your body burns every day. Already you recognize that too numerous unused calories are bad for a wellness, so you want to begin to pay attention to how much muscle is on the body. It is worth it.
If you're eating fewer calories than you're burning, you'll lose weight. How much? Well, look at it this technique - by burning an additional 500 calories a day, you'll lose one pound each week. Slow progress, sure, however, it's a perfect illustration of how, by keeping track of what you're doing, you can succeed at losing fat.
Body Surface Area: Your height plus fat contribute a lot in determining bmr. The better is your body surface area, the high is a BMR. Thin, tall persons have a high BMR.
Most immediate fat loss diets don't include any shape of physical workout. They motivate we to get rid of fat rapidly by eating extremely small. While that will cause a fast initial fat loss, the fat can come back whenever you start to eat normally again.
So, if you are 40-year-old female whom is 55 plus 150 lb, and we get light exercise, we want 1,959 calories to keep the weight. To lose a pound a week, we have to eat about 1,460 calories a day. If thats too difficult (and it happens to be very low), try upping your exercise. Then youll reach eat 1,700 calories a day.