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  2. Need of Security • For the first few decades computer networks were primarily used by university researchers for sending e-mail and by corporate employees for sharing printers. • In these conditions, security did not get a lot of attention. • As we know that presently, millions of ordinary citizens are using networks for banking, shopping, and filing their tax returns, so that network security potentially considerable (huge/gigantic) problem. • Security is a broad topic and covers a large amount of commitment: 1) It is concerned with making sure that nosy people cannot read, or secretly modify messages intended for other recipients. 2) It is concerned with people trying to access remote services that they are not authorized to use. 3) Security also deals with the problems of legitimate (legal) messages being captured and replayed, and with people trying to deny that they sent certain messages.

  3. Need for Security Most security problems are intentionally caused by malicious people trying to gain some benefit, get attention, or to harm someone. A few of the most common harmful/illegal are listed in below table: Some people who cause security problems and why.

  4. Network security problems can be divided roughly into four closely intertwined (twist) areas: • Secrecy (Message Confidentiality): • It is also known as confidentiality. • Message confidentiality or privacy means that the sender and the receiver expect confidentiality. • The transmitted message must make sense to only the intended receiver. • To all others, the message must be garbage. • When a customer communicates with her/his bank, she expects that the communication is totally confidential. • It means that keeping information out of the hands of unauthorized users. • Authentication (Message Authentication): • In message authentication the receiver needs to be sure of the sender's identity and that an imposter (fraud) has not sent the message. • It deals with determining whom we are talking to before revealing sensitive information or entering into a business deal. • Message authentication is a service beyond message integrity.

  5. 3) Nonrepudiation (Message Nonrepudiation): • Message nonrepudiation means that a sender must not be able to deny sending a message that he or she did send. • The burden of proof falls on the receiver. • For example, when a customer sends a message to transfer money from one account to another, the bank must have proof (in terms of signatures) that the customer actually requested this transaction. Another example is how we prove that our customer really placed an electronic order? 4)Integrity Control (Message integrity): • Integrity means that the data must arrive at the receiver exactly as they were sent. It means that how can we sure that a message we received was really the one which is sent by actual recipient and not modified during the transit or concocted by malicious challenger. • There must be no changes during the transmission, neither accidentally nor maliciously. • As more and more monetary exchanges occur over the Internet, integrity is crucial. • For example, it would be disastrous if a request for transferring $100 changed to a request for $10,000 or $100,000. • The integrity of the message must be preserved in a secure communication. • Integrity and secrecy are achieved by using registered mail and locking documents up.

  6. People authenticate other people by recognizing their faces, voices, and handwriting. • Proof of signing is handled by signatures on letterhead paper, raised seals, and so on. • Tampering can usually be detected by handwriting, ink, and paper experts. • For the electronically devices none of the above options are available. Clearly, other solutions are needed. • There is probably no one single place considering where in the protocol stack network security belong. • Every layer has something to contribute. • In the physical layer, wiretapping can be foiled (blocked) by enclosing transmission lines in sealed tubes containing gas at high pressure. Any attempt to drill into a tube will release some gas, reducing the pressure and triggering an alarm. Some military systems use this technique. • In the data link layer, packets on a point-to-point line can be encrypted as they leave one machine and decrypted as they enter another. All the details can be handled in the data link layer, with higher layers unaware to what is going on. This solution breaks down when packets have to traverse multiple routers, because packets have to be decrypted at each router, leaving them vulnerable to attacks from within the router. Also, it does not allow some sessions to be protected (e.g., those involving on-line purchases by credit card) and others not. However, link encryption can be added to any network easily and is often useful.

  7. In the network layer, firewalls can be installed to keep good packets and bad packets out. IP security also functions in this layer. • In the transport layer, entire connections can be encrypted, end to end, that is, process to process. For maximum security, end-to-end security is required. • Finally, issues such as user authentication and nonrepudiation can only be handled in the application layer. • Cryptography is a method of storing and transmitting data in a form that only those it is intended for can read and process. It is a science of protecting information by encoding it into an unreadable format. Cryptography is an effective way of protecting sensitive information as it is stored on media or transmitted through network communication paths.

  8. Some Terms • 2)Plaintext and Ciphertext • The original message, before being transformed, is called plaintext. • After the message is transformed, it is called ciphertext. • An encryption algorithm transforms the plaintext into ciphertext; a decryption algorithm transforms the ciphertext back into plaintext. • The sender uses an encryption algorithm, and the receiver uses a decryption algorithm. 1) Cryptography • Cryptography comes from the Greek words, it means that ''secret writing”. It refers to the science and art of transforming messages to make them secure and protected to attacks.

  9. 3) Cipher • A cipher is a character-for-character or bit-for-bit transformation, without regard to the linguistic structure of the message. • We refer to encryption and decryption algorithms as ciphers. • The term cipher is also used to refer to different categories of algorithms in cryptography. • A code replaces one word with another word or symbol. • The most successful code ever devised was used by the U.S. armed forces during World War II in the Pacific. 4) Key • A key is a number (or a set of numbers) that the cipher as an algorithm operates on. • To encrypt a message, we need an encryption algorithm, an encryption key, and the plaintext. • These create the ciphertext. • To decrypt a message, we need a decryption algorithm, a decryption key, and the ciphertext. • These reveal the original plaintext.

  10. Algorithm Set of mathematical rules used in encryption and decryption Cryptography Science of secret writing that enables you to store and transmit data in a form that is available only to the intended individuals Cryptosystem Hardware or software implementation of cryptography that transforms a message to ciphertext and back to plaintext Cryptanalysis Practice of obtaining plaintext from ciphertext without a key or breaking the encryption Cryptology The study of both cryptography and cryptanalysis Ciphertext Data in encrypted or unreadable format Encipher Act of transforming data into an unreadable format Decipher Act of transforming data into a readable format Key Secret sequence of bits and instructions that governs the act of encryption and decryption Key clustering Instance when two different keys generate the same ciphertext from the same plaintext Keyspace Possible values used to construct keys Plaintext Data in readable format, also referred to as cleartext Work factor Estimated time, effort, and resources necessary to break a cryptosystem

  11. An Introduction to Cryptography The encryption model (for a symmetric-key cipher). Dk(Ek(P))=P

  12. The messages to be encrypted, known as the plaintext, are transformed by a function that is parameterized by a key. • The output of the encryption process, known as the ciphertext, is then transmitted, often by messenger or radio. • We assume that the enemy, or intruder, hears and accurately copies down the complete ciphertext. • However, unlike the intended recipient, he does not know what the decryption key is and so cannot decrypt the ciphertext easily. • Sometimes the intruder can not only listen to the communication channel (passive intruder) but can also record messages and play them back later, inject his own messages, or modify legitimate messages before they get to the receiver (active intruder). • The art of breaking ciphers called cryptanalysis, and the art devising them (cryptography) is collectively known as cryptology. • It will often be useful to have a notation for relating plaintext, ciphertext, and keys. • We will use C = EK(P) to mean that the encryption of the plaintext P using key K gives the ciphertext C. • Similarly, P = DK(C) represents the decryption of C to get the plaintext again. • It then follows that

  13. This notation suggests that E and D are just mathematical functions, which they are. • The only tricky part is that both are functions of two parameters, and we have written one of the parameters (the key) as a subscript, rather than as an argument, to distinguish it from the message. • A fundamental rule of cryptography is that one must assume that the cryptanalyst knows the methods used for encryption and decryption. • In other words, the cryptanalyst knows how the encryption method, E, and decryption, D, as shown in diagram. • The amount of effort necessary to invent, test, and install a new algorithm every time the old method is compromised (or thought to be compromised) has always made it impractical to keep the encryption algorithm secret. • Thinking it is secret when it is not does more harm than good. • This is where the key enters. • The key consists of a (relatively) short string that selects one of many potential encryptions. • In contrast to the general method, which may only be changed every few years, the key can be changed as often as required. • Thus, our basic model is a stable and publicly-known general method parameterized by a secret and easily changed key.

  14. The idea that the cryptanalyst knows the algorithms and that the secrecy lies completely in the keys is called Kerckhoff's principle, named after the Flemish military cryptographer Auguste Kerckhoff who first stated it in 1883. • Thus, we have: • Kerckhoff's principle: All algorithms must be public; only the keys are secret • The nonsecrecy of the algorithm cannot be emphasized enough. • Trying to keep the algorithm secret, known in the trade as security by obscurity, never works. • Also, by publicizing the algorithm, the cryptographer gets free consulting from a large number of academic cryptologists eager to break the system so they can publish papers demonstrating how smart they are. • If many experts have tried to break the algorithm for 5 years after its publication and no one has succeeded, it is probably pretty solid. • Since the real secrecy is in the key, its length is a major design issue. • Consider a simple combination lock. The general principle is that we enter digits in sequence. • Everyone knows this, but the key is secret. • A key length of two digits means that there are 100 possibilities.

  15. A key length of three digits means 1000 possibilities, and a key length of six digits means a million. • The longer the key, the higher the work factor the cryptanalyst has to deal with. • The work factor for breaking the system by exhaustive search of the key space is exponential in the key length. • Secrecy comes from having a strong (but public) algorithm and a long key. • To prevent our kid brother from reading our e-mail, 64-bit keys will do. • For routine commercial use, at least 128 bits should be used. • To keep major governments at bay, keys of at least 256 bits, preferably more, are needed. • From the cryptanalyst's point of view, the cryptanalysis problem has three principal variations. • When he has a quantity of ciphertext and no plaintext, he is confronted with the ciphertext-only problem. The cryptograms that appear in the puzzle section of newspapers pose this kind of problem. • When the cryptanalyst has some matched ciphertext and plaintext, the problem is called the known plaintext problem. • when the cryptanalyst has the ability to encrypt pieces of plaintext of his own choosing, we have the chosen plaintext problem.

  16. Newspaper cryptograms could be broken trivially if the cryptanalyst were allowed to ask such questions as: What is the encryption of ABCDEFGHIJKL? • Novices in the cryptography business often assume that if a cipher can withstand a ciphertext-only attack, it is secure. • This assumption is very inexperienced. • In many cases the cryptanalyst can make a good guess at parts of the plaintext. • For example, the first thing many computers say when we call them up is login: . Equipped with some matched plaintext-ciphertext pairs, the cryptanalyst's job becomes much easier. • To achieve security, the cryptographer should be conservative and make sure that the system is unbreakable even if his opponent can encrypt arbitrary amounts of chosen plaintext.

  17. Categories of Cryptography • We can divide all the cryptography algorithms (ciphers) into two groups: symmetric key (also called secret-key) cryptography algorithms and asymmetric (also called public-key) cryptography algorithms.

  18. Symmetric-Key Cryptography • In symmetric-key cryptography, the same key is used by both parties. • The sender uses this key and an encryption algorithm to encrypt data; the receiver uses the same key and the corresponding decryption algorithm to decrypt the data.

  19. Asymmetric-Key Cryptography • In asymmetric or public-key cryptography, there are two keys: a private key and a public key. • The private key is kept by the receiver. The public key is announced to the public. • In public-key encryption/decryption, the public key that is used for encryption is different from the private key that is used for decryption. • The public key is available to the public; the private key is available only to an individual.

  20. Three Types of Keys • The three types of keys in cryptography: • The secret key: The secret key is the shared key used in symmetric-key cryptography. • The public key: used in asymmetric-key cryptography. • The private key: used in asymmetric-key cryptography. • We will use three different icons for these keys to distinguish one from the others, as shown in below diagram:

  21. Comparison • Let us compare symmetric-key and asymmetric-key cryptography. • Encryption can be thought of as electronic locking; decryption as electronic unlocking. • The sender puts the message in a box and locks the box by using a key; the receiver unlocks the box with a key and takes out the message. • The difference lies in the mechanism of the locking and unlocking and the type of keys used. • In symmetric-key cryptography, the same key locks and unlocks the box. • In asymmetric-key cryptography, one key locks the box, but another key is needed to unlock it. • Given below diagram shows the difference.

  22. Traditional Ciphers • We can divide traditional symmetric-key ciphers into two broad categories: substitution ciphers and transposition ciphers. OR • Encryption methods have been divided into two categories: substitution ciphers and transposition ciphers.

  23. Substitution Ciphers • In a substitution cipher each letter (character) or group of letters is replaced by another letter (character) or group of letters to disguise it. • One of the oldest known ciphers is the Caesar cipher, attributed to Julius Caesar. This is referred to as a shift alphabet cipher. • In this method, a becomes D, b becomes E, c becomes F, ... , and z becomes C. • If the symbols are digits (0 to 9), we can replace 3 with 7, and 2 with 6. • For example, attack becomes DWWDFN. • In examples, plaintext will be given in lower case letters, and ciphertext in upper case letters. • A slight generalization of the Caesar cipher allows the ciphertext alphabet to be shifted by k letters, instead of always 3. In this case k becomes a key to the general method of circularly shifted alphabets. • If we use 4 as a key then attack becomes the EXXEGO.

  24. monoalphabetic substitution: • The next improvement is to have each of the symbols in the plaintext map onto some other letter. • For example, plaintext: a b c d e f g h i j k l m n o p q r s t u v w x y z ciphertext: Q W E R T Y U I O P A S D F G H J K L Z X C V B N M • In a monoalphabetic cipher, a character (or a symbol) in the plaintext is always changed to the same character (or symbol) in the ciphertext regardless of its position in the text. (i.e. The general system of symbol-for-symbol substitution is called a monoalphabetic substitution, with the key being the 26-letter string corresponding to the full alphabet.) • For example, if the algorithm says that character A in the plaintext is changed to character D, every character A is changed to character D. • In other words, the relationship between characters in the plaintext and the ciphertext is a one-to-one relationship. • For the key above, the plaintext attack would be transformed into the ciphertext QZZQEA.

  25. At first glance this might appear to be a safe system because though the cryptanalyst knows the general system (letter-for-letter substitution), he does not know which of the 26! 4 x 1026 possible keys is in use. • In contrast with the Caesar cipher, trying all of them is not a promising approach. • Even at 1 nsec per solution, a computer would take 1010 years to try all the keys. • However, given a surprisingly small amount of ciphertext, the cipher can be broken easily. • The basic attack takes advantage of the statistical properties of natural languages. • In English, for example, e is the most common letter, followed by t, o, a, n, i, etc. • The most common two-letter combinations, or digrams, are th, in, er, re, and an. • The most common three-letter combinations, or trigrams, are the, ing, and, and ion.

  26. A cryptanalyst trying to break a monoalphabetic cipher would start out by counting the relative frequencies of all letters in the ciphertext. • Then he might tentatively assign the most common one to e and the next most common one to t. • He would then look at trigrams to find a common one of the form tXe, which strongly suggests that X is h. • Similarly, if the pattern thYt occurs frequently, the Y probably stands for a. • With this information, he can look for a frequently occurring trigram of the form aZW, which is most likely and. • By making guesses at common letters, digrams, and trigrams and knowing about likely patterns of vowels and consonants, the cryptanalyst builds up a tentative plaintext, letter by letter. • Another approach is to guess a probable word or phrase. • For example, consider the following ciphertext from an accounting firm (blocked into groups of five characters): CTBMN BYCTC BTJDS QXBNS GSTJC BTSWX CTQTZ CQVUJ QJSGS TJQZZ MNQJS VLNSX VSZJU JDSTS JQUUS JUBXJ DSKSU JSNTK BGAQJ ZBGYQ TLCTZ BNYBN QJSW

  27. A likely word in a message from an accounting firm is financial. • Using our knowledge that financial has a repeated letter (i), with four other letters between their occurrences, we look for repeated letters in the ciphertext at this spacing. • We find 12 hits, at positions 6, 15, 27, 31, 42, 48, 56, 66, 70, 71, 76, and 82. • However, only two of these, 31 and 42, have the next letter (corresponding to n in the plaintext) repeated in the proper place. • Of these two, only 31 also has the a correctly positioned, so we know that financial begins at position 30. • From this point on, deducing the key is easy by using the frequency statistics for English text.

  28. The simplest monoalphabetic cipher is probably the shift cipher. • We assume that the plaintext and ciphertext consist of uppercase letters (A to Z) only. • In this cipher, the encryption algorithm is "shift key characters down," with key equal to some number. • The decryption algorithm is "shift key characters up." • For example, if the key is 5, the encryption algorithm is "shift 5 characters down" (toward the end of the alphabet). • The decryption algorithm is "shift 5 characters up" (toward the beginning of the alphabet). • Of course, if we reach the end or beginning of the alphabet, we wrap around.

  29. Example: Use the shift cipher with key = 15 to encrypt the message "HELLO." Solution: We encrypt one character at a time. Each character is shifted 15 characters down. Letter H is encrypted to W. Letter E is encrypted to T. The first L is encrypted to A. The second L is also encrypted to A. And 0 is encrypted to D. The cipher text is WTAAD. Example: Use the shift cipher with key =15 to decrypt the message "WTAAD." Solution: We decrypt one character at a time. Each character is shifted 15 characters up. Letter W is decrypted to H. Letter T is decrypted to E. The first A is decrypted to L. The second A is decrypted to L. And, finally, D is decrypted to O. The plaintext is HELLO.

  30. Transposition Ciphers • A transposition cipher is a rearrangement of the letters in the plaintext according to some specific system & key (i.e. a permutation of the plaintext). • In a transposition cipher, there is no substitution of characters; instead, their locations change. • A character in the first position of the plaintext may appear in the tenth position of the ciphertext. • A character in the eighth position may appear in the first position. • In other words, a transposition cipher reorders the symbols in a block of symbols. • In this example, MEGABUCK is the key. • The purpose of the key is to number the columns, column 1 being under the key letter closest to the start of the alphabet, and so on. • The plaintext is written horizontally, in rows. • The ciphertext is read out by columns, starting with the column whose key letter is the lowest.

  31. Transposition Ciphers A transposition cipher.

  32. Key In a transposition cipher, the key is a mapping between the position of the symbols in the plaintext and cipher text. For example, the following shows the key using a block of four characters: • Plaintext: 2 4 1 3 • Ciphertext: 1 2 3 4 • In encryption, we move the character at position 2 to position 1, the character at position 4 to position 2, and so on. • In decryption, we do the reverse. • For the more effective security provide, the key should be long which means encryption and decryption of long blocks of data.

  33. Simple example: A route cipher: we arrange the plaintext in a geometrical figure, then copy it out following a different route. e.g. P/T: Now is the time for all good men . . . We arrange this in a rectangle of K columns and extract the ciphertext by the columns: N O W I S T H E T I M E F O R A L L G O O D M E N Ciphertext: NTMAO OHELD WEFLM ITOGE SIRON How do we detect this? Well, the character frequency should be the same as English. More generally, we deal with: Rectangular Columnar Transposition: 1) Arrange horizontally in a rectangle. 2) Use a key to generate a permutation of the columns 3) Read vertically.

  34. Key: SCHMID 613542 Plaintext: sell all stock on Monday 6 1 3 5 4 2 s e l l a l l s t o c k o n M o n d a y Ciphertext: ESNYL KDLTM ACNLO OSLOA

  35. To break a transposition cipher, the cryptanalyst must first be aware that he is dealing with a transposition cipher. • By looking at the frequency of E, T, A, O, I, N, etc., it is easy to see if they fit the normal pattern for plaintext. • If so, the cipher is clearly a transposition cipher, because in such a cipher every letter represents itself, keeping the frequency distribution intact. • The next step is to make a guess at the number of columns. • In many cases a probable word or phrase may be guessed at from the context. • For example, suppose that our cryptanalyst suspects that the plaintext phrase million dollars occurs somewhere in the message. • Observe that digrams MO, IL, LL, LA, IR and OS occur in the ciphertext as a result of this phrase wrapping around. • The ciphertext letter O follows the ciphertext letter M (i.e., they are vertically adjacent in column 4) because they are separated in the probable phrase by a distance equal to the key length. • If a key of length seven had been used, the digrams MD, IO, LL, LL, IA, OR, and NS would have occurred instead. • In fact, for each key length, a different set of digrams is produced in the ciphertext. By hunting for the various possibilities, the cryptanalyst can often easily determine the key length.

  36. The remaining step is to order the columns. • When the number of columns, k, is small, each of the k *(k - 1) column pairs can be examined to see if its digram frequencies match those for English plaintext. • The pair with the best match is assumed to be correctly positioned. • Now each remaining column is tentatively tried as the successor to this pair. • The column whose digram and trigram frequencies give the best match is tentatively assumed to be correct. • The predecessor column is found in the same way. • The entire process is continued until a potential ordering is found. • Chances are that the plaintext will be recognizable at this point (e.g., if milloin occurs, it is clear what the error is). • Some transposition ciphers accept a fixed-length block of input and produce a fixed-length block of output. • These ciphers can be completely described by giving a list telling the order in which the characters are to be output. • For example, the cipher of shown in diagram can be seen as a 64 character block cipher. • Its output is 4, 12, 20, 28, 36, 44, 52, 60, 5, 13 , ... , 62. • In other words, the fourth input character, a, is the first to be output, followed by the twelfth, f, and so on.

  37. One-Time Pads • Constructing an unbreakable cipher is actually quite easy. • First choose a random bit string as the key. • Then convert the plaintext into a bit string, for example by using its ASCII representation. • Finally, compute the XOR of these two strings, bit by bit. • This method, known as the one-time pad, is protected to all present and future attacks no matter how much computational power the intruder has. • The reason derives from information theory: there is simply no information in the message because all possible plaintexts of the given length are equally likely.

  38. An example of how one-time pads are used is given in diagram. • First, message 1, ''I like you.'' is converted to 7-bit ASCII. • Then a one-time pad, pad 1, is chosen and XORed with the message to get the ciphertext. • A cryptanalyst could try all possible one-time pads to see what plaintext came out for each one. • For example, the one-time pad listed as pad 2 in the figure could be tried, resulting in plaintext 2, ''Elvis lives'', which may or may not be probable. • In fact, for every 11-character ASCII plaintext, there is a one-time pad that generates it. • That is what we mean by saying there is no information in the ciphertext: we can get any message of the correct length out of it.

  39. Disadvantage of One-Time Pad • One-time pads are great in theory but have a number of disadvantages in practice. • The key cannot be memorized, so both sender and receiver must carry a written copy with them. If either one is subject to capture, written keys are clearly undesirable. • Additionally, the total amount of data that can be transmitted is limited by the amount of key available. • Another problem is the sensitivity of the method to lost or inserted characters. If the sender and receiver get out of synchronization, all data from then on will appear garbled. • With the advent of computers, the one-time pad might potentially become practical for some applications. • The source of the key could be a special DVD that contains several gigabytes of information and if transported in a DVD movie box and prefixed by a few minutes of video, would not even be suspicious.

  40. Of course, at gigabit network speeds, having to insert a new DVD every 30 sec could become tedious. • And the DVDs must be personally carried from the sender to the receiver before any messages can be sent, which greatly reduces their practical utility. • Solution to the One Time Pad is Quantum Cryptography

  41. Quantum Cryptography • Alice and Bob wants to communicate who is also known as the Principals. • Trudy (Jealous) is intruder. • This algorithm is called BB84 (Bennet & Brassard, 1984) • Quantum cryptography is based on fact that light comes in little packets called Photons. • Photons can be polarized using polarizing filters. • After passing through second filter, intensity of light is proportional to square of cosine of angle between axes. • To generate one-time pad, Alice needs two sets of polarizing filters. • Two filters, vertical and horizontal is called rectilinear basis. • Two filters running 45 degrees is called diagonal basis. • To transform original one time pad to different one for Trudy’s misinterpretation is called privacy amplification. • See bit 7, 10, 11, 14. • Observe next figure.

  42. Two Fundamental Cryptography Principles • Redundancy Cryptographic principle 1: “Messages must contain some redundancy” • User large size of message • Use CRC, Cryptographic Hash, Hamming Code for error detection and correction. • Freshness Cryptographic principle 2: “Some method is needed to foil replay attacks” • Include timestamp in every message. • Suppose after 10 sec, message must be thrown out of the network.

  43. SYMMETRIC-KEY ALGORITHMS • DES –The Data Encryption Standard • AES –The Advanced Encryption Standard • Cipher Modes • Other Ciphers • Cryptanalysis Symmetric Key Algorithms • They use same key for encryption and decryption, that’s why called symmetric key algorithms. • Block Ciphers: which take an n-bit block of plaintext as input and transform it using the key into n-bit block of ciphertext.

  44. P (Permutation) Box Cipher • A P-box (permutation box) cryptographic algorithms can be implemented in either hardware (for speed) or in software (for flexibility), but hardware is faster. • It can performs a transposition at the bit level; it transposes bits. • Transpositions and substitutions can be implemented with simple electrical circuits. • P-boxes are normally keyless (the number of rotations is fixed) . • Given diagram shows a device which is known as a P-box (P stands for permutation), used to effect a transposition on an 8-bit input. • If the 8 bits are designated from top to bottom as 01234567, the output of this particular P-box is 36071245.

  45. By appropriate internal wiring, a P-box can be made to perform any transposition and do it at practically the speed of light since no computation is involved, just signal propagation. • The attacker knows that the general method is permuting the bits. • But it does not known to attackers that which bit goes where it means which is the key.

  46. There are three types of permutations in P-boxes (shown in diagram): • straight permutation • expansion permutation • compression permutation • A straight permutation cipher or a straight P-box has the same number of inputs as outputs. In other words, if the number of inputs is N, the number of outputs is also N. • In an expansion permutation cipher, the number of output ports is greater than the number of input ports. • In a compression permutationcipher, the number of output ports is less than the number of input ports.

  47. S (substitutions) Box Cipher • The input to an S-box is a stream of bits with length N; the result is another stream of bits with length M. • It is not necessarily that the N and M are same. • Given below diagram shows an S-box. • The S-box is normally keyless (the number of rotations is fixed) and is used as an intermediate stage of encryption or decryption. • The function that matches the input to the output may be defined mathematically or by a table.

  48. Substitutions are performed by S-boxes, as shown in diagram. • In this example a 3-bit plaintext is entered and a 3-bit cipher text is output. • The 3-bit input selects one of the eight lines exiting from the first stage and sets it to 1; all the other lines are 0. The second stage is a P-box. The third stage encodes the selected input line in binary again. • With the wiring shown, if the eight octal numbers 01234567 were input one after another, the output sequence would be 24506713. • In other words, 0 has been replaced by 2, 1 has been replaced by 4, etc. • Again, by appropriate wiring of the P-box inside the S-box, any substitution can be accomplished. A device can be built in hardware and can achieve great speed since encoders and decoders have only one or two (subnanosecond) gate delays and the propagation time across the P-box may well be less than 1 picosecond.