Introduction to cryptography with coding theory pdf download

Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Yevgeny Zamyatin. Robert W. Strayer , Eric W. Since Free ebooks since ZLibrary app. Download Coding Theory Cryptography And Related Areas books , A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects.

The book will be useful to students, researchers, professionals, and tutors interested in this area of research. Download Coding Theory And Cryptography books , Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes.

Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, designed for an introductory course on the subject.

Download Algebraic Geometry In Coding Theory And Cryptography books , This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields.

This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available.

Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books.

The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects.

Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.

Download Topics In Geometry Coding Theory And Cryptography books , The theory of algebraic function fields over finite fields has its origins in number theory.

This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles. Download Introduction To Cryptography books , This text is for a course in cryptography for advanced undergraduate and graduate students.

Material is accessible to mathematically mature students having little background in number theory and computer programming. One way uses public key cryptography. A different approach to this problem is to have a trusted third party give keys to Alice and Bob. S e c re t s h a rin g : In Chapter 12, we introduce secret sharing schemes.

Suppose th at you have a combination to a bank safe, but you don't want to trust any single person with the combination to the safe. R ather, you would iike to divide the combination among a group of people, so th a t at least two of these people must be present in order to open the safe.

Secret sharing solves this problem. S e c u rity p ro to c o ls: How can we carry out secure transactions over open channels such as the Internet, and how can we protect credit card 1. C r y p t o g r a p h ic A p p l ic a t io n s 11 information from fraudulent merchants?

E le c tro n ic cash: Credit cards and similar devices are convenient but do not provide anonymity. Clearly a form of electronic cash could be useful, a t least to some people. However, electronic entities can be copied.

We give an example of an electronic cash system th a t provides anonymity but catches counterfeiters. G am e s: How can you flip coins or play poker with people who are not in the same room as you? Dealing the cards, for example, presents a problem. We show how cryptographic ideas can solve these problems. In tliis chapter we shall cover some of the older cryptosystems th a t were primarily used before the advent of the computer.

These cryptosystems are too weak to be of much use today, especially with computers at our disposal, but they give good illustrations of several of the im portant ideas of cryptology.

First, for these simple cryptosystems, we make some conventions. This is even more annoying, but it is alm ost always possible to replace the spaces in the plaintext after decrypting. If spaces were left in, there would be two choices. S h if t C ip h e r s They could be left as spaces; but this yields so much information on the structure of the message th a t decryption becomes easier. O r they could be encrypted; but then they would dom inate frequency counts unless the message averages at least eight letters per word , again simplifying decryption.

Note: In this chapter, we'll be using some concepts from number theory, especially m odular arithm etic. If you are not familiar with congruences, you should read the first three sections of C hapter 3 before proceeding.

He shifted each letter by three places, so a became D, b became E, c became F, etc. The end of the alphabet wrapped around to the beginning, so x became A , y became B, and z became C. Decryption was accomplished by shifting back by three spaces and trying to figure out how to put the spaces back in. We now give the general situation. I f you are not fam iliar with modular arithmetic, read the first few pages of Chapter 3 before continuing.

Label the letters as integers from 0 to T he key is an integer k with 0 i -i- k mod C ip h e r te x t o n ly : Eve has only the ciphertext.

Her best strategy is an exhaustive search, since there are only 26 possible keys. If the message is longer than a few letters we will make this more precise later when we discuss entropy , it is unlikely th at there is more than one meaningful message th a t could be the plaintext. One such is given in Exercise 1. Another possible attack, if the message is sufficiently long, is to do a frequency count for C h a p t e r 2. The letter e occurs most frequently in most English texts.

Suppose the letter L appears most frequently in the ciphertext. However, for shift ciphers this method takes much longer than an exhaustive search, plus it requires many more letters in the message in order for it to work anything short, such as this, might not contain a common symbol, thus changing statistical counts. K n o w n p la in te x t: If you know just one letter of the plaintext along with the corresponding letter of ciphertext, you can deduce the key.

T he ciphertext gives the key. For example, if the ciphertext is H, then the key is 7. Each 0 or 1 is called a b it, A representation th a t takes 8 bits is called an 8-bit number, or a b y te. The largest number th a t 8 bits can represent is , and the largest number th a t 16 bits can represent is Often, we w ant to deal with more than just numbers.

In this case, words, symbols, letters, and numbers are given binary representations. There are many possible ways of doing this. Each character is represented using 7 bits, allowing for possible characters and symbols to be represented.

Eight bit blocks are common for computers to use, and for this reason, each character is often represented using 8 bits. T he eighth bit can be used for checking parity to see if an error occurred in transmission, or is often used to extend the list of characters to include symbols such as ii and e.

Table 2. We'll never use them in this book. They are included simply to show how text can be encoded as a sequence of Os and Is. S tart by representing 40 C h a p t e r 2. T his can be accomplished by writing nil numbers in binary, for example, or by using ASCII, as discussed in the previous section.

B ut the message could also be a digitalized video or audio fiIkiiiU. The key is a random sequence of Os and Is of the same length as the mc nnKe. Once a key is used, it is discarded and never used again.

The encryption consists of adding the key to the message mod 2, bit by bit. This Is often called e x c lu siv e or, and is denoted by X O R. A variation is to leave th e plaintext as a sequence of letters. The key is then ft random sequence of shifts, each one between 0 and Decryption iiioa the same key, but subtracts instead of adding the shifts. This encryption method is completely unbreakable for a ciphertext only attack. The plaintext could be wewillwinthewar or it could be theduckuiantsout.

Each one Is equally likely, along with all other messages of the same length. This will be made more precise when we discuss Shannon's theory of entropy in C hapter If we have a piece of the plaintext, we can find the corresponding piece of the key, but it will tell us nothing about the remainder of the key.

In most cases a chosen plaintext or chosen ciphertext attack is not possible. But such an attack would only reveal the part of the key used during the attack, which would not be useful unless this part of the key were to be reused. How do we implement this system, and where can it be used? T he key can be generated in advance. Of course, there is the problem of generating a truly random sequence of 0s and Is.

One way would be to have some people sitting in a room flipping coins, but this would be too slow for most purposes. We could also take a Geiger counter and count how many clicks It makes in a small tim e period, recording a 0 if this number is even and 1 if It Is odd.

There are other ways th a t are faster but not quite as random th at can be used in practice see Section 2. Once the key is generated, it can be sent by a trusted courier to the recipient. The message can then be sent when 2. A disadvantage of the one-time pad is th a t it requires a very long key, which is expensive to produce and expensive to transm it.

Once the key is used up, it is dangerous to reuse it for a second message; any knowledge of the first message would give knowledge of the second, for example. T he am ount of information carried by the courier is then several orders of m agnitude smaller than the messages th at will be sent. One such m ethod, which is fast but not very secure, is described in the Section 2.

A variation of the one-time pad has been developed by Maurer, Rabin, Ding, and others. Suppose it is possible to have a satellite produce and broadcast several random sequences of bits at a rate fast enough th at no com puter can store more than a very small fraction of the outputs.

Alice wants to send a message to Bob. They use a public key m ethod such as RSA see C hapter 6 to agree on a method of sampling bits from the random bit streams. By the time Eve has decrypted the public key transmission, the random bits collected by Alice and Bob have disappeared, so Eve cannot decrypt the message. In fact, since the encryption used a one-time pad, she can never decrypt it, so Alice and Bob have achieved everlasting security for their message.

Note th a t bounded storage is an integral assumption for this procedure. The production and the accurate sampling of the bit streams are also im portant implementation issues. For example, the therm al noise from a semiconductor resistor is known to be a good source of randomness. We would therefore like a method for generating randomness that can be done in software. Most com puters have a method C h a p t e r 2. C l a s s ic a l C r y p t o s y s t e m s 42 for generating random numbers that is readily available to the user.

For example, the standard C library contains a function rand th a t generates pseudo-random numbers between 0 and The m nd function and many other pseudo-random num ber generators are based on linear congruential generators. This is because they are predictable even if the param eters a, b, and m are not known , in the sense th a t an eavesdropper can use knowledge of some bits to predict future bits with fairly high probability.

In fact, it has been shown th a t any polynomial congruential generator is cryptographically insecure. In cryptographic applications, we need a source of bits th a t is nonpredictable. We now discuss two ways to create such non-predictable bits. T he first method uses one-way functions. This method of random bit generation is often used, and has proven to be very practical. As an example, the cryptographic pseudo-random number generator in the OpenSSL toolkit used for secure communications over the Internet is based on SHA.

In this scheme, one first generates two large primes p and q th a t are both congruent to 3 mod 4. To initialize the BBS generator, set the initial seed to 5 x 2 mod n.

See BlumBlum-ShubJ. A problem with BBS is th a t it can be slow to calculate. One way to improve its speed is to extract the k least significant bits of Xj. As long aa k 2. In many situations involving encryption, there is a trade-off between speed and security. For example, in cable television, many bits of d ata are being transm itted, so speed of encryption is im portant. On the other hand, security is not usually as im portant since there is rarely an economic advantage to m ounting an expensive attack on the system.

In this section, we describe a method th a t can be used when speed is more im portant than security. This sequence repeats after 31 terms. The resulting sequence of 0s and Is can be used os the key for encryption. One advantage of this method is th a t a key with large period can be generated using very little information. Therefore, 62 bits produce more than two billion bits of 2.

This is a great advantage over a one-time pad, where the full two billion bits m ust be sent in advance.

This method can be implemented very easily in hardware using w hat is known as a lin e a r fe e d b a c k s h ift re g is te r LFSR and is very fast.

In Figure 2. T he output, which is the bit x m , is added to the next bit of plaintext to produce the ciphertext. T he diagram in Figure 2. U nfortunately, the preceding encryption method succumbs easily to a known plaintext attack. More precisely, if we know only a few consecutive bits of plaintext, along with the corresponding bits of ciphertext, we can determine the recurrence relation and therefore com pute all subsequent bits of the key.

Therefore, for the rest of this discussion, we will ignore the ciphertext and plaintext and assume we have discovered a portion of the key sequence. Our goal is to use this portion of the key to deduce the coefficients of the recurrence and consequently com pute the rest of the key. For example, suppose we know the initial segment of the sequence How do we determine the coefficients of the recurrence? We do not necessarily know even the length, so we s ta rt with length 2 length 1 would produce a constant sequence.

We first make a few remarks on the length of recurrences. Then there is a nonzero row vector b — 6q,. This contradicts the assum ption th a t N is smallest. If f T is irreducible mod 2 this means th a t it is not cpngruent to the product of two lower-degiee polynomials , then it can be shown th a t the period divides 2m — 1.

An interesting case is when 2m — I is prime these are called Mersenne primes. The example where the period is —1 is of this type. Linear feedback shift register sequences have been studied extensively. For example, see [Golomb] or [van der Lubbe]. However, we shall not discuss them here.

It was believed to be very secure and several attem pts at breaking the system ended in failure. Their techniques were passed to the British in , two m onths before Germany invaded Poland. The fact that Enigma had been broken remained a secret for almost 30 years after the end of the war, partly because the British had sold captured Enigma machines to former colonies and didn't want them to know th a t the system had been broken.

In the following, we give a brief description of Enigma and then describe an attack developed by Rejewski. For more details, see for example [Kozaczuk]. This book contains appendices by Rejeweski giving details of attacks on Enigma. We give a basic schematic diagram of the machine in Figure 2. For more details, we urge the reader to visit some of the many websites th at can 2.

E n ig m a 51 be found on the Internet th a t give pictures of actual Enigma machines and extensive diagrams of the internal workings of these machines. F igure 2. L, M , N are the rotors. On the other side are 26 spring-loaded contacts, again arranged in a circle so as to touch the Fixed contacts of the adjacent rotor.

Inside each rotor, the fixed contacts are connected to the spring-loaded contacts in a somewhat random manner. These connections are different in each rotor. Each rotor has 26 possible initial settings.

R is the reversing drum. It has 26 spring-loaded contacts, connected in pairs. K is the keyboard and is the same as a typewriter keyboard.

S is the plugboard. It has approximately six pairs of plugs th a t can be used to interchange six pairs of letters. Then, starting from the key, electricity passes through S , then through the rotors N ,M ,L. I could have sworn I've been to this site before but after browsing through many of the articles I realized it's new to me. Regardless, I'm certainly happy I found it and I'll be book-marking it and checking back regularly!

At this time it looks like Wordpress is the best blogging platform available right now. Here is my blog post: Cascade Dishwasher Detergent. Author s : Wade Trappe, Lawrence C. Material is accessible to mathematically mature students having little background in number theory and computer programming.

Core material is treated in the first eight chapters on areas such as classical cryptosystems, basic number theory, the RSA algorithm, and digital signatures. The remaining nine chapters cover optional topics including secret sharing schemes, games, and information theory. The text can be taught without computers.

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