## Applications of Abstract Algebra with Maple and MATLAB, Second EditionEliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields. Carefully integrating MapleTM and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems. New to the Second Edition With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists. |

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### Contents

Preliminary Mathematics | 1 |

Block Designs | 29 |

Error Correcting Codes | 53 |

BCH Codes | 93 |

ReedSolomon Codes | 135 |

Algebraic Cryptography | 169 |

Vigenere Ciphers | 219 |

The RSA Cryptosystem | 259 |

The Advanced Encryption Standard | 335 |

Polya Theory | 389 |

Graph Theory | 417 |

Appendices | 445 |

B UserWritten MATLAB Functions | 461 |

481 | |

493 | |

Elliptic Curve Cryptography | 293 |

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AES encryption process affine cipher BCH code beads block design CD-ROM Chapter ciphertext codewords coefficients colleague column complete summary compute construct contains convert cosets crcpress ctext cycle index cycles of length decrypt the ciphertext determine downloaded at www.crcpress.com/e_products/downloads/download.asp?cat_no=C6102 encrypt the message encryption exponent entering the following error correction Euclidean algorithm field elements finite field found in Appendix group G Hadamard matrix Hamming code Hill cipher included index of coincidence initial key initial round input parameter insecure line intruder key matrix keyword linear code loop M-file Maple session maple('modp MATLAB MATLAB session modulo necklace nonzero elements ordered pairs output partition pattern inventory permutation plaintext positive integer preceding command prime primitive polynomial ptext Reed-Muller code RSA cryptosystem S-box session and saved shift cipher Suppose Theorem undirected graphs user-written function variable vertices Vigenere cipher write a complete written separately