## Applied Algebra: Codes, Ciphers, and Discrete AlgorithmsFor junior/senior-level courses in Abstract Algebra and Cryptography in departments of mathematics, computer science, and engineering. Emphasizing the fact that solid mathematics leads to solid applications, this text builds a mathematical foundation that includes topics in number theory and the theory of infinite fields. - Hints for using Maple, MultiPAD, and Scientific Notebook. - Supplies students with explicit examples of how to use these technology products to perform calculations related to the course, and enables them to better understand the ideas developed in the text. - An entire chapter devoted to the Rijndael Algorithm - Featuresm the interesting mathematics upon which it is based. - Enables students to focus on and understand the recently adopted Advanced Encryption Standard (replacing the Data Encryption Standard) as the default for financial and web transactions. - Solutions to selected exercises. - Shows students how the solution was worked out - not just the correct answer. - A comprehensive presentation. - Provides students with numerous topics in cryptology, number theory, and error correcting codes - not found in other texts. |

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addition and multiplication affine cipher arithmetic ASCII Assume bar code binary bits calculations characters Chinese remainder theorem ciphertext codeword coefficients column computer algebra hints computer algebra system congruence decode Decrypt the message define Definition digits encoded equation Evaluate Example Exercises extended Euclidean algorithm factor Fermat's little theorem finite Galois field gcd(a GFpn given greatest common divisor Hamming hence iiiii integer integers modulo inverse irreducible polynomial Kyle letters linear lmod2 Maple mathematical matrix minimal polynomial mod q mod x2 mod2 modm modp modular modulo multiplication table MuPAD nonzero Note number theory pair permutation plaintext Playfair Playfair cipher polynomial of degree polynomial q positive integer primitive element private key Proof public key relatively prime representation residue system root rotor Sarah Scientific Notebook sequence single error solution solve the system substitution cipher two-out-of-five vector Verify x2 mod yields zero