{"product_id":"a-course-in-number-theory-and-cryptography-9780387942933","title":"A Course in Number Theory and Cryptography","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI. Some Topics in Elementary Number Theory.- 1. Time estimates for doing arithmetic.- 2. Divisibility and the Euclidean algorithm.- 3. Congruences.- 4. Some applications to factoring.- II. Finite Fields and Quadratic Residues.- 1. Finite fields.- 2. Quadratic residues and reciprocity.- III. Cryptography.- 1. Some simple cryptosystems.- 2. Enciphering matrices.- IV. Public Key.- 1. The idea of public key cryptography.- 2. RSA.- 3. Discrete log.- 4. Knapsack.- 5 Zero-knowledge protocols and oblivious transfer.- V. Primality and Factoring.- 1. Pseudoprimes.- 2. The rho method.- 3. Fermat factorization and factor bases.- 4. The continued fraction method.- 5. The quadratic sieve method.- VI. Elliptic Curves.- 1. Basic facts.- 2. Elliptic curve cryptosystems.- 3. Elliptic curve primality test.- 4. Elliptic curve factorization.- Answers to Exercises.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI. Some Topics in Elementary Number Theory.- 1. Time estimates for doing arithmetic.- 2. Divisibility and the Euclidean algorithm.- 3. Congruences.- 4. Some applications to factoring.- II. Finite Fields and Quadratic Residues.- 1. Finite fields.- 2. Quadratic residues and reciprocity.- III. Cryptography.- 1. Some simple cryptosystems.- 2. Enciphering matrices.- IV. Public Key.- 1. The idea of public key cryptography.- 2. RSA.- 3. Discrete log.- 4. Knapsack.- 5 Zero-knowledge protocols and oblivious transfer.- V. Primality and Factoring.- 1. Pseudoprimes.- 2. The rho method.- 3. Fermat factorization and factor bases.- 4. The continued fraction method.- 5. The quadratic sieve method.- VI. Elliptic Curves.- 1. Basic facts.- 2. Elliptic curve cryptosystems.- 3. Elliptic curve primality test.- 4. Elliptic curve factorization.- Answers to Exercises.  ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":53733838946647,"sku":"9780387942933","price":41.79,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/a-course-in-number-theory-and-cryptography-9780387942933","provider":"Book Curl","version":"1.0","type":"link"}