1. Mathematical Background. - 1 1 Divisibility and the residue class ring ?n. - 1. 2 Polynomials. - 1. 3 Euler's totient function and ?n*. - 1. 4 Polynomial congruences and systems of linear congruences. - 1. 5 Quadratic residues. - 2. Computational Complexity. - 2. 1 Turing machines. - 2. 2 Deterministic and nondeterministic machines. - 2. 3 Decision problems and complexity classes. - 2. 4 Reductions completeness and oracle computations. - 2. 5 coNP. - 2. 6 Efficient computation and randomized complexity classes. - 3. Public Key Cryptography. - 3. 1 Public key cryptography. - 3. 2 Permutation polynomials and RSA-type cryptosystems. - 3. 3 Efficient implementation of RSA. - 3. 4 One-way functions. - 3. 5 On the complexity of an attack against RSA. - 4. Factorization Methods. - 4. 1 Trial division and Fermat factorization. - 4. 2 Monte-carlo factorization. - 4. 3 Factor base methods. - 4. 4 The continued fraction method. - 4. 5 Quadratic sieve. - 4. 6 Other Factorization Methods. - 5. Properties of the RSA Cryptosystem. - 5. 1 Computing the decryption exponent. - 5. 2 Partial decryption. - 5. 3 Cycling attacks and superencryption. - 5. 4 Incorrect keys. - 5. 5 Partial information on RSA and hard-core predicates. - 6. Low-Exponent RSA. - 6. 1 Wiener's attack. - 6. 2 Lattice basis reduction. - 6. 3 The attack of Boneh and Durfee. - 6. 4 Low public exponents. - 6. 5 Polynomially related messages. - 6. 6 Partial key exposure. - 7. Protocol and Implementation Attacks. - 7. 1 Simple protocol attacks against RSA. - 7. 2 Håstad's broadcast attack. - 7. 3 Effective security of small RSA messages. - 7. 4 Optimal Asymmetric Encryption. - 7. 5 Faulty encryption. - 7. 6 Timing attacks. - 8. RSA Signatures. - 8. 1 Attacks on RSA signatures with redundancy. - 8. 2 Security of hash-and-sign signatures. - 8. 3 Provably secure RSA signatures. - 8. 4 Undeniablesignatures. - 8. 5 Threshold signatures. - References. Language: English