Cryptanalytic Attacks on RSA

1. Computational/Mathematical Preliminaries -- 1.1. Introduction -- 1.2. Computability, Complexity and Intractability -- 1.3. Efficient Number-Theoretic Algorithms -- 1.4. Intractable Number-Theoretic Problems -- 1.5. Chapter Notes and Further Reading -- 2. RSA Public-Key Cryptography -- 2.1. Introduction -- 2.2. Public-Key Cryptography -- 2.3. RSA Public-Key Cryptography -- 2.4. RSA Problem and RSA Assumption -- 2.5. RSA-Type Cryptosystems -- 2.6. Chapter Notes and Further Readings -- 3. Integer Factorization Attacks -- 3.1. Introduction -- 3.2. Fermat Factoring Attack -- 3.3. "p [plus or minus] 1" and ECM Attacks -- 3.4. Quadratic Sieve Attack -- 3.5. Successful QS Attack -- 3.6. Number Field Sieve Attack -- 3.7. Chapter Notes and Further Reading -- 4. Discrete Logarithm Attacks -- 4.1. Introduction -- 4.2. Baby-Step Giant-Step Attack -- 4.3. Silver-Pohlig-Hellman Attack -- 4.4. Index Calculus Attacks -- 4.5. Xedni Calculus Attack -- 4.6. Chapter Notes and Further Reading -- 5. Quantum Computing Attacks -- 5.1. Introduction -- 5.2. Order Finding Problem -- 5.3. Quantum Order Finding Attack -- 5.4. Quantum Integer Factorization Attack -- 5.5. Quantum Discrete Logarithm Attack -- 5.6. Chapter Notes and Further Reading -- 6. Simple Elementary Attacks -- 6.1. Introduction -- 6.2. Guessing Plaintext Attacks -- 6.3. Blinding Attack on RSA Signatures -- 6.4. Guessing [phi](N) Attack -- 6.5. Guessing d Attack -- 6.6. e[superscript th] Root Attack -- 6.7. Common Modulus Attack -- 6.8. Fixed-Point Attack -- 6.9. Chapter Notes and Further Readings -- 7. Public Exponent Attacks -- 7.1. Introduction -- 7.2. Theorem of Coppersmith -- 7.3. Short e Attacks for Same Messages -- 7.4. Short e Attacks for Related Messages -- 7.5. Lattice Attack for Stereotyped Messages -- 7.6. Chapter Notes and Further Reading -- 8. Private Exponent Attacks -- 8.1. Introduction -- 8.2. Diophantine Attack -- 8.3. Extended Diophantine Attacks -- 8.4. Small Private CRT-Exponent Attacks -- 8.5. Partial Private Key Exposure Attacks -- 8.6. Chapter Notes and Further Reading -- 9. Side-Channel Attacks -- 9.1. Introduction -- 9.2. Modular Exponentiation Revisited -- 9.3. Timing Attacks -- 9.4. Time Attacks on RSA in OpenSSL -- 9.5. Power (Analysis) Attacks -- 9.6. Random Fault Attacks -- 9.7. Chapter Notes and Further Reading -- 10. Road Ahead -- 10.1. Introduction -- 10.2. Elliptic Curve-Based Cryptography -- 10.3. Coding-Based Cryptography -- 10.4. Lattice-Based Cryptography -- 10.5. Quantum Cryptography -- 10.6. Conclusions -- 10.7. Chapter Notes and Further Reading.