The main purpose of this course is to introduce the student to central concepts and methods in cryptology.

• Do calculations in modular arithmetic, including Euclid's algorithms and the Chinese Remainder Theorem.
• Discuss the differences between classical (symmetric) cryptology and public-key (asymmetrical) cryptologi.
• Define the discrete logarithm problem modulo a prime number and demonstrate the applications in cryptology.
• Explain how to find big prime numbers for use in public-key cryptology.
• Define the properties of a digital signature and explain the details in El-Gamal's signature system.
• Outline the applications of cryptographic hash functions in cryptology, and describe the desired properties of the functions in the particular application.
• Explain how the symmetric cryptosystems, DES and AES, are used for encryption and authentication.
• Present the RSA public-key cryptosystem in all details, and explain how the system is used for encryption and to construct digital signatures.
• Explain what secret-sharing is for and how to share a secret.
• Demonstrate how to exchange a key for symmetric encryption securely.

Classical cryptology, DES and AES, the RSA-System, digital signatures, key exchange, the discrete logarithm problem and its applications and secret-sharing.