An introduction to fundamental algorithms that play an important role in modern engineering science: finite field arithmetic (crucial for cryptography and coding theory) as well as solving systems of nonlinear equations (central to many areas of computer science and enigeering). The focus is on acquiring mathematical tools to solve problems in practice. En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:

• Efficiently compute over finite fields: addition, multiplication, squaring, exponentiation
• Apply the algorithms for efficient finite field arithmetic to implement real-world cryptographic protocols
• Represent classes of real-world problems as systems of nonlinear equations
• Solve systems of nonlinear equations by applying such algorithms as Buchberger's algorithm and SAT solvers
• Apply a computer algebra system to solve computational problems in practice
• Determine complexity of algorithms
• Write quality technical reports
• Present results concisely and informatively
• Efficiently work and communicate in teams

Rings, finite fields, arithmetic in finite fields (efficient addition, multiplication, squaring), algorithms for exponentiation, algorithms for solving nonlinear systems of equations (such as SAT solvers or Gröbner-basis finding Buchberger's algorithm), computer algebra systems 28. oktober, 2016