Bachelor's Thesis on the Schoof Algorithm

I need a comprehensive bachelor's thesis that delves into the Schoof algorithm, renowned for its efficiency in determining the number of points on elliptic curves over finite fields. The thesis should cover both the theoretical aspects and practical implementations of the algorithm, as well as comparisons with other algorithms in the same domain. A key focus will be on providing a clear explanation of the mathematical foundations underpinning the algorithm, including the Frobenius endomorphism and the Chinese Remainder Theorem.

Key aspects of the project:
- A thorough examination of the theoretical foundations of the Schoof algorithm
- Practical implementation of the algorithm in Java
- A comparative analysis with other algorithms
- Inclusion of some key proofs within the mathematical foundations
- Highlighting the significance of the Schoof algorithm for Elliptic Curve Cryptography (ECC)

The ultimate goal of this project is to produce a thesis that not only demonstrates an understanding of the Schoof algorithm, but also articulates its wider significance in the field of cryptography.

Ideal skills and experience for the job:
- Strong background in mathematics and computer science
- Proficiency in Java programming
- Experience in academic writing and thesis preparation
- Familiarity with the concepts of elliptic curves and cryptography
- Ability to explain complex ideas in a clear and concise manner