On finding the eigenvalues of the matrix of rotation symmetric Boolean functions and generalizations using character theory

Digital signatures are an important feature in any encryption/decryption scheme, providing a message with integrity, authenticity, and nonrepudiation. The problem occurs when long messages are being exchanged with equally long signatures. By using hash functions, a “fingerprint” of the message can be used along with the message for verification, making the process computationally inexpensive. Considering a single iteration of a general hashing algorithm, we see Rotation Symmetric Boolean Functions (RSBFs) allow for more efficient evaluation. This is when RSBFs were studied more deeply. This thesis focuses on a matrix that comes up when investigating these functions. We not only answer an open question about this matrix, but we also generalize this matrix using another area of mathematics, Representation Theory.