ABSTRACT
Cryptography without mathematics is something like earth without sun. Strong mathematical fundamentals help the cryptography researcher to understand and to develop new protocols. The chapter discusses basic mathematical aspects of cryptography starting from basic foundations like polynomial and group theory. It also discusses some advanced concepts of elliptic curves and hash functions. Elliptic curve cryptography attracted many researchers due to its smaller key size requirement compared to other cryptography algorithms. The finite field is the foundation stone for elliptic curve cryptography. Elliptic curve cryptography is the most suitable cryptography protocol for the emerging authentication techniques for devices where power backup is low and computation capabilities are less. The scalar multiplication problem defines implementation of elliptic curve cryptography in hardware and software. SHA series and MD5 series are most commonly used algorithms in cryptography. The chapter enables basic knowledge of other cryptographic maths like bi-linear pairing and Chebyshev chaotic map.
