Iwasawa theory is a branch of number theory that studies the behavior of certain objects associated to a $\mathbb{Z}_p$-extension. We will focus our attention to the cyclotomic $\mathbb{Z}_p$-extensions of imaginary quadratic fields for varying primes p, and will give some conditions for when the corresponding lambda-invariants are greater than…

If quantum computing becomes feasible, many popular cryptographic schemes, such as RSA, Diffie-Helman, and methods using elliptic curves will no longer be secure. This paper explores code-based cryptography, specifically looking the McEliece cryptosystem, as well as the more recent Classical McEliece cryptosystem, which was proposed to the National Institute of…