Recently, there has been a renewed interest in code based cryptosystems. Amongst the reasons for this interest is that they have shown to be resistant to quantum at- tacks, making them candidates for post-quantum cryptosystems. In fact, the National Institute of Standards and Technology is currently considering candidates for secure communication in the post-quantum era. Three of the proposals are code based cryp- tosystems. Other reasons for this renewed interest include e cient encryption and decryption. In this dissertation, new code based cryptosystems (symmetric key and public key) are presented that use high rate codes and have small key sizes. Hence they overcome the drawbacks of code based cryptosystems (low information rate and very large key size). The techniques used in designing these cryptosystems include random bit/block deletions, random bit insertions, random interleaving, and random bit ipping. An advantage of the proposed cryptosystems over other code based cryp- tosystems is that the code can be/is not secret. These cryptosystems are among the rst with this advantage. Having a public code eliminates the need for permutation and scrambling matrices. The absence of permutation and scrambling matrices results in a signi cant reduction in the key size. In fact, it is shown that with simple random bit ipping and interleaving the key size is comparable to well known symmetric key cryptosystems in use today such as Advanced Encryption Standard (AES). The security of the new cryptosystems are analysed. It is shown that they are immune against previously proposed attacks for code based cryptosystems. This is because scrambling or permutation matrices are not used and the random bit ipping is beyond the error correcting capability of the code. It is also shown that having a public code still provides a good level of security. This is proved in two ways, by nding the probability of an adversary being able to break the cryptosystem and showing that this probability is extremely small, and showing that the cryptosystem has indistinguishability against a chosen plaintext attack (i.e. is IND-CPA secure). IND-CPA security is among the primary necessities for a cryptosystem to be practical. This means that a ciphertext reveals no information about the corresponding plaintext other than its length. It is also shown that having a public code results in smaller key sizes. / Graduate

To the field of cryptography, quantum mechanics is a game changer. The exploitation of quantum mechanical properties through the manipulation of quantum information, the information encoded in the state of quantum systems, would allow many protocols in use today to be broken as well as lead to the expansion of cryptography to new protocols. In this thesis, quantum encryption, i.e. encryption schemes for quantum data, is defined, along with several definitions of security, broadly divisible into semantic security and ciphertext indistinguishability, which are proven equivalent, in analogy to the foundational result by Goldwasser and Micali. Private- and public-key quantum encryption schemes are also constructed from quantum-secure cryptographic primitives, and their security is proven. Most of the results are in the joint paper Computational Security of Quantum Encryption, to appear in the 9th International Conference on Information Theoretic Security (ICITS2016).