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
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/10655 |
| Date | 19 March 2019 |
| Creators | Esmaeili, Mostafa |
| Contributors | Gulliver, T. Aaron |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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