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Title: Public key cryptosystem based on error control coding and its applications to network coding
Author: Rashwan , Haitham
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2011
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attack; the recent introduction of list decoding for binary Goppa codes; and the possibility of choosing code lengths that are not a power of 2. The resulting public-key sizes are considerably smaller than previous parameter choices for the same level of security. The smallest key size against all known attacks is 460 647 bits which is too large for practical implementations to be efficient. In this thesis, we attempt to reduce McEliece's public key size by using other codes instead of Goppa codes. This thesis focuses on Gabidulin -Paramonov-Trejtakov (GPT) cryptosystem which is based on rank distance codes, which is connected to the difficulty of general decoding problem. The GPT cryptosystem is a variant of the McEliece cryptosystem. The use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This has enabled using public keys of a smaller size. Respective structural attacks against this system were proposed by Gibson and recently by Overbeck. Overbeck's attacks break many variants of the GPT cryptosystem in polynomial time. Gabidulin has introduced Advanced approach to prevent Overbeck's attacks. We evaluate the overall security of the GPT cryptosystem and its variants against both the structural attacks and the decoding (Brute force) attacks. Furthermore, we apply the Advanced approach to secure other variants of the GPT cryptosystem which are still vulnerable to Overbeck's attacks. Moreover, we introduce two new approaches to combating the GPT cryptosystem against all known attacks; the first approach is called Smart approach and the second one is called constructed Smart approach. We study how to choose the GPT PKC parameters so as to minimize the public key size and implementation complexity, and to maximize the overall security of the GPT cryptosystem against all known attacks in order to make an efficient system for low power handsets. We present different trade-offs for using a combined system for error protection and cryptography. Our results suggest that the McEliece key size has been reduced just 4000 bits with security of 280 , a public key size of 4800 bits with security of 276 , and a public key size of 17 200 bits with security of 2116 that corresponds respectively with the Advanced approach for standard variant of GPT, Advanced approach for simple variant of GPT, and - - ~- - - - . - - - ---- - - _. ~- ---. --- ~- -- ~-- - - ---~- - -- . - .• -.• '- ' . , ....- ..-.......iI: - ...... ... :. . -------~-- ABSTRACT iv Advanced approach for the simple variant of OPT based on reducible rank codes. Similarly, the Smart approach and the constructed Smart approach for simple variant of OPT cryptosystem have reduced McEliece's key size to 5000 bits with security of 294 for the Smart approach and to 7200 bits with security of 295 for the constructed Smart approach. By using the OPT PKC and its variants, we have approximately a 99% reduction in the size of the public key than McEliece cryptosystem with reasonable security level against all known attacks. Network coding substantially increases network throughput. Random network coding is an effective technique for information dissemination in communications networks. The security of network coding is designed against two types of attacks: Wiretapping and Byzantine attacks. The Wiretapping attack can tap some original packets, outgoing from the source to the destination with the purpose of recovering the message; The Byzantine attack can inject error packets; this type of attack has the potential to affect all packets gathered by an information receiver. We introduce a new scheme to provide information security by using the OPT public key cryptosystem together with Silva- Kotter-Kschischang random network codes. Moreover, we investigate the performance of the system, transmitting the encrypted packets to the destination (sink) through wire communication networks using different random network coding models. Our results show that the introduced scheme is secure against Wiretapping and Byzantine attacks under some conditions which depend on rank code parameters.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available