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Fast and secure chaos-based cryptography

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  • Full or part time
    Dr M S Baptista
    Dr A Moura
  • Application Deadline
    Applications accepted all year round
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

We all live today in a cyber world. Half of the world web traffic is encrypted because of security threats, occurring among different societies, and within several societal levels. The threat is real, and it is escalating. Governments, as well as companies, academic, non-academic organizations and users are relying on encryption to protect their services and sensitive information. Security measures to attend the actual enormous demand from internet and mobile communication users, require encryption (and decryption) to be fast, not to alter performance of streaming/or communication, light (do not require much computational power), and efficient (e.g. speed, energy efficiency, hardware and software low complexity). The current project is devoted to solve this challenge, using chaos to create a practical, but secure, fast and light cryptosystem.

This project aims at creating fast, efficient and secure cryptosystems structurally and functionally based on nonlinear chaotic mathematical operations that transform a message (encrypt) in a way that allows its secure and private transmission. So, we aim at proposing solutions for the challenges to the improvement of performance and efficiency of cryptographic solutions. The scientific pathway to achieve our grand goal relies on several properties and manifestations of chaos (and their circuit generators) that this project wants to explore to develop technology for the creation of state-of-the-art cryptosystems. Chaos manifests not only desired random properties necessary to cause confusion and diffusion to encrypt information, but can also do the job quickly, conveniently allowing the design of very light and energy efficient cryptosystems.

There are several secure systems in place that surround our lives. What is common among all these systems is that they require the use of pseudo-random numbers (PRNs) for seeds, secret or public keys or to algorithmic processes, or to generate key streams (a sequence of symbols, ‘0’ and ‘1’ if a binary digital process is in place). A promising and effective alternative to generating cryptographically-secure PRNs is offered by chaotic systems.

A first goal for this PhD proposal is to determine how a chaotic system must be observed in space and in time and how parameters of this system must be set, such that the correlation of the observed points decays very rapidly to values arbitrarily close to zero. Thus, providing rigorous conditions to create cryptographically secure PRNs and their associated key streams. Additionally, we search for the conditions such that the created PRNs and key streams are sufficiently complex, but that can be generated as fast as possible with the minimum required computational power.

Cryptosystems do not only rely on PRNs and the key stream secret keys they generate. They also rely on complex mixing mathematical operations to the plaintext to cause confusion and diffusion, operations that enables the creation of cryptosystem that are irreducible to any other form, not allowing for the cryptanalysis of the parts. And chaos is also the key for such operations. Chaotic transformations can naturally create the two basic properties for a good cipher, confusion (also known as permutation for images, since it transposes elements of the plain text) and diffusion (value modification).

A stream cipher is a cryptosystem that typically encrypts a message by symbolic transforming it with the key stream (using for example the XOR logical operation). A block cryptosystem makes other additionally 2 operations. The confusion, also known as permutation, which shuffles the position of the symbols of the plain message (or “pixels” if the “message” is an image), so there is no change in the symbol value, and diffusion, which transforms the (values of the) symbols in the message

A second goal of this project is to create fast, efficient and secure state-of-the-art chaos-based block (often used to encode objects such as images or videos) and stream ciphers (often used to encode plain messages or digitalized signals).

The successful candidate should have (or expect to have) a UK Honours Degree (or equivalent) at 2.1 or above in Natural and Computing Sciences, but with a good background of mathematical and computational methods.

Knowledge: It would be advantageous that the applicant has a sufficient good knowledge of the theories of Dynamical Systems and Ergodic Systems, and is proficient in one or more computer languages.

Funding Notes

There is no funding attached to this project, it is for self-funded students only


M. S. Baptista, “Cryptography with chaos,” Phys. lett. A, vol. 240, p. 50, 1998.

A. N. Pisarchik and M. Zanin, “Chaotic map cryptography and security,” Int. J. of Computer Research, vol. 19, no. 1, 2012.

G. Vidal, M. S. Baptista and H. Mancini, “A fast and light stream cipher for smartphones,” The European Phys. J., vol. 223, p. 1601, 2014.

This project is advertised in relation to the research areas in the discipline of Physics and Applied Mathematics. Formal applications can be completed online: You should apply for PhD in Physics, to ensure that your application is passed to the correct College for processing. NOTE CLEARLY THE NAME OF THE SUPERVISOR and EXACT PROJECT TITLE ON THE APPLICATION FORM.

Informal inquiries can be made to Dr M Baptista (murilo.baptista) with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Graduate School Admissions Unit ([email protected]).

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