Project 174008

Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security

Leader: Dr. Miodrag Mihaljević

Abstract

The project is dedicated to research activates on advanced techniques for information security regarding data secrecy and authentication control. Accordingly, the main goals of the project are at the following directions:

(i) techniques for security evaluation of certain symmetric encryption techniques and authentication protocols;

(ii) advanced stream ciphers and authentication protocols which provide high security and low implementation complexity;

(iii) advanced techniques for the key management (including the broadcast encryption ones);

(iv) advanced techniques for biometric authentication;

(v) application of the results achieved within (i)-(iv) for developing advanced mechanisms of information security in certain ICT systems including ones related to elements of medical ICT and smart grid.

The main expected outcomes of the project are within domains of cryptology, image processing and computational topology and include the following:

- Design and security evaluation of advanced cryptographic techniques based on joint effects of pseudo-randomness, randomness and dedicated coding;

- Improvement of existing and development of new methods for shape characterization at sub-pixel precision and further enhance their applicability and particularly regarding processing of 3D images and the biometric;

- Employment of computational topology methods for cryptographic keys management issues involving advanced method of partitioning and covering of topological and discrete structures.

Aims and Objectives

The project is dedicated to the research activates on advanced techniques for information security regarding data security and authentication control. Accordingly, the main goals of the project are at the following directions:

(i) techniques for security evaluation of certain symmetric encryption techniques;

(ii) advanced symmetric encryption techniques which provide at the same time high security and low implementation complexity;

(iii) advanced techniques for symmetric key management (including the broadcast encryption ones);

(iv) advanced techniques for biometric authentication;

The planned research activities for realization of the goals (i)-(v) are in the following domains:

01. cryptology;

02. image processing;

03. certain topics of mathematics and particularly the computational topology.

- advanced techniques for security evaluation of certain cryptographic primitives and particularly the techniques for cryptanalysis based on the algorithms for the LPN problem (Learning Parity in Presence of Noise), advanced dedicated decoding techniques and the techniques for inversion of one-way functions employing time-memory and time-memory-data trade-off;

- developing of advanced stream ciphers based on results from coding theory;

- advanced techniques for the secret keys management in multicast and broadcast scenarios;

- authentication protocols for implementation in heavily restrictive environments (including RFID and sensor networks).

02. Biometric methods and methods for user identification/authentication, largely rely on information extracted form digital images. Research in the field of digital image processing within this project will include analysis of specific characteristics of 3D objects as well as analysis of objects at any resolution (potentially insufficient) and/or in the presence of noise. The research is motivated by the need to bridge the existing gap between:

- the recent fast development in 3D imaging technologies; and

- a lack of algorithmic tools for the manipulation and processing of data being available.

Considering that precision is a key requirement for methods used for biometric applications and person identification, the development of methods that maximally utilize information present in images, transcending limitations of low resolution and poor image quality, is also of great importance. In the development of methods for analysis of 3D shape, the project will, apart from well known approaches, explore a new concept of multi-component 3D shape analysis. Despite the fact that, in many situations, a number of real objects are better to be considered as a multi-component object, and, also, certain objects are better considered as multi-component objects consisting of their naturally defined components (e.g. a human face), there are not yet methods for the analysis of such objects and for measuring their related properties. This research will be among the first attempts to offer solution to such problems. Immediate applicability of developed methods is expected in the areas of person identification, classification and recognition (objects, shapes, people). Furthermore, the research will address the analysis of images with insufficient resolution, with a goal of developing robust methods for feature estimation and object description with sub-pixel precision, improving the existing methods for extracting information from images of relatively low quality. Finally, efficient and flexible optimization methods for solving non-linear non-convex minimization problems, essential for addressing many problems in the field of image processing such as image de-noising, segmentation and image registration, will be developed.

03. In the domain of computational topology, which includes the methods of algebraic topology, the planed research activities are within the following main topics:

- analysis and classifications of large data sets "data clouds" (Vietoris Rips complex, Persistent homology);

- the partitioning according to the given requirements and methods of covering of certain geometric spaces regarding the problems of the key management;

- complexity estimation of the fundamental algorithms for discrete geometry purposes.

It is expected that the techniques of computational topology support the research activities regarding a number of the project goals and particularly towards identification of "hidden and useful" topological structures and employment of topological approaches regarding certain algorithms of cryptology and image processing.

Also, we point out that the activities within the project include an extensive international collaboration and education of yang researchers (Ph.D. students). The planned international collaboration is mainly a continuation of the existing one which has appeared as a fruitful one and yields a solid background for the further joint activities. The planned international collaboration should provide a framework for achieving top level results and it will be mainly related to the following institutions: Research Center for Information Security (RCIS), National institute AIST, Tokyo, Japan; University of Exeter, U.K.; University of Manchester, U.K., Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University, Uppsala, Sweden; Technical University (TU) Berlin. The educational dimension of the project will be focused towards the following issues: Education of yang researchers (Ph.D. students) and their involvement in research activities in the domains relevant for the current and future information security systems, which appear as a priority on the national as well as international level.

Research Impact

The proposed project belongs to the area of information-communications technologies (ICT) and addresses one of the hot topics within ICT - information security which has been recognized as one of the priority topics in the strategic research agenda in Republic Serbia as well as on the lists of research priorities in EU, US and Japan, for example.
The importance of the proposed project is a direct implication of the information security significance and its position on the lists of research and social priorities from the international and national points of view. As an illustration, it is worth noting that one of EU FP7 priorities is development of trustful and secure information society. Accordingly, importance of the proposed research activities appears as a direct consequence of importance of cryptology, biometric and certain topics of mathematics for developing advanced mechanisms for information security which reduces the overheads introduced by the information security requirements.
An additional benefit of the proposed project appears as a consequence of integration of the research activities of cryptology, image processing and particular topics of "pure" mathematics on the benefits of all these disciplines because the application oriented ones are provided with certain sophisticated mathematical tools and "pure" mathematics is related to certain practical and novel challenges.
Particular technical research impacts of the project include the following:

01. In the domain of cryptology the expected outcomes include the following:

(i) advanced techniques for security evaluation of the building components for information security mechanisms;

(ii) advanced cryptographic primitives for steam ciphering, authentication and keys management which have high security and low implementation complexity.

02. The proposed research within the field of image processing will be of high interest for researchers who are, by nature of their research, dealing with digital images (e.g., in computer graphics and image processing), and, due to the great tuning possibilities and high applicability of the developed methods, for any user of the latest 3D imaging technologies (in biometrics, medicine, robotics, biology, etc.). We expect to establish several breaking results (benchmarks for further research) on topics which will be increasingly interesting due to the recent progress in 3D image technology, which has not been followed by appropriate theoretical developments.

Precision, which is often a key factor in many applications of image processing, including biometrics as authentication mechanism for the implementation of information security, is a challenge in focus of this project. The development of image processing methods that maximally utilize existing information, and overcome limitations imposed by resolution and/or low image quality, is of particular importance to achieve the desired precision and will be addressed by methods for feature estimation and object description with sub-pixel precision. The development of efficient numerical optimization methods is, furthermore, of great importance for successful practical application of image processing algorithms in real applications.

03. The relevance of proposed research directions within computational topology is a consequence of the following:

- they are of potential interest for developing advanced techniques in the both areas cryptology and image processing employing geometrical approaches;

- some models of the addressed problems in cryptology and image processing can be considered employing results and tools from area of computational topology;

- it is expected that the addressed problems of topology will contribute to development of advanced key management techniques and analysis/improvement of certain algorithms for image processing.

Also it is worth noting that, the research activities within computational topology are of wider interest as can be seen at the following prestigious institutions "Mathematical Sciences Research Institute Berkeley" (

https://www.msri.org/calendar/programs/ProgramInfo/243/show_program ) and "Stanford University" (https://comptop.stanford.edu/ ).

Ten Selected References from the Project Proposal

[01] M. Mihaljević and H. Imai, "An approach for stream ciphers design based on joint computing over random and secret data", Computing , vol. 85, no. 1-2, pp. 153-168, June 2009.

[02] M. Mihaljević, M. Fossorier and H. Imai, "Security Evaluation of Certain Broadcast Encryption Schemes Employing a Generalized Time-Memory-Data Trade-Off", IEEE Communications Letters , vol. 11, no. 12, pp. 988-990, Dec. 2007.

[03] M. Fossorier, M. Mihaljević and H. Imai, "Modeling Block ecoding Approaches for Fast Correlation Attack", IEEE Transactions on Information Theory , vol. 53, no. 12, pp. 4728-4737, Dec. 2007.

[04] M. Mihaljević, "Generic framework for secure Yuan 2000 quantum encryption protocol employing the wire-tap channel approach'", Physical Review A, vol. 75, no. 5, pp. 052334-1-5, May 2007.

[05] J. Đ. Golić and M. Baltatu, "Entropy analysis and new constructions of biometric key generation systems", IEEE Transaction on. Information Theory , vol. 54, pp. 2026-2040, May 2008.

[06] Joviša Žunić, Kaoru Hirota, Paul L. Rosin, "A Hu Invariant as a Shape Circularity Measure", Pattern Recognition , vol. 43, no. 1, pp. 47-57, 2010.

[07] Joviša Žunić, Paul L. Rosin, "An Alternative Approach to Computing Shape Orientation with an Application to Compound Shapes", International Journal of Computer Vision , vol. 81, no. 2, pp. 138-154, 2009.

[08] Nataša Sladoje, Joakim Lindblad, "High-Precision Boundary Length Estimation by Utilizing Gray-Level Information", IEEE Transactions on Pattern Analysis and Machine Intelligence , Vol. 31, no. 2, pp. 357-363, 2009.

[09] Nataša Sladoje, Ingela Nyström, Punam Kumar Saha, "Measurements of digitized objects with fuzzy borders in 2D and 3D", Image and Vision Computing , vol. 23, no. 2, pp. 123-132, 2005.

[10] Imre Barany, Pavle V. Blagojević and Andreas Szucs, "Equipartitioning by a convex 3-fan", Advances in Mathematics , vol. 223, br. 2, str. 579-593, 2010.