Entropy Extraction and Error Correction of Images for Cryptographic Applications

Currently prevailing techniques in cryptography and computer security rest on the tacit assumption that all communication partners can safely and permanently store a secret key (i.e., a secret digital number) that remains unknown to adversaries. Unfortunately, various strategies for extracting such keys from electronic systems, such as invasive, side-channel, or malware attacks, have been developed over the years.

The novel, innovative primitive of Strong Physical Unclonable Functions (Strong PUFs) offers a seminal alternative in this situation: It empowers communicants to identify themselves to others without permanently storing digital keys in their systems. This enables certain forms of advanced, “keyfree” security. The currently most promising implementation of Strong PUFs are complex optical systems, in which laser light is scattered multiple times, creating a highly complex interference pattern as output [1]. The situation is shown schematically in Figure I.

Figure I: Basic schematics of an optical Strong PUF [1]: A laser beam hits a randomly structured scattering token. The laser light is scattered multiple times and creates a highly complex interference pattern, which must be postprocessed, producing a stable bitstring. This bitstring should be stable upon multiple measurements (in opposition to the interference pattern and its small fluctuations). The bitstring should also have maximal entropy (again in opposition to the interference pattern and its grain-like structure). Both tasks can be accomplished in combination by choosing and applying the right image transformation.

The general goal of this project is to identify, optimize and apply various numerical image processing algorithms. They shall extract or “distil” a short numeric bitstring (few thousand bits) from a complex optical image (with millions of bits measured by a CCD camera), as shown in Figure I. An optimal image transformation algorithm should meet the following requirements:

This means that we have to optimize the solution along two partly conflicting dimensions. Among the different filtering algorithms that have been studied in the literature so far, the B-spline wavelet transformation promises an efficient entropy extraction [2]. They allow for a multiresolution analysis that can be tailored in order to extract the “fingerprint” of the image under analysis.


The candidate should have a strong background in mathematics or computer science. You should have basic knowledge of mathematical transforms, image processing and programming. You will work in an international research team with partners from the European Laboratory for Nonlinear Spectroscopy in Italy, the Ludwig Maximilian University of Munich, and the University of Passau.

Overview of tasks:

Basis Literature:

  1. Pappu, R., Recht, B., Taylor, J. and Gershenfeld, N., “Physical one-way functions.”, Science 2002, 297, 2026.
  2. Rührmair, U., Hilgers, C., Urban, S., Weiershäuser, A., Dinter, E., Forster, B. and Jirauschek, C., “Optical pufs reloaded.”, Eprint. Iacr. Org. 2013


Prof. Dr. D. Kranzlmüller

Dauer der Arbeit:

Anzahl Bearbeiter: 1


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