Caroline Fontaine

A survey of homomorphic encryption for nonspecialists

Processing encrypted signals requires special properties of the underlying encryption scheme. A possible choice is the use of homomorphic encryption. In this paper, we propose a selection of the most important available solutions, discussing their properties and limitations.

Watermarking security: theory and practice

This paper proposes a theory of watermarking security based on a cryptanalysis point of view. The main idea is that information about the secret key leaks from the observations, for instance, watermarked pieces of content, available to the opponent. Tools from information theory (Shannons mutual information and Fishers information matrix) can measure this leakage of information. The security level is then defined as the number of observations the attacker needs to successfully estimate the secret key. This theory is applied to two common watermarking methods: the substitutive scheme and the spread spectrum-based techniques. Their security levels are calculated against three kinds of attack. The experimental work illustrates how Blind Source Separation (especially Independent Component Analysis) algorithms help the opponent exploiting this information leakage to disclose the secret carriers in the spread spectrum case. Simulations assess the security levels derived in the theoretical part of the paper.

StirMark benchmark: audio watermarking attacks

We briefly present the architecture of a public automated evaluation service we are developing for still images, sound and video. We also detail new tests that will be included in this platform. The set of tests is related to audio data and addresses the usual equalisation and normalisation but also time stretching, pitch shifting and specially designed audio attack algorithms. These attacks are discussed and results on watermark attacks and perceived quality after applying the attacks are provided.

Highly nonlinear balanced Boolean functions with a good correlation-immunity

We study a corpus of particular Boolean functions: the idempotents. They enable us to construct functions which achieve the best possible tradeoffs between the cryptographic fundamental properties: balancedness, correlation-immunity, a high degree and a high nonlinearity (that is a high distance from the affine functions). They all represent extremely secure cryptographic primitives to be implemented in stream ciphers.

Public automated web-based evaluation service for watermarking schemes: StirMark benchmark

One of the main problems, which darkens the future of digital watermarking technologies, is the lack of detailed evaluation of existing marking schemes. This lack of benchmarking of current algorithms is blatant and confuses rights holders as well as software and hardware manufacturers and prevents them from using the solution appropriate to their needs. Indeed basing long-lived protection schemes on badly tested watermarking technology does not make sense. In this paper we will present the architecture of a public automated evaluation service we have developed for still images, sound and video. We will detail and justify our choice of evaluation profiles, that is the series of tests applied to different types of wa-termarking schemes. These evaluation profiles allow us to measure the reliability of a marking scheme to different levels from low to very high. Beside the known StirMark transformations, we will also detail new tests that will be included in this platform. One of them is intended to measure the real size of the key space. Indeed, if one is not careful, two different watermarking keys may produce interfering watermarks and as a consequence the actual space of keys is much smaller than it appears. Another set of tests is related to audio data and addresses the usual equalisation and normalisation but also time stretching, pitch shifting. Finally we propose a set of tests for fingerprinting applications. This includes: averaging of copies with different fingerprint, random ex-change of part between different copies and comparison between copies with selection of most/less frequently used position differences.

Propagation characteristics and correlation-immunity of highly nonlinear boolean functions

We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with respect to a linear subspace of codimension 1 or 2 has a high nonlinearity. We also point out that most highly nonlinear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.

Recent Advances in Homomorphic Encryption: A Possible Future for Signal Processing in the Encrypted Domain

Since the introduction of the notion of privacy homomorphism by Rivest et al. in the late 1970s, the design of efficient and secure encryption schemes allowing the performance of general computations in the encrypted domain has been one of the holy grails of the cryptographic community. Despite numerous partial answers, the problem of designing such a powerful primitive has remained open until the theoretical breakthrough of the fully homomorphic encryption (FHE) scheme published by Gentry in the late 2000s. Since then, progress has been fast-paced, and it can now be reasonably said that practical homomorphic encryption-based computing will become a reality in the near future.

Secure delivery of images over open networks

We present architectures for the secure delivery of images over open networks, such as the Internet or broadcast networks. Those systems integrate access control mechanisms and tracking procedures, once the pictorial material has been accessed. We show how these architectures have been tested in the context of the connection of cultural databases to the Internet (AQUARELLE system) and in the context of broadcasting of high-value TV programs (OCTALIS system used during the football World Cup). This work shows the interest for a global integrated design of delivery systems in which watermarking, monitoring, and public key infrastructures based on trusted third parties are designed according to coherent functional models.

On-off keying modulation and tardos fingerprinting

We consider a particular design of fingerprinting code for multimedia contents, carefully motivated by a detailed analysis. This design is based on a two-layer approach: a probabilistic fingerprinting code a la Tardos coupled with a zero-bit side informed watermarking technique. The detection of multiple watermark presences in content blocks give birth to extended accusation processes, whose performances, assessed experimentally, are excellent. This prevents the colluders from mixing different content blocks, a class of collusion which is not encompassed in the classical marking assumption. Therefore, the collusion must stick to the block exchange strategy which is fully tackled by the fingerprinting code.

On some cosets of the first-order Reed-Muller code with high minimum weight

We study a family of particular cosets of the first-order Reed-Muller code R(1,m): those generated by special codewords, the idempotents. Thus we obtain new maximal weight distributions of cosets of R(1,7) and 84 distinct almost maximal weight distributions of cosets of R(1,9), that is, with minimum weight 240. This leads to crypotographic applications in the context of stream ciphers.