In this paper, we propose a novel method of Cancelable Biometrics for correlation-based matching. The biometric image is transformed by Number Theoretic Transform (Fourier-like transform over a finite field), and then the transformed data is masked with a random filter. By applying a particular kind of masking technique, the correlation between the registered image and the input matching image can be computed in masked domain (i.e., encrypted domain) without knowing the original images. And we proved theoretically that in our proposed method the masked version does not leak any information of the original image, in other words, our proposed method has perfect secrecy. Additionally, we applied our proposed method to finger-vein pattern verification and experimentally obtained very high verification performance.

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Cancelable Biometrics with Perfect Secrecy for Correlation-Based Matching

Multimedia contents are inherently sensitive signals that must be protected whenever they are outsourced to an untrusted environment. This problem becomes a challenge when the untrusted environment must perform some processing on the sensitive signals; a paradigmatic example is Cloud-based signal processing services. Approaches based on Secure Signal Processing (SSP) address this challenge by proposing novel mechanisms for signal processing in the encrypted domain and interactive secure protocols to achieve the goal of protecting signals without disclosing the sensitive information they convey. This paper presents a novel and comprehensive set of approaches and primitives to efficiently process signals in an encrypted form, by using Number Theoretic Transforms (NTTs) in innovative ways. This usage of NTTs paired with appropriate signal pre-and post-coding enables a whole range of easily composable signal processing operations comprising, among others, filtering, generalized convolutions, matrix-based processing or error correcting codes. Our main focus is on unattended processing, in which no interaction from the client is needed; for implementation purposes, efficient lattice-based somewhat homomorphic cryptosystems are used. We exemplify these approaches and evaluate their performance and accuracy, proving that the proposed framework opens up a wide variety of new applications for secured outsourced-processing of multimedia contents.

Number Theoretic Transforms for Secure Signal Processing

In this paper, a fast algorithm is developed to compute two-dimensional convolutions of an array of d 1 × d 2 complex number points where d 2 =2mand d 1 =2m-r+1for some 1\leq r \leq m . This new algorithm requires fewer multiplications and about the same number of additions as the conventional FFT method for computing the two-dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

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On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

Multimedia contents are inherently sensitive signals that must be protected whenever they are outsourced to an untrusted environment. This problem becomes a challenge when the untrusted environment must perform some processing on the sensitive signals; a paradigmatic example is Cloud-based signal processing services. Approaches based on Secure Signal Processing (SSP) address this challenge by proposing novel mechanisms for signal processing in the encrypted domain and interactive secure protocols to achieve the goal of protecting signals without disclosing the sensitive information they convey. 
This work presents a novel and comprehensive set of approaches and primitives to efficiently process signals in an encrypted form, by using Number Theoretic Transforms (NTTs) in innovative ways. This usage of NTTs paired with appropriate signal pre- and post-coding enables a whole range of easily composable signal processing operations comprising, among others, filtering, generalized convolutions, matrix-based processing or error correcting codes. The main focus is on unattended processing, in which no interaction from the client is needed; for implementation purposes, efficient lattice-based somewhat homomorphic cryptosystems are used. We exemplify these approaches and evaluate their performance and accuracy, proving that the proposed framework opens up a wide variety of new applications for secured outsourced-processing of multimedia contents.

Publisher Summary This chapter introduces the concepts of number theoretic transforms (NTT) and their applications to 2-D convolutions. The use of NTT's for 2-D convolutions is discussed and a method for calculating them without matrix transpose and without overlap is explained with examples. Although the transform domain for 2-D NTTs is not as simple to interpret as for some other transforms, the 2-D Fermat number transform (FNT) domain does have special patterns of zeros and nonzero values that could find applications. These are discussed for a number of simple images and for 2-D periodic structures. The effects of small errors in the periodic data on the 2-D FNT are discussed and applications are considered. Another family of transforms based upon the Mersenne numbers is introduced together with its separable form. The transform is extended to the multidimensional case. The chapter provides an overview of how this transform can be combined with the 2-D FNT, using the 2-D mixed radix conversion, to provide extended dynamic range and great parallelism using simple and convenient moduli leading to an efficient method for parallel image-processing applications. Because of the somewhat inconvenient word lengths required by some NTTs, the use of very-large-scale integration (VLSI), where the word length can be chosen to suit the design, has had a dramatic effect on circuit design for NTTs. A number of designs for pipeline FNT processors, including a vector radix structure, are discussed in the chapter.

Number Theoretic Transforms and their Applications in Image Processing

A transform analogous to the discrete Fourier transform is defined on the Galois field GF(p), where p is a prime of the form k X 2n + 1, where k and n are integers. Such transforms offer a substantial variety of possible transform lengths and dynamic ranges. The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT. A transform of this type is used to filter a two-dimensional picture (e.g., 256 X 256 samples), and the results are presented with a comparison to the standard FFT. An absence of roundoff errors is an important feature of this technique.

Hall

Papers

Image Processing by Transforms Over a Finite Field