## 1 Introduction
For example, alternatives to perform audio identification by microphone capture have been presented [5], where one of the best known cases is that of Shazam, a company that has multiple patents in this regard [18; 19]. Other cases include the identification of the audio environment to present related content (Google) [20], or in general, perceptual methods presented by companies such as Philips, Microsoft or Gracenote [5]. Different approaches to perceptual hash functions have also been presented in scientific literature. In general, perceptual hash methods may use one or more of the following blocks: (i) Divide the input signal into contiguous time windows with some overlap and apply some kind of analysis to them; (ii) separate the frequency components of the signal according to the human auditory system; (iii) apply some dimensional reduction technique. In the first case, different types of time-frequency transformations have been used, such as the FFT (fast Fourier transform ), DWT (discrete wavelet transform) [2; 21], SWT (stationary wavelet transform) [22], modified discrete cosine transform [23], and Radon transform [24], among others. In the second case, the use of techniques related to MFCC (Mel-frequency cepstrum coefficients) [25], SFM (spectral flatness measure), or SCF (spectral correlation function) have been proposed [5]. Finally, it is pertinent to use any size reduction technique that facilitates obtaining a short and constant code, for example using NMF (non-negative matrix factorization) [21; 24] or PCA (principal component analysis). In [2], the authors use the approximation coefficients of a 3-level wavelet decomposition as the perceptual feature value, and a measurement matrix to reduce its dimension. According to the results, the approach shows improvements in terms of low pass filtering and MP3 compression. However, for lossy audio encoding the results are not consistent, as the error is lower for a low bit rate (average BER = 0.0042 for a 48 kbps bit rate), compared to a higher bit rate (BER = 0.2189 for a 128 kbps bit rate). In any case, research related to perceptual hash functions is an active topic, mainly because tolerance to some types of modifications depends on the application. Therefore, there are still some challenges to be solved in this area. For example, in digital forensics it is required to identify content when the whole data is not available, or when the content has been manipulated through content-preserving operations (perceptual). Additionally, it is necessary to take into account the computational cost, both in the generation and in the process of searching for the hash value in a database. Accordingly, this document proposes a new and robust hash function methodology for integrity verification in audio signals. In other words, what is expected is that the hash value be invariable or at least almost insensitive to moderate or permissible transformations in audio signals, such as format changes. This can facilitate chain of custody processes for digital evidence, even with unintended errors in the processing of information. The proposed method begins with the characterization of the speech signal by calculating the MFCC and reducing dimensions by PCA. Subsequently, the data given by PCA is encrypted, using as inputs, two values that come from a particular binarization system that uses the Collatz conjecture as a basis. Finally, a robust 96-bit code is obtained that can support input data modifications such as compression, amplitude modification, re-sampling and re-quantization. The rest of the paper is organized as follows: Section 2 explains the concepts that will serve as a basis for the following sections. Section 3 presents the proposed method to summarize a speech signal. Section 4 shows the experimental validation, results and comparison of the proposed method. Finally, in Section 5 the conclusion is given.