# High-Capacity Data-Hiding Scheme on Synthesized Pitches Using Amplitude Enhancement—A New Vision of Non-Blind Audio Steganography

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## Abstract

**:**

## 1. Introduction and Related Work

## 2. Materials and Methods

#### 2.1. Fundamentals

#### 2.2. Data Hiding Scheme

Algorithm 1 Encoding Procedure | |

Input: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$ and reference instrumental pitch P |

Output: | a stego-synthesized pitch |

Step 1: | find ${a}_{1},{a}_{2},\dots ,{a}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ by referencing P |

Step 2: | for all ${a}_{i},1\le i\le k$, obtain $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ as follows; |

if ($b{t}_{i}=1$) | |

set $a{\prime}_{i}=\sigma {a}_{i}$ | |

else | |

set $a{\prime}_{i}={a}_{i}$ | |

Step 3: | use $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ to create a pitch p |

Step 4: | return p |

Algorithm 2 Encoding Procedure | |

Input: | length of secret k, reference pitch P and received pitch p |

Output: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$ |

Step 1: | use standard pattern in Section 2.1 to obtain ${A}_{1},{A}_{2},\dots ,{A}_{k}$ of P |

Step 2: | use standard pattern in Section 2.1 to obtain ${a}_{1},{a}_{2},\dots ,{a}_{k}$ of p |

Step 3: | for each ${A}_{i}$ and ${a}_{i}$, decode secret bit $b{t}_{i}$ as follows. |

if (${A}_{i}\ne {a}_{i}$) | |

set $b{t}_{i}=1$ | |

else | |

set $b{t}_{i}=0$ | |

Step 4: | concatenate ${b}_{1},{b}_{2},\dots ,{b}_{i},\dots ,{b}_{k},1\le i\le k$ to form a bit stream B |

Step 5: | return B |

Algorithm 3 Encoding Procedure | |

Input: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$, secret order R and reference instrumental pitch P |

Output: | a stego-synthesized pitch |

Step 1: | find ${a}_{1},{a}_{2},\dots ,{a}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ by referencing P |

Step 2: | for all ${R}_{i},1\le i\le k$, obtain $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ as follows. |

if ($b{t}_{i}=1$) | |

set $a{\prime}_{{R}_{i}}=\sigma {a}_{{R}_{i}}$ | |

else | |

set $a{\prime}_{{R}_{i}}={a}_{{R}_{i}}$ | |

Step 3: | use $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ to create a pitch p |

Step 4: | return p |

Algorithm 4 Encoding Procedure | |

Input: | secret order R, reference pitch P and received pitch p |

Output: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$ |

Step 1: | use standard pattern in Section 2.1 to obtain ${A}_{1},{A}_{2},\dots ,{A}_{k}$ of P |

Step 2: | use standard pattern in Section 2.1 to obtain ${a}_{1},{a}_{2},\dots ,{a}_{k}$ of p |

Step 3: | for all ${R}_{i},1\le i\le k$, decode secret bit $b{t}_{i}$ with reference to the following condition: |

if (${A}_{{R}_{i}}\ne {a}_{{R}_{i}}$) | |

set $b{t}_{i}=1$ | |

else | |

set $b{t}_{i}=0$ | |

Step 4: | concatenate ${b}_{1},{b}_{2},\dots ,{b}_{i},\dots ,{b}_{k},1\le i\le k$ to form a bit stream B |

Step 5: | return B |

Algorithm 5 Encoding Procedure | |

Input: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$, secret order R and reference instrumental pitch P |

Output: | a stego-synthesized pitch |

Step 1: | find ${a}_{1},{a}_{2},\dots ,{a}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ by referencing P |

Step 2: | initialize AC = 0 |

Step 3: | for all ${R}_{i},1\le i\le k$, obtain $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ as follows. |

if ($b{t}_{i}=1$) | |

if(AC = 0) | |

set $a{\prime}_{{R}_{i}}=\sigma {a}_{{R}_{i}}$ | |

set AC = 1 | |

else | |

set $a{\prime}_{{R}_{i}}=\frac{1}{\sigma}{a}_{{R}_{i}}$ | |

set AC = 0 | |

else | |

set $a{\prime}_{{R}_{i}}={a}_{{R}_{i}}$ | |

Step 4: | use $a{\prime}_{1},a{\prime}_{2},\dots ,a{\prime}_{k}$ and ${b}_{1}{f}_{ap},{b}_{2}{f}_{ap},\dots ,{b}_{k}{f}_{ap}$ to create a pitch p |

Step 5: | return p |

Algorithm 6 Encoding Procedure | |

Input: | secret order R, reference pitch P and received pitch p |

Output: | secret bit stream $b{t}_{1},b{t}_{2},\dots ,b{t}_{k}$ |

Step 1: | use standard pattern in Section 2.1 to obtain ${A}_{1},{A}_{2},\dots ,{A}_{k}$ of P |

Step 2: | use standard pattern in Section 2.1 to obtain ${a}_{1},{a}_{2},\dots ,{a}_{k}$ of p |

Step 3: | for all ${R}_{i},1\le i\le k$, decode secret bit $b{t}_{i}$ with reference to the following condition: |

if (${A}_{{R}_{i}}\ne {a}_{{R}_{i}}$) | |

set $b{t}_{i}=1$ | |

else | |

set $b{t}_{i}=0$ | |

Step 4: | concatenate ${b}_{1},{b}_{2},\dots ,{b}_{i},\dots ,{b}_{k},1\le i\le k$ to form a bit stream B |

Step 5: | return B |

## 3. Results

## 4. Discussion

#### 4.1. Comparisons with Related Work

**LPF**(3 kHz) filters all signals with frequencies lower than 3 kHz.**mp3**(64 kbps) adopts an existing multimedia tool (Adobe Audition) to compress the stego-pitch (.wav file->.mp3 file) and decompress back to .wav file format.**Re-quantization**(16 to 32 bits) adopts an existing multimedia tool (Adobe Audition) to re-quantize the sampling point from 16 bits to 32 bits and then to re-quantize it back to 16 bits.**Re-quantization**(16 to 8 bits) adopts an existing multimedia tool (Adobe Audition) to re-quantize the sampling point from 16 bits to 8 bits and then to re-quantize it back to 8 bits.

#### 4.2. Performances under Other Attacks

#### 4.3. Theoretical Analysis

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

## 5. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) An application of a user backing up his sensitive data on a cloud storage service; (

**b**) an application of a user making digital rights; and (

**c**) an application of a user achieving an un-perceptual communication.

**Figure 2.**A square wave signal [38].

**Figure 8.**The time-domain comparison between simulated piano with: (

**a**) $k=10,000$; and (

**b**) real piano.

**Figure 10.**The time-domain comparison between: (

**a**) cover pitch; and (

**b**) stego-pitch with $k=10$ and $\sigma =1.01$.

**Figure 14.**The curve of capacity (k) to distortion (PSNR) between real and simulated stego-pitches with different $\sigma $ values.

**Figure 16.**The curve of the trend of distortion and capacity: (

**a**) proposed in [17]; and (

**b**) the work presented by the authors.

**Table 1.**The values of ${a}_{i}$, ${b}_{i}$ and ${b}_{i}{f}_{ap}$ of Middle C of a piano with $k=10$.

i | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}{\mathit{f}}_{\mathit{a}\mathit{p}}$ |
---|---|---|---|

1 | 0.2635 | 1.0000 | 262 |

2 | 0.7042 | 1.0038 | 263 |

3 | 0.5050 | 1.0077 | 264 |

4 | 0.3326 | 2.0038 | 525 |

5 | 0.8000 | 2.0077 | 526 |

6 | 0.2255 | 2.0115 | 527 |

7 | 0.3013 | 5.0345 | 1320 |

8 | 0.2823 | 7.0766 | 1854 |

9 | 0.2631 | 7.0805 | 1855 |

10 | 0.2402 | 7.0843 | 1856 |

**Table 2.**The modified parameters after embedding secret 1001101101 in Middle C of a simulated piano with $\sigma =1.01$.

i | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}{\mathit{f}}_{\mathit{a}\mathit{p}}$ |
---|---|---|---|

1 | 0.2661 | 1.0000 | 262 |

2 | 0.7042 | 1.0038 | 263 |

3 | 0.5050 | 1.0077 | 264 |

4 | 0.3359 | 2.0038 | 525 |

5 | 0.8080 | 2.0077 | 526 |

6 | 0.2255 | 2.0115 | 527 |

7 | 0.3043 | 5.0345 | 1319 |

8 | 0.2851 | 7.0766 | 1854 |

9 | 0.2631 | 7.0805 | 1855 |

10 | 0.2426 | 7.0843 | 1856 |

**Table 3.**The modified parameters after embedding secret 1001101101 in Middle C of a simulated piano with $R=\left\{3,1,7,9,2,10,4,6,5,8\right\}$ and $\sigma =1.01$.

i | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}{\mathit{f}}_{\mathit{a}\mathit{p}}$ |
---|---|---|---|

1 | 0.2635 | 1.0000 | 262 |

2 | 0.7112 | 1.0038 | 263 |

3 | 0.5101 | 1.0077 | 264 |

4 | 0.3359 | 2.0038 | 525 |

5 | 0.8000 | 2.0077 | 526 |

6 | 0.2278 | 2.0115 | 527 |

7 | 0.3013 | 5.0345 | 1320 |

8 | 0.2851 | 7.0766 | 1854 |

9 | 0.2657 | 7.0805 | 1855 |

10 | 0.2402 | 7.0843 | 1856 |

**Table 4.**The modified parameters after embedding secret 1001101101 in Middle C of a simulated piano using the alternating current (AC) algorithm with $R=\left\{3,1,7,9,2,10,4,6,5,8\right\}$ and $\sigma =1.01$.

i | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}{\mathit{f}}_{\mathit{a}\mathit{p}}$ |
---|---|---|---|

1 | 0.2635 | 1.0000 | 262 |

2 | 0.7112 | 1.0038 | 263 |

3 | 0.5101 | 1.0077 | 264 |

4 | 0.3293 | 2.0038 | 525 |

5 | 0.8000 | 2.0077 | 526 |

6 | 0.2278 | 2.0115 | 527 |

7 | 0.3013 | 5.0345 | 1320 |

8 | 0.2795 | 7.0766 | 1854 |

9 | 0.2605 | 7.0805 | 1855 |

10 | 0.2402 | 7.0843 | 1856 |

**Table 5.**The bit error ratio (BER) of the proposed methods and related work. LPF: low pass filter; HQ: hard quantization; SQ: soft quantization.

Methods/Attacks | LPF (3 kHz) | mp3 (64 kbps) | Re-Quantization 16–32 bits | Re-Quantization 16–8 bits |
---|---|---|---|---|

Ours (k = 40) | 0.0% | 0.0% | 0.0% | 0.0% |

Akhaee et al. [17]: HQ, SQ | 15.0%, 15.0% | 10.2%, 0.1% | $0.0\text{\%}$, 0.0% | 0.0%, 0.0% |

Wu et al. [40] | $\varnothing $ | 4.3% | $\varnothing $ | $\varnothing $ |

Chen et al. [41] | $\varnothing $ | 6.5% | $\varnothing $ | 11.9% |

**Table 6.**The BER of the proposed methods and related work. HPF: high pass filter; DC: direct current.

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## Share and Cite

**MDPI and ACS Style**

Shiu, H.-J.; Lin, B.-S.; Cheng, C.-W.; Huang, C.-H.; Lei, C.-L.
High-Capacity Data-Hiding Scheme on Synthesized Pitches Using Amplitude Enhancement—A New Vision of Non-Blind Audio Steganography. *Symmetry* **2017**, *9*, 92.
https://doi.org/10.3390/sym9060092

**AMA Style**

Shiu H-J, Lin B-S, Cheng C-W, Huang C-H, Lei C-L.
High-Capacity Data-Hiding Scheme on Synthesized Pitches Using Amplitude Enhancement—A New Vision of Non-Blind Audio Steganography. *Symmetry*. 2017; 9(6):92.
https://doi.org/10.3390/sym9060092

**Chicago/Turabian Style**

Shiu, Hung-Jr., Bor-Shing Lin, Chia-Wei Cheng, Chien-Hung Huang, and Chin-Laung Lei.
2017. "High-Capacity Data-Hiding Scheme on Synthesized Pitches Using Amplitude Enhancement—A New Vision of Non-Blind Audio Steganography" *Symmetry* 9, no. 6: 92.
https://doi.org/10.3390/sym9060092