Tamper recovery algorithm for digital speech signal based on DWT and DCT

Abstract

It is a challenging work to design tamper recovery schemes for digital speech signal. Briefly, there are two problems need to be solved. One is that the signals used to tamper recovery are difficult to generate and embed, and the second is that it’s hard to tamper location precisely for attacked speech signal. In this paper, compression and reconstruction method based on discrete wavelet transform (DWT) and discrete cosine transform (DCT) is given, to obtain the compressed signals used to tamper recovery. And then frame number and compressed signals are embedded based on block-based method. Attacked signal can be located by frame number, and compressed signals are extracted and used to reconstruct the attacked signal. Theory analysis and experimental results indicate that the scheme proposed not only improves the accuracy of tamper localization, but also can reconstruct the attacked signals.

1 Introduction

With the development of internet and multimedia technology, the authentication of digital media becomes more and more important. And much research has been done in this field [10, 14]. In this paper, we limit our attention to digital speech forensics. On the one hand, speech signal often implies some instructions. If users consider the attacked signal is the original one and act according to the instructions of the attacked signal, it may cause serious consequences. On the other hand, speech signals are more likely to cause attacker’s interest and be maliciously attacked. So, as to recipient, verifying the integrity and authenticity of received speech signal is the first and essential step. Fortunately, the forensic technology based on digital watermarking [1, 9, 17, 18] gives a method to verify the authenticity of digital speech.

For speech signals, most of the results are focused on speaker recognition and identification [5, 6, 15, 20]. For the existed content authentication schemes, there are shortcomings more or less. In [16], a speech authentication scheme based on digital watermarking and pattern recovery is proposed. By using the cyclic pattern embedding method, the scheme has the ability of tamper location. While the method increases the load of the watermarked signal. In [3], an authentication scheme based on compression technique and codebook-excited linear prediction for compressed speech is proposed. In the paper, watermark bits are generated by the features extracted during compression process based on codebook-excite linear prediction. For speech signals compressed based on other speech codecs, the scheme is ineffective. The watermark bits are embedded based on least significant bits (LSBs), which is fragile to signal processing operations. As to the scheme, signal processing will be regarded as hostile attack. Therefore the scheme is powerless in some applications. In [24], authors introduced an integrity and authenticity mechanic for real-time multimedia communication, and produced a method for real-time speech integrity and authentication incorporating with GSM 610 full-rate coder. And a speech authentication scheme mainly used in the real-time communication process is proposed. For some signals saved on a hard drive, the scheme is unsuitable.

The expressed meaning of hostile attacked speech signal is different to the original one, which may cause serious consequences. If one speech is attacked and the instruction is an urgent task, maybe the greatest wish is to acquire the meaning of the original one. So, reconstructing the attacked signal is the users to pray in this case. Currently, there has been a considerable amount of work on authentication and recovery for digital images [2, 7, 11, 19]. It’s a pity that, there are comparatively few schemes for digital speech [4, 13].

For tamper recovery schemes, the first step is to locate the attacked signals precisely. But so far the problem has not been solved well. When it comes to the problem of tamper location, the first method thought is based on synchronization code [8, 21, 22]. Indeed the method can locate watermarked signal. However, they have some shortcomings. (1) Synchronization codes embedded based on public features are vulnerable to substitution attack [12]. (2) For the schemes, the content between two neighboring synchronization codes is regarded as the watermarked signal. But the authenticity of the watermarked signal is not verified. So, it can locate the watermarked signal only, but not locate the signal attacked. (3) For the short-time stationarity of speech signal, the synchronization codes can be extracted from some segments, but not only one. Therefore, the schemes can locate watermarked signal roughly not precisely.

Considering the background and motivation above, the tamper recovery algorithm for digital speech is proposed. One compression and reconstruction method for speech signal based on discrete wavelet transform (DWT) and discrete cosine transform (DCT) is given. Compressed signal is as watermark and comprise approximate coefficients from DWT and some DCT coefficients. Approximate coefficients are used to reconstruct the approximate signal, and DCT coefficients are used to reconstruct the residual signal. Then original signal can be obtained by combining the approximate signal and residual signal. Frame number and compressed signal are embedded based on block-based method. Frame number is used for tamper localization, and compressed signals are used to reconstruct the attacked frames. Theoretical analysis and experimental evaluation demonstrate that the scheme has ability of tamper localization, and can recover the attacked signal.

The remainder of this paper is organized as follows. Section 2 shows the fundamental theory for the scheme proposed. Section 3 gives the recovery scheme based on digital watermark. Section 4 analyzes the performance of the algorithm theoretically. The simulation results are presented in Section 5. Finally, some conclusions are included in Section 6.

2 Fundamental theory

2.1 Discrete Wavelet Transform

Discrete wavelet transform (DWT) can be viewed as the multiresolution decomposition of a sequence. It takes a length J sequence u(j), and generates an output sequence of length N. The output is the multiresolution representation of u(j). It has J/2 values at the highest resolution, J/4 values at the next resolution, and so on.

The structure of the DWT is due to the dyadic nature of its time-scale grid, shown in Fig. 1, in which AC _q and DC _q represent the approximate and detail coefficients from q-level DWT, respectively. The length of AC _q is J/2^q, equal to DC _q .

Fig. 1

The structure of the DWT

2.2 Compressed signal generation

In this paper, speech signal is compressed, and the compressed signal is as watermark and embedded. Denote A as the original speech signal, the method of compressed signal generation is as follows.

2.2.1 Down sampling and DWT

• Step 1 Cut A into P frames, and the length of each frame is N. The i-th frame is denoted by A _i .

• Step 2 Re-sampling the speech signal A, and the sampling frequency is dropped from f to f′, where f denotes the sampling frequency of original signal, and f′ denotes that after re-sampling. The signal re-sampled is denoted by A′.

• Step 3 A′ is cut into P frames. The i-th frame is denoted by A _i ′, and the length is N′ (N′ = N ⋅ f′/f).

• Step 4 D-level DWT is performed on A _i ′, and the approximate coefficient is denoted by C1 _i , which is as one part of the compressed signal. And the length of C1 _i is M, M = N′/2^D.

2.2.2 DCT on residual signal

• Step 1 Reset the detail coefficients to 0.

• Step 2 D-level inverse DWT is performed on the approximate coefficient C1 _i and the detail coefficients. The signal obtained is denoted by IA _i ′.

• 3. Step 3: The difference between A _i ′ and IA _i ′ is regarded as the residual signal, denoted by E _i , which can be obtained by Eq. 1.

  $$ {E}_i={A_i}^{\prime }-I{A_i}^{\prime } $$

  (1)

• Step 4 DCT is performed on the residual signal E _i , ${E}_i=\left\{{e}_1,{e}_2,\cdots, {e}_{N^{\prime }}\right\}$. Rearrange |e _t | (1 ≤ t ≤ N′) in order of large to small, and denote the M/2 -th value as |e _M/2|.

• Step 5 Record the coefficients (amplitude larger than |e _M/2|) and the location, as another part of compressed signal, denoted by C2 _i and C3 _i , respectively.

  Let C _i  = C1 _i  ∪ C2 _i  ∪ C3 _i as the compressed signal of A _i .

2.3 Reconstruction

• Step 1 Perform D-level inverse DWT on the approximate coefficient C1 _i and the 0 value detail coefficients, to generate the approximate signal R1, as the first part of reconstructed signal.

• Step 2 Perform inverse DCT on the coefficients obtained by the Step 5 in Section 2.2.2, to reconstruct the residual signal R2, as the second part of reconstructed signal.

• Step 3 Combine the approximate and residual signal by R1 + R2.

• Step 4 Resample the signal obtained in Step 3, using the sampling frequency f, to obtain the reconstructed signal.

As an example, one signal is selected, and the reconstructed signal is given. In this section, the length of the signal after down-sampling is N′ = 1024, D = 3, M = 128. Figure 2 is the speech signal after down-sapling. Figure 3 is the approximate signal (R1), obtained by inverse DWT on approximate coefficients C1 _i and 0 value detail coefficients. Figure 4 is the residual signal, obtained by inverse DCT. And Fig. 5 is the signal combined by R1 and R2.

Fig. 2

The original signal after down-sampling

Fig. 3

The signal R1 by inverse DWT

Fig. 4

The signal R2 by inverse DCT

Fig. 5

The signal combined by R1 and R2

Based on the results shown above, it can be seen that the signal shown in Fig. 5 is close to that shown Fig. 2, which demonstrates that the original speech can be reconstructed approximately based on the compressed signal.

2.4 Embedding strategy

For watermarked speech, if one frame is attacked, watermark embedded in the frame will be destroyed too. So, the compressed signal of one frame should be embedded into other non-attacked frame.

For the scheme proposed, the compressed signals are scrambled before embedding, aiming to make the compressed signal is embedded into other non-attacked frame. The strategy is shown in Fig. 6.

Fig. 6

Scrambling the compressed signal

In Fig. 6, A _i denotes the i-th frame of the speech signal, C _i denotes the compressed signal of i-th frame. C _i ′ denotes the i-th compressed signal after being scrambled. For the proposed scheme, C _i ′ is the signal that will be embedded into the i-th frame A _i .

3 The scheme

Denote A = {a _l |1 ≤ l ≤ L} as original speech signal, where a _l represents the l-th sample. The recovery scheme is described as follows.

3.1 Preprocessing

• Step 1 Cut A into P frames, and N is the length of each frame. Denote A _i  = {a _i,j |1 ≤ j ≤ N} as the i-th frame, 1 ≤ i ≤ P, N = L/P.

• Step 2 By using the compression method in Section 2.2, the compressed signal of A _i can be obtained, denoted by C _i . Then all the compressed signals C _i (1 ≤ i ≤ P) are scrambled using chaotic address index sequence.

  Denote X = {x _i |i = 1, 2, ⋯, P} as the pseudo-random sequence. The elements of X are generated by the Logistic chaotic mapping shown in Eq. (2).

  $$ {x}_{i+1}=\mu {x}_i\left(1-{x}_i\right),\kern0.5em {x}_0=k,\kern0.5em 3.5699\le \mu \le 4 $$

  (2)

  where k is the initial value and as key of the system. The elements of X are sorted in ascending order shown in Eq. (3), where h(i) is the address index of the sorted chaotic sequence.

  $$ {x}_{h(i)}=\mathrm{ascend}\left({x}_i\right),\kern0.5em i=1,2,\cdots P $$

  (3)

  Denote C _i ′ as the compressed signal after being scrambled, C _i ′ = C _h(i), 1 ≤ i ≤ P.

• Step 3 Scrambling the samples of A _i by using the same method above, denoted by S _i , S _i  = {s _i,j , 1 ≤ j ≤ N}, where s _i,j  = a _i,h(j), j = 1, 2, ⋯, N.

• Step 4 Divide S _i into 3 parts, denoted by S1 _i , S2 _i and S3 _i , respectively. The length of S1 _i and S2 _i is N ₁, and the length of S3 _i is N ₂.

• Step 5 The frame number i is mapped to the sequence of integers Y _i  = {y _n , y _n − 1, ⋯ y ₁}, and the elements can be obtained by Eq. (4).

  $$ i={y}_n\cdot {10}^{n-1}+{y}_{n-1}{10}^{n-2}+\cdots +{y}_1 $$

  (4)

  In this paper, Y _i is as the identifier of i-th frame and embedded into S1 _i and S2 _i , respectively. The compressed signal C _i ′ is embedded into S3 _i . The method of segmentation is shown in Fig. 7.

  Fig. 7

  

  Segmentation method

3.2 Watermark Embedding

3.2.1 Embed frame number

Y _i  = {y _n , y _n − 1, ⋯ y ₁} as the identifier of i-th frame is embedded into S1 _i and S2 _i , respectively. Denote $S{1}_i=\left\{s{1}_1,s{1}_2,\cdots s{1}_{N_1}\right\}$, y _n is embedded into the first 3 consecutive samples s1₁, s1₂ and s1₃. The embedding method is described as follows.

• Step 1 Denote z _m  = ⌊|100 ⋅ s1 _m |⌋ mod 10, where ⌊ ⋅ ⌋ returns the largest integer less than the original value, 1 ≤ m ≤ 3. v _m  = sign(s1 _m ), if s1 _m  ≥ 0, v _m  = 0, and if s1 _m  < 0, v _m  = 1. For z _m  = 0, set z _m  = 1. Calculate V = f(z ₁, z ₂, z ₃, v ₁, v ₂, v ₃) according to the Eq. (5).

  $$ f\left({z}_1,{z}_2,{z}_3,{v}_1,{v}_2,{v}_3\right)=\left[\left({v}_1+{v}_2+{v}_3+{z}_1\right)\times 1+{z}_2\times 2+{z}_3\times 3\right] \mod 10 $$

  (5)

  If y _n  = V, z _m , 1 ≤ m ≤ 3, are not need to be quantified.

  If y _n  ≠ V, quantify z ₁, z ₂ or z ₃, to make y _n  = V, under the condition that the original values are as close as possible to that after being quantified.

  The quantitative method is z ₁ ± 1, z ₂ ± 1 or z ₃ ± 1. Using the quantified values substitute z ₁, z ₂ and z ₃, to embed y _n . For example, if s1₁ = 0.5692, s1₂ = − 0.3817, s1₃ = 0.3271 and y _n  = 2, it’s got that z ₁ = 6, z ₂ = 8, z ₃ = 2, v ₁ = 0, v ₂ = 1, v ₃ = 0. Based on Eq. (5), V = 9. In order to make V = y _n , set z ^′₃  = z ₃ + 1. z ^′₃ is the value after being quantified.

• Step 2 Using the same method above, y _n  , y _n − 1, ⋯, y ₁ are embedded into the two segments S1 _i and S2 _i .

  The quantified signal is denoted by W1 _i and W2 _i .To clearly show the embedding method, an example is given in Table 1, i = 272, Y _i  = {2, 7, 2}, n = 3.

  Table 1 An example of quantifying method

3.2.2 Embed compressed signal

Denote C _i ′ = {c _t , 1 ≤ t ≤ 2M} as the compressed signal, which is embedded into S3 _i based on the block-based method [13], and $S{3}_i=\left\{s{3}_1,s{3}_2,\cdots s{3}_{N_2}\right\}$.

For each coefficient in C _i ′, sign (“+” or “-“) and five numbers are embedded. Let c ₁ ∈ C _i ′ as the first coefficient, and denote c ¹₁  = ⌊|c ₁|⌋ mod 10, c ²₁  = ⌊|10 ⋅ c ₁|⌋ mod 10, c ³₁  = ⌊|100 ⋅ c ₁|⌋ mod 10, c ⁴₁  = ⌊|1000 ⋅ c ₁|⌋ mod 10 and c ⁵₁  = ⌊|10000 ⋅ c ₁|⌋ mod 10, which are the five numbers of c ₁. For example, if c ₁ = 1.3628, sign is “+”, and the five numbers are 1, 3, 6, 2 and 8. They are embedded into the first 6 consecutive samples of S3 _i .

Let the 6 samples as s3₁, s3₂, ⋯, s3₆. Partition them into 6 blocks, denoted by B ₁, B ₂, …, B ₆, respectively. B ₁ = {b ¹₁ , b ²₁ , b ³₁ , b ⁴₁ , b ⁵₁ , b ⁶₁ }, where b ¹₁  = sign(s3₁), b ²₁  = sign(s3₂), b ³₁  = sign(s3₃), b ⁴₁  = ⌊|10 ⋅ s3₁|⌋, b ⁵₁  = ⌊|10 ⋅ s3₂|⌋, b ⁶₁  = ⌊|10 ⋅ s3₃|⌋. B ₂ = {b ¹₁ , b ²₁ , b ³₁ , b ⁴₂ , b ⁵₂ , b ⁶₂ }, where b ⁴₂  = ⌊|10 ⋅ s3₄|⌋, b ⁵₂  = ⌊|10 ⋅ s3₅|⌋, b ⁶₂  = ⌊|10 ⋅ s3₆|⌋. By using the same method, other blocks can be obtained.

As an example, 6 samples are selected, and the partition result is shown in Table 2. Based on the partition, the embedding method is as follows.

Table 2 The partition result

• Step 1 Embed the sign of c ₁, “+” or “-” into B ₁.

  Calculate the sum of 6 values in B ₁, which is denoted by T. If 1  0 ≤ c₁, and T mod 2=1, quantify b ⁴₁ , b ⁵₁ or b ⁶₁ , to make T mod 2 = 0 and embed the sign “+”, such as b ⁴₁ + 1, or b ⁴₁ −1. If c₁ < 0, and T mod 2 = 0 , quantify b ⁴₁ , b ⁵₁ or b ⁶₁ , to make T mod 2 = 1 and embed the sign “-”. For other conditions, the values in B ₁ remain the same without modification.

• Step 2 Embed the five numbers of c ₁ (c ¹₁ , c ²₁ , c ³₁ , c ⁴₁ , c ⁵₁ ) into B ₂, B ₃, ⋯, B ₆, respectively.

  • (1) Based on the values in B ₂, V can be obtained by using the Eq. (5). Using the same method of frame number embedding in Section 3.2.1, c ¹₁ can be embedded by quantifying b ⁴₂ , b ⁵₂ and b ⁶₂ .

  • (2) Similarly, c ²₁ , c ³₁ , c ⁴₁ and c ⁵₁ are embedded into the blocks of B ₃, B ₄, B ₅ and B ₆. Suppose c ₁ = − 1.3551, the quantitative method is show in Table 3, B ^′ _t , 1 ≤ t ≤ 6, represent the corresponding values after being quantified.

    Table 3 The embedding method for c ₁ = − 1.3551

  • Step 3 By using the steps 1–2 above, the compressed signal C _i ′ = {c _t , 1 ≤ t ≤ 2M} can be embedded into S3 _i , and signal after embedding is denoted by W3 _i .

    Concatenate W1 _i , W2 _i and W3 _i , then inverse scrambling is performed to obtain the watermarked signal of the i-th frame. The embedding process is shown in Fig. 8.

    Fig. 8

    

    The process of watermark embedding

3.2.3 Content authentication and tamper recovery

Denote W as the watermarked speech signal.

• (1) Cut W into P frames, and the samples of each frame are scrambled. The i-th frame after being scrambled is denoted by W _i . W1 _i , W2 _i and W3 _i are the 3 segments of W _i . The length of W1 _i and W2 _i is N ₁, the length of W3 _i is N ₂.

• (2) Extract the sequence of integers from $W{1}_i=\left\{w{1}_1,w{1}_2,\cdots, w{1}_{N_1}\right\}$ and $W{2}_i=\left\{w{2}_1,w{2}_2,\cdots, w{2}_{N_1}\right\}$, denoted by Y ¹ _i  = {y ¹ _n , y ¹ _n − 1 , ⋯, y ¹₁ } and Y ² _i  = {y ² _n , y ² _n − 1 , ⋯, y ²₁ }, respectively.

  • Step 1 According to the embedding method in Section 3.2.1, the integers in Y ¹ _i and Y ² _i can be calculated by using Eq. (5).

  • Step 2 Reconstruct the frame number based on Y ¹ _i and Y ² _i , denoted by i ¹ = y ¹ _n  × 10^n − 1 + y ¹ _n − 1  × 10^n − 2 + ⋯ + y ¹₁ and i ² = y ² _n  × 10^n − 1 + y ² _n − 1  × 10^n − 2 + ⋯ + y ²₁ , which are the frame number extracted.

• (3) Content authentication

  If i ¹ = i ², it indicates that the i-th frame is intact. Otherwise, it indicates that the i-th frame has been tampered. The process of content authentication is shown in Fig. 9.

  Fig. 9

  

  The process of content authentication

• (4)* Tamper recovery

  Suppose that the frames of 1st to i-1th are all intact and the next N successive samples are subjected to malicious attack, the tamper recovery method is as follows.

  • Step 1 Move and authenticate the next N successive samples, until the samples can pass the authentication. Then reconstruct the frame number, denoted by i′. The signal between i-1th and i′ th is regarded as the attacked frame. Tamper location process is shown in Fig. 10.

    Fig. 10

    

    The processes of tamper location

  • Step 2 According to the address index of the sorted chaotic sequence, find the frame, from which the compressed signal of attacked frame can be extracted. Let W _i ′ as the frame, and CS _i ′ = {cs ₁, cs ₂, ⋯, cs _2M } as compressed signal. The extraction method is described as follows.

    • ① Cut W _i ′ into 3 segments, and the 3rd segment is denoted by $W{3_i}^{\prime }=\left\{{w}_1,{w}_2,\cdots, {w}_{N_2}\right\}$.

    • ② Take the extraction of cs ₁ as an example, which is extracted from the first 6 consecutive samples of W3 _i ′. Based on the block-based method (shown in Tables 2 and 3), the sign of cs ₁ can be extracted from the values in B ₁, by using Eq. (6).

      $$ U={T}^{\prime } \mod 2 $$

      (6)

      where T′ represents the sum of the values in B ₁. And U = 0 indicates that the sign of cs ₁ is “+”, U = 1 indicates that the sign of cs ₁ is “-”.

    • ③ According to the values in B ₂, cs ¹₁  = ⌊|cs ₁|⌋ can be calculated by using the Eq. (5). Similarly, cs ²₁ , cs ³₁ , cs ⁴₁ , cs ⁵₁ can be extracted. Then cs ₁ can be constructed by the Eq. (7).

      $$ c{s}_1= sign\left(c{s}_1\right)\times \left(c{s}_1^1+\frac{c{s}_1^2}{10}+\frac{c{s}_1^3}{100}+\frac{c{s}_1^4}{1000}+\frac{c{s}_1^5}{10000}\right) $$

      (7)

    • ④ By using the same method, the compressed signal CS _i ′ = {cs ₁, cs ₂, ⋯, cs _2M } can be extracted. Then the attacked frame can be reconstructed approximatively using the method in Section 2.3

4 Performance analysis

4.1 Compression ratio

In this paper, speech is compressed firstly, which is as watermark and embedded. Embedding inevitably degrade the quality of speech signal. So, the signal as watermark should be compressed as possible. The compression ratio (CR) is defined by CR = N _c /N _o , where N _c represents the length of compressed signal, and N _o represents the length of original one. For the compression method proposed, CR can be calculated by

$$ CR=\frac{f^{\prime }}{2^{D-1}\cdot f} $$

(8)

where D denotes the level of DWT, and the meaning of f and f′ are same to that in section 2.2.1.

4.2 Ability of tamper recovery

Compressed signal is as watermark and embedded. If watermarked signal is attacked, the watermark embedded will be attacked too. So, the compressed signal of one frame should not be embedded into itself, but be embedded into other non-attacked frame. In this paper, the compressed signals are scrambled before embedding, in order to ensure that the compressed signal of the attacked frame can be extracted correctly from other frame. If compressed signal of one attacked frame can be extracted correctly, the attacked signal can be reconstructed. So, the tamper recovery ability is related to the performance of scrambling method.

Denote AC as the ability of tamper recovery, and it’s defined by the Eq. (9).

$$ AC=\frac{F_a}{F} $$

(9)

where F _a represents the number of frames can be recovered, and F represents frame number of watermarked signal. Supposed that, half of frames of watermarked signal are attacked, and the compressed signals of attacked frames are embedded into other half frames and all intact, the attacked frames can be recovered. The tamper recovery can reach the maximum capacity in this case. That is the maximum value of F _a is F/2. So, the maximum recovery ability of the scheme is 1/2.

4.3 Security

For some watermark schemes, watermark embedded is based on public features. From the analysis in [12], we can get that the schemes are vulnerable subjected to substitution attack.

In this paper, samples of each frame are scrambled before embedding, and frame number and watermark are embedded into scrambled samples. After that, anti-scrambling is performed to get watermarked signal. So, watermarked samples are randomly throughout the whole frame, and the features used to embed watermark are secret for attackers. It’s difficult to get the embedding position to perform attack without the key. If one frame is attacked, the attacked frame can be detected with high probability 1/2 ⋅ 10ⁿ, where n is the number of integers in Y _i (generated by Eq. (4)). The ability of the scheme to resist attack is

$$ {R}_A=1-1/2\cdot {10}^n $$

(10)

4.4 Performance of tamper location

4.4.1 Shortcomings of the scheme based on synchronization codes

Desynchronization attacks can disrupt the location of watermark, and cause the watermark bits extracted incorrect. So, desynchronization attack is considered to be one of the most difficult attacks to resist [22]. Most of the schemes robust against desynchronization attacks are based on synchronization code [8, 21, 22]. Based on the analysis in [12], we can get that the scheme based on synchronization code has some shortcomings. ①It can locate the watermarked signal only, but not locate the signal attacked. ②There are some segments, but not only one, from which the synchronization codes can be extracted, for short-time stationarity of speech signals. In order to confirm the conclusion, some test results are shown in the following.

Select one segment of speech signal randomly, and the length is 3000. Denote SC = {1010011101} as the synchronization code. The test signal is divided into 3 frames, and synchronization code is embedded into 1st and 3rd frame, shown in Fig. 11.

Fig. 11

The signal synchronization code embedded

• ① If the 2nd frame is subjected to attack, deletion, insertion or substitution, the attacked content cannot be detected by the two adjacent synchronization codes, extracted from the 1st and 3rd frame. As an example, Fig. 12 shows the test result for deletion attack.

  Fig. 12

  

  The synchronization code embedded signal subjected to deletion attack

• ② Search the synchronization code from the test signal, and the result is shown in Fig. 13. It is found that the synchronization code can be extracted correctly from the signals within rectangle. So, the method can locate the watermarked signal roughly not precisely.

  Fig. 13

  

  Searching result for synchronization code

4.4.2 The ability of precisely tamper location for the scheme proposed

The reason of the scheme tamper location roughly is that, one code is embedded by quantifying the feature generated by many samples. The more samples selected, the more tamper location roughly is. To address the above problems, and in consideration of inaudibility and robustness, one code is embedded into a few samples (three samples) in this paper.

For the scheme, one frame is located and authenticated by the sequence of n integers. The probability of false tamper location for one frame is 1/2 ⋅ 10ⁿ, approximate to zero with the increasing of n. So the method can tamper location precisely, and the probability of tamper location R _L is computed theoretically by Eq. (10).

Based on the analysis in this section, Table 4 gives the comparison of various abilities for some different schemes [8, 18, 21–23], containing the security and the ability of tamper location precisely, which are denoted by AI and AII, respectively. In Table 4, DYWT represents Dyadic Wavelet Transform. From the results shown in Table 4, it can be concluded that the scheme proposed has many advantages comparing with the schemes, [8, 18, 21–23].

Table 4 Comparison of abilities for different schemes

5 Experimental results

We use MATLAB to simulate and analyze the performance of the recovery scheme proposed. And the computer used is powered by a 3.4-GHz Intel Core i7 processor and has 8GBs of RAM and an AMD R9 360 for graphics. 100 test signals are selected, contain 5 types. The number of each type signal is 20. Type 1 to type 4 are recorded by digital voice recorder, SONY PCM-D100, and the recording environments are quiet room, noisy room, open field and noisy station. Type 5 is selected for the library. The signals selected are WAVE format 16-bit quantified mono signals, sampled at 44.1 kHz. The parameters are set as follows, L = 81920, P = 20, N = 4096, f = 44100, f _r  = 11025, D = 3, N ₁ = 12, N ₂ = 4072, n = 4, k = 0.68, μ = 3.9728.

5.1 Inaudibility

In the paper, subjective difference grades (SDG) and objective difference grades (ODG) are used to test the inaudibility of the watermarked speech. The meaning of the scores in SDG and ODG are listed in Table 5.

Table 5 Subjective and objective difference grades

The SDG and ODG values of five types watermarked signal are listed in Table 6, in which SDG values are obtained from 10 listeners, and ODG values are acquired by using the PEAQ system. Based on the test results, it can be seen that the watermarked signal is inaudibility.

Table 6 The SDG and ODG values of different type watermarked signals

5.2 Reconstruction quality

One part of the original signal (called approximate signal) can be generated based on the approximate coefficients from DWT, and another part of the original signal (called residual signal) can be obtained by DCT coefficients. And then, original signal are reconstructed approximately by summing the two part signals.

In the following, the difference of original speech and reconstructed one, caused by different ways, are tested and compared. Select one part of the speech signal, from the library randomly, shown in Fig. 14. Compress and reconstruct the signal by using the two different methods, proposed in this paper and in [13]. The reconstructed signals are shown in Figs. 15 and 16, with the same compression ratio. Then the two residual signals are shown in Figs. 17 and 18, respectively.

Fig. 14

Speech signal selected from the library randomly

Fig. 15

Reconstructed signal based on the method in this paper

Fig. 16

Reconstructed signal based on the method in [13]

Fig. 17

The residual signal caused by the method in this paper

Fig. 18

The residual signal caused by the method in [13]

The energy of the residual signal generated by the method is calculated and compared with that generated by [13]. It’s got that the energy the energy in this paper is less than that in [13]. For the signals in Figs. 17 and 18, the energy is 1.5607 and 2.4626, respectively. So, the reconstruction method in this paper can result in less energy loss than the method in [13]. Table 7 lists the SDG and ODG values of some reconstructed signals, by using different methods. It can be concluded that the reconstructed signals by using the method in this paper have better perceptual quality than that in [13], with the same compression ratio. Therefore the compression and reconstruction method is more effective.

Table 7 SDG and ODG values of some reconstructed signals by different methods

5.3 Tamper Recovery

For all attack channels can be viewed as deletion, insertion and substitution channel for watermarking [23]. In this section, one watermarked speech signal is selected from the library randomly shown in Fig. 19, which will be subjected to the 3 types attack. And Fig. 20 shows the watermarked signal after being scrambled for each frame. Then the corresponding tamper location and tamper recovery results are given.

Fig. 19

Watermarked speech

Fig. 20

Watermarked speech after each frame being scrambled

For deletion attack, the detailed steps are given, aiming to make the method of tamper location and recovery explicitly. While for other attacks, the results of tamper location and tamper recovery are given only.

5.3.1 Tamper recovery for deletion attack

The watermarked speech shown in Fig. 19 is subjected to deletion attack, and the detailed tamper recovery steps are shown as follows.

• Step 1 The samples 65001th to 72800th are selected and deleted, shown in Fig. 21.

  Fig. 21

  

  Watermarked speech subjected to deletion attack

• Step 2 For the attacked signal, each frame is scrambled and authenticated from the first frame using the method proposed, until that the N successive samples cannot pass authentication. The authentication result for intact frames is shown in Fig. 22.

  Fig. 22

  

  Authentication result for intact frames

• Step 3 Move and scramble next N successive samples, until the samples can pass authentication successfully. The result is shown in Fig. 23. Then extract and reconstruct the frame number.

  Fig. 23

  

  Search result for next frame through authentication

• Step 4 The frame number reconstructed, shown in in Fig. 24, is as the tamper location result, in which TL = 1 indicates that the corresponding frame is intact. Based on the result, the 16th to 18th frame number can’t be reconstructed. So, the 16th to 18th frame of watermarked signal is regarded to be attacked.

  Fig. 24

  

  Tamper location result of deletion attack

• Step 5 Compressed signals of attacked frame are embedded into the 19th, 2nd and 6th frame. Extract the compressed signals from the frames, and reconstruct attacked signals to perform tamper recovery. The tamper recovery result is shown in Fig. 25.

  Fig. 25

  

  Tamper recovery result for deletion attack

5.3.2 Tamper recovery for insertion attack

Insert 4000 samples after the 17,000-th sample of watermarked speech. The attacked signal is shown in Fig. 26. And the tamper location result is shown in Fig. 27, from which it can be seen that the 5th frame is attacked. Extract the compressed signal from 1st frame of watermarked speech, and reconstruct the attacked signal to perform tamper recovery. The result is shown in Fig. 28.

Fig. 26

Watermarked speech subjected to insertion attack

Fig. 27

Tamper location result of insertion attack

Fig. 28

Tamper recovery result for insertion attack

5.3.3 Tamper recovery for substitution attack

The samples of 48001th to 55000th of watermarked signal are substituted by using other samples. The attacked signal is shown in Fig. 29, and the tamper location result is shown in Fig. 30, from which it can be seen that the 12th, 13th and 14th frame are attacked. Then extract the compressed signals from 8th, 17th and 4th frame to reconstruct the attacked signals, and the tamper recovery result is shown in Fig. 31.

Fig. 29

Watermark speech subjected to substitution attack

Fig. 30

Tamper location result of substitution attack

Fig. 31

Tamper recovery result for substitution attack

From the tamper localization and recovery results, it can be concluded that the scheme proposed can locate the attacked frames precisely, and has a good ability of tamper recovery.

6 Conclusion

In order to increase the credibility of digital speech signal, an authentication and tamper recovery scheme is proposed. The compression and reconstruction method for speech signal based on DWT and DCT is given. Firstly, speech signal is framed and segmented, and frame number is embedded into the first two segments. Secondly, each frame is compressed, and all the compressed signals are scrambled, which are as watermark and embedded based on block-based method. For the scheme, attacked frames can be located precisely by frame number extracted. And the compressed signal of attacked frame is extracted to perform tamper recovery. Experimental results show that the authentication and recovery scheme is effective.