JP2007214721A - Decoding method, decoding apparatus and decoding program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a decoding method, a decoding apparatus and a decoding program capable of decoding a received binary sequence by estimating a generation polynomial at a higher speed than that of conventional arts. <P>SOLUTION: An irreducible polynomial table 11 prepares all irreducible polynomials up to estimated orders in advance. A descrambler 14 sequentially descrambles a binary sequence to be analyzed by the irreducible polynomials, the irreducible polynomial used when the entropy of the binary sequence is decreased is registered to an irreducible polynomial list 19, and adoption of the sequence descrambled by the irreducible polynomial to be a new binary sequence to be analyzed is applied to all the irreducible polynomials in the table 11. Finally, a polynomial resulting from totalizing the irreducible polynomials registered in the irreducible polynomial list 19 is used for an estimate candidate of a generation polynomial of a scrambler. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a decoding method, a decoding device, and a decoding program, and more particularly to a decoding method, a decoding device, and a decoding program that perform decoding by estimating a scrambler generating polynomial of a received signal.

  In general, in order to prevent eavesdropping or the like of a third party, in a data transmission / reception system, for example, after scrambled a binary sequence that is data to be transmitted using a predetermined generator polynomial, the scrambled data is transmitted, When receiving and decrypting this, the receiving side knows the predetermined generator polynomial used on the transmitting side to generate the encrypted data, and descrambles the received data using it. .

  Here, the scrambled data has the characteristics that the more ideal the encryption, the higher the randomness and the greater the entropy of the information source. Therefore, the entropy size of the decrypted data is calculated, and the safety of the data is calculated. In some cases, verification is performed (see, for example, Patent Document 1).

  Therefore, in the data transmission / reception system using the scramble described above, in order to input a binary sequence to the scrambler and mix it, a primitive polynomial is usually used as a generator polynomial, so the generator polynomial used on the transmission side is not known. However, the received binary sequence can be input to the descrambler using a primitive polynomial of the assumed order and decoded, and the generator polynomial used on the transmission side can be estimated by the entropy size of the decoded data. The received data can be almost decrypted. That is, it can be estimated that the smaller the entropy of the decrypted data, the farther from the random number, the more correctly decrypted.

  FIG. 3 shows a block diagram of an example of a conventional decoding apparatus for estimating the above generator polynomial. In the figure, the generator polynomial table 1 stores in advance all generator polynomials (primitive polynomials) up to the assumed order in a table format. The entropy Emin of the input binary sequence to be received and decoded is calculated by the entropy calculator 2 and supplied to the descrambler 3. First, the descrambler 3 uses the first generator polynomial of the generator polynomial table 1 to generate an output sequence by descrambling the binary sequence, and generates an entropy E of the output sequence as an entropy calculator 4. Calculate with

  The comparator 5 compares the entropies Ein and E described above. If E <Emin, the updater 6 updates Emin to E, and the generator polynomial at that time is held in the generator polynomial buffer 7. Similarly, the above operation is repeated until there is no more generator polynomial in the generator polynomial table 1, and as a result, the generator polynomial that is finally stored in the generator polynomial buffer 7 and obtains the minimum value of entropy E is an input binary. A candidate for estimation of a scrambler generating polynomial of a sequence. Then, descrambling is performed using this scrambler generating polynomial estimation candidate to obtain decoded data of the input binary sequence.

  As described above, conventionally, descrambling is performed on all binary input polynomials (primitive polynomials), and the generator polynomial when the entropy of the descrambling output is the lowest is used as the scrambler estimation candidate. .

JP 2003-124924 A (page 3, FIG. 1)

  By the way, in recent years, while it has become possible to digitize amateur radios, radios that can be used for confidential communications, which are prohibited in Japan by the Radio Law, can be reimported and participate in terrorism and crimes. Sex is a concern. When listening to wireless communication using such an illegal digital amateur radio device, it is conceivable to perform decoding by estimating a generator polynomial of the scrambler using the conventional decoding device.

  However, since the generator polynomial is not necessarily a primitive polynomial in the above-described digital amateur radio, the number of generator polynomials of the assumed order becomes enormous, and there is a problem that it takes time to estimate the generator polynomial.

  The present invention has been made in view of the above points, and an object of the present invention is to provide a decoding method, a decoding apparatus, and a decoding program that can decode an input binary sequence by estimating a generator polynomial faster than conventional methods.

  In order to achieve the above object, a decoding method according to a first aspect of the present invention is a decoding method for estimating a generator polynomial from a binary sequence scrambled with an unknown generator polynomial that has been received, and the binary received as an initial value. A first descrambling is performed on an analysis binary sequence that is a sequence using one irreducible polynomial from storage means in which all irreducible polynomials up to the order assumed in the binary sequence are stored in advance. The entropy of the analysis binary sequence, the second step of calculating and comparing each entropy of the descrambled output sequence descrambled in the first step, and the entropy of the descrambled output sequence However, if a comparison result smaller than the entropy of the binary analysis series is obtained, then the irreducible polynomial used in the descrambling of the first step is registered as a list. In addition, the third step of registering the entropy of the descrambling output sequence as the minimum entropy Emin and updating the descrambling output sequence as an analysis binary sequence, and all the irreducible polynomials stored in the storage means The first to third steps are repeated until it is used in the descrambling in the first step, and the irreducible polynomial registered in the list at the time when all the irreducible polynomials are used in the descrambling is raised to the power And a fourth step of using a polynomial obtained by the power of the sum as a candidate for estimating a generating polynomial of a binary sequence scrambler.

  In this invention, all the irreducible polynomials up to the order assumed in the binary sequence scrambled with the received unknown generator polynomial are prepared in advance, and the entropy of the analysis binary sequence for descrambling is calculated, Next, descrambling with the irreducible polynomial sequentially for the binary analysis sequence, registering the irreducible polynomial when entropy is reduced to the list, and making the descramble output sequence a new analysis binary sequence, Descrambling the analysis binary sequence with the remaining irreducible polynomials in sequence, registering the irreducible polynomial when entropy decreases further in the list, and the sequence descrambled with the irreducible polynomial as a new analysis binary sequence For all remaining irreducible polynomials, and a polynomial that is the sum of the irreducible polynomials registered in the list is used as the scrambler generator polynomial estimation candidate. Since it so that can reduce the entropy calculation times.

  In order to achieve the above object, a decoding method of a second invention is a decoding method for estimating a generator polynomial from a received binary sequence scrambled with an unknown generator polynomial, and comprising a binary sequence entropy. Descrambling a binary sequence using a first irreducible polynomial from a storage means in which all the irreducible polynomials up to the order assumed in the binary sequence are stored in advance. The second step, the third step for calculating the entropy of the output sequence descrambled in the second step, and the fourth step for comparing the entropies calculated in the first step and the third step, respectively. When the entropy calculated in the third step is smaller than the entropy calculated in the first step by the fourth step, At that time, the irreducible polynomial used in the descrambling in the third step is registered as a list, the entropy calculated in the third step is registered as the minimum entropy Emin, and the entropy is registered in the third step. The fifth step of storing the calculated descrambling output sequence as an analysis binary sequence and the analysis binary sequence stored in the fifth step are still used in the irreducible polynomial stored in the storage means. A sixth step of performing descrambling using no irreducible polynomial, a seventh step of calculating entropy of the output sequence descrambled in the sixth step, and a minimum entropy Emin and the seventh step. The 8th step of comparing the entropy with the 8th step and the 8th step, the energy calculated in the 7th step. When the comparison result obtained by the tropy is smaller than the minimum entropy Emin, the irreducible polynomial used in the descrambling in the sixth step is registered as a list and calculated in the seventh step. The entropy is updated as the minimum entropy Emin, and the descramble output sequence for which the entropy is calculated in the seventh step is stored as an analysis binary sequence, and the irreducible polynomial stored in the storage means The sixth to ninth steps are repeated until all of the irreducible polynomials are used in the descrambling, and the irreducible polynomials registered in the list when all the irreducible polynomials are used in the descrambling are raised to the total power. A tenth step of setting a polynomial obtained by multiplication to an estimation candidate of a generating polynomial of a binary sequence scrambler; It is characterized by including.

  In the present invention, the number of entropy calculations can be reduced because the polynomial obtained by multiplying the irreducible polynomials registered in the list is used as the scrambler generation polynomial estimation candidate in the same manner as in the first invention. Here, the binary series of the above invention may be data wirelessly communicated with a digital amateur radio.

  In order to achieve the above object, a decoding device according to a third aspect of the present invention is a decoding device for estimating a generator polynomial from a received binary sequence scrambled with an unknown generator polynomial, and is assumed to be a binary sequence. The storage means for storing all the irreducible polynomials up to the order to be used in advance and the analysis binary sequence that is the binary sequence received by the initial value, using one irreducible polynomial from the storage means Descramble means for performing descrambling, entropy of the analysis binary sequence, entropy calculation means for calculating each entropy of the descramble output sequence descrambled in the first step, entropy and descrambling of the analysis binary sequence Compared with the entropy of the output sequence, the entropy of the descramble output sequence is smaller than the entropy of the analytic binary sequence. In this case, the irreducible polynomial used by the descrambling means at that time is registered as a list, the entropy of the descrambling output sequence is registered as the minimum entropy Emin, and the descrambling output sequence is updated as an analysis binary sequence. Until all of the irreducible polynomials stored in the comparison / registration means and the storage means are used in the descrambling means, the operations of the descrambling means, entropy calculation means, and comparison / registration means are repeated until all irreducible polynomials are Control means for summing the irreducible polynomial registered in the list of points in use when descrambling, and using the polynomial obtained by the sum as a candidate for estimation of a generating polynomial of a binary sequence scrambler It is characterized by that.

  In the present invention, all irreducible polynomials up to the order assumed in the binary sequence scrambled with the received unknown generator polynomial are prepared in the storage means in advance, and the analysis binary for performing descrambling by the descrambling means The entropy of the sequence is calculated, and then the descrambling with the irreducible polynomial is sequentially performed on the binary analysis sequence, the irreducible polynomial when the entropy decreases is registered in the list, and the descrambling output sequence is A new analysis binary sequence is used, and the analysis binary sequence is subsequently descrambled with the remaining irreducible polynomials, and the irreducible polynomials when entropy is reduced are registered in the list, and descrambling with the irreducible polynomials. The sequence is converted to a new analysis binary sequence for all remaining irreducible polynomials, and the polynomial that is the sum of the irreducible polynomials registered in the list is added. Since that set as the estimated candidate generator polynomial of Kuranbura, it can reduce the entropy calculation times.

  In order to achieve the above object, a decoding device according to a fourth aspect of the present invention is a decoding device that estimates a generator polynomial from a received binary sequence scrambled with an unknown generator polynomial, and is assumed to be a binary sequence. Storage means in which all the irreducible polynomials up to the order to be stored are stored in advance, buffer means for storing an analysis binary sequence whose initial value is a binary series, and analysis binary series from the buffer means Descrambling means for performing descrambling using one irreducible polynomial stored in the storage means and outputting a descrambling output sequence, a first entropy of the analysis binary sequence, and a second descrambling output sequence The entropy calculating means for calculating the entropy of the first, the comparing means for comparing the first and second entropies calculated by the entropy calculating means, and the comparing means, When a comparison result smaller than the first entropy is obtained, the irreducible polynomial used in the descrambling means when outputting the descramble output sequence of the second entropy is registered as a list. A minimum entropy update registration means for updating and registering the second entropy as the minimum entropy Emin when the second entropy obtains a comparison result smaller than the first entropy by the registration means and the comparison means; When the comparison means obtains a comparison result in which the second entropy is smaller than the first entropy, the analysis binary sequence update is performed to update the descrambling output sequence of the second entropy as an analysis binary sequence. And all the irreducible polynomials stored in the storage means for the updated analysis binary sequence Until used in scrambling, the operations of descrambling means, entropy calculating means, comparing means, list registering means, minimum entropy update registering means and analysis binary sequence updating means were repeated, and all irreducible polynomials were used in descrambling. And a control means for multiplying the irreducible polynomial registered in the list of time points by a sum of powers, and using the polynomial obtained by the power of the sum as a candidate for estimation of a generating polynomial of a binary sequence scrambler.

  In the present invention, the number of entropy calculations can be reduced since the polynomial obtained by multiplying the irreducible polynomial registered in the list is used as the estimation candidate of the generating polynomial of the scrambler, as in the decoding device of the third invention. . Here, the binary series of the above invention may be data wirelessly communicated with a digital amateur radio.

  In order to achieve the above object, the decoding program of the present invention is characterized in that each step of the first invention or each step of the second invention is executed by a computer. In the present invention, the number of entropy calculations can be reduced when a computer performs a process of estimating a generator polynomial from a binary sequence scrambled with an unknown generator polynomial.

  According to the present invention, when a process for estimating a generator polynomial from a binary sequence scrambled with an unknown generator polynomial is performed, for example, when the order of the generator polynomial is up to 30, the conventional method has approximately 1 billion times. Entropy calculation is required, but only about 70 million entropy calculations are required, and the number of entropy calculations can be reduced.

  Next, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 shows a block diagram of an embodiment of a decoding apparatus according to the present invention. As shown in the figure, this embodiment includes an irreducible polynomial table 11, entropy calculators 12 and 15, an analysis binary sequence buffer 13, a descrambler 14, a comparator 16, a descramble output sequence buffer 17, an updater. 18 and an irreducible polynomial list 19.

  The irreducible polynomial table 11 includes, for example, a storage device in which all irreducible polynomials up to the assumed order are stored in advance in a table format in signals transmitted and received by wireless communication by the illegal digital amateur radio device described above. And a counter for counting the number of irreducible polynomials used, and a function for determining whether all stored irreducible polynomials have been used.

  The entropy calculator 12 receives the received binary sequence as input, and calculates entropy Ein. The analysis binary sequence buffer 13 holds the entropy Ein. The descrambler 14 descrambles the binary sequence from the analysis binary sequence buffer 13 using the irreducible polynomial input from the irreducible polynomial table 11. The entropy calculator 15 calculates the entropy E of the descrambling output sequence output from the descrambler 14. The entropy calculation method itself is described in, for example, Patent Document 1 and is well known, and thus the description thereof is omitted.

  The comparator 16 first compares the entropies Ein and E with each other. If E <Ein, the updater 18 replaces Emin with E and registers the irreducible polynomial at that time in the irreducible polynomial list 19. To do. In the second and subsequent times, the comparator 16 entropy Emin registered in the updater 18 (referred to as Ea) and entropy E newly input from the entropy calculator 15 (referred to as Eb). When Eb <Ea, Eb is updated and registered in the updater 18 as Emin, and the irreducible polynomial at that time is registered in the irreducible polynomial list 19. The irreducible polynomial list 19 has not only a storage function for registering irreducible polynomials as a list but also a function for multiplying (multiplying) all registered irreducible polynomials.

  The descrambling output sequence buffer 17 temporarily stores the descrambling output sequence every time the descrambling output sequence is output from the descrambler 14 and when the comparator 16 obtains a comparison result of Eb <Ea. Based on the output of the comparator 16, the stored descrambling output sequence is transferred to the analysis binary sequence buffer 13. When the comparison result of Eb <Ea is not obtained, the updating operation in the updating unit 18 and the descrambling output sequence transfer from the descrambling output sequence buffer 17 to the analysis binary sequence buffer 13 are not performed. The updater 18 initially stores the entropy Ein, and then updates and stores the entropy Eb input by the comparator 16 as Emin.

  The above operation is repeated one by one for a plurality of irreducible polynomials stored in advance in the irreducible polynomial table 11, and when the descrambling process for all irreducible polynomials is completed, the irreducible polynomial list 19 is entered. The registered polynomial sum is used as a scrambler generating polynomial estimation candidate. Then, using this scrambler generator polynomial estimation candidate, the input binary sequence is descrambled to obtain decoded data.

  Next, the operation of the embodiment of the decoding method of the present invention will be described with reference to the flowchart of FIG. Here, for example, in the signal transmitted / received by the wireless communication by the illegal digital amateur radio described above, all n irreducible polynomials Ir (n) up to the assumed order are generated and stored in a table format. It is assumed that the irreducible polynomial table 11 is created in advance. Here, n is an irreducible polynomial number in the irreducible polynomial table 11 of FIG.

  In this state, initialization is first performed (step S1). In the initialization in step S1, the irreducible polynomial number n in the irreducible polynomial table 11 and the irreducible polynomial number m registered in the irreducible polynomial list 19 are initialized to “0”. The input binary sequence is supplied to the entropy calculator 12 to calculate the binary sequence entropy Hm (0) (corresponding to the Ein), and is temporarily stored in the analysis binary sequence buffer 13 as the analysis binary sequence Ts. Remembered. Accordingly, at this time, in step S1, the entropy Hm (Ts) of the analysis binary sequence Ts temporarily stored in the analysis binary sequence buffer 13 is set as the entropy Hm (0) of the binary sequence.

  Subsequently, in the descrambler 14, one irreducible polynomial Ir (first output from the irreducible polynomial table 11 (n = 1)) with respect to the analysis binary sequence Ts output from the analysis binary sequence buffer 13. The descrambling output sequence obtained thereby is temporarily stored in the descrambling output sequence buffer 17, and the entropy calculator 15 uses the entropy Hm (1) (corresponding to E above). ) Is calculated (step S2). Note that Hm (Ts · Ir (n)) in step S2 of FIG. 2 indicates the entropy of the analysis binary sequence Ts descrambled by the descrambler 14 using the irreducible polynomial Ir (n). However, at this time, n = 1.

  Subsequently, in the comparator 16, the calculated entropies Hm (0) and Hm (1) are compared in magnitude to determine whether or not Hm (0)> Hm (1) (step S3). . If Hm (0)> Hm (1), the irreducible polynomial Ir (n) at that time (where n = 1 at this time) is registered in the irreducible polynomial list 19 as an irreducible polynomial g (m) ( Step S4). Subsequently, the analysis binary sequence Ts · Ir (n) to be descrambled using the irreducible polynomial Ir (n) stored in the descrambling output sequence buffer 17 at that time (where n = 1 ) Is moved to the analysis binary sequence buffer 13 to be Ts, and Hm (0) stored in the updater 18 is replaced with Hm (1), and the registered irreducible polynomial number m is incremented by one (step S5). ).

  After the process of step S5 or when it is determined in step S3 that Hm (0) ≦ Hm (1), the value of n, that is, the irreducible polynomial number is incremented by one (step S6). It is determined whether n has reached the total number N of irreducible polynomials (step S7). This determination is made based on whether or not the counter in the irreducible polynomial table 11 has reached N.

  If n = N is not satisfied in step S7, there is an irreducible polynomial that has not yet been used for descrambling by the descrambler 14 in the irreducible polynomial table 11, and therefore, an irreducible polynomial number n (n = 2 at this time) In the descrambler 14 using the irreducible polynomial of), descrambling is performed on the analysis binary sequence Ts output from the analysis binary sequence buffer 13, and the resulting descrambling output sequence is descrambled output. The entropy calculator 15 calculates the entropy Hm (1) (corresponding to the E) while being temporarily stored in the sequence buffer 17 (step S2).

  Thereafter, the processes in steps S3 to S6 or steps S3 and S6 are performed again, and it is determined in step S7 whether n has reached the total number N of irreducible polynomials. In this way, the processes of steps S2 to S7 are repeated, and when it is determined in step S7 that n has reached N, all of the irreducible polynomials in the irreducible polynomial table 11 are used for descrambling by the descrambler 14. A generator polynomial obtained by summing up m irreducible polynomials stored in the irreducible polynomial list 19 at that time is obtained and used as an estimation candidate (step S8). The operation of multiplying the m irreducible polynomials stored in the irreducible polynomial list 19 in step S8 is performed by the irreducible polynomial list 19. That is, the irreducible polynomial list 19 is not only a storage device, but also has an arithmetic means.

  Thus, according to the present embodiment, all irreducible polynomials up to the assumed order are prepared in advance, the entropy of the binary sequence input to the descrambler 14 is calculated, Descrambling with irreducible polynomials is sequentially performed on the binary analysis series, and the irreducible polynomials when entropy is reduced are registered in the irreducible polynomial list 19, and the series descrambled with these irreducible polynomials is newly analyzed. The binary series is then descrambled with the remaining irreducible polynomials in sequence, and the irreducible polynomials when entropy is reduced are registered in the irreducible polynomial list 19, and the irreducible polynomials are used as the irreducible polynomials. The scrambled sequence is converted to a new analytic binary sequence for all remaining irreducible polynomials, and the irreducible polynomials registered in the irreducible polynomial list 19 are summed up as a polynomial. Since that set as the estimated candidate generator polynomial of assembler can reduce the entropy calculation times. For example, when the order of the generator polynomial is up to 30, the conventional method required about 1 billion entropy calculations, but in the present embodiment, it was confirmed that about 70 million calculations are sufficient.

  The present invention is not limited to the above-described embodiment, and includes, for example, a computer program that causes a computer to sequentially execute each procedure of the flowchart shown in FIG. In addition, the present invention can be applied to data other than data wirelessly communicated with a digital amateur radio.

It is a block diagram of one embodiment of the device of the present invention. It is a flowchart of one embodiment of the method of the present invention. It is a block diagram of an example of a conventional device.

Explanation of symbols

11 irreducible polynomial table 12, 15 entropy calculator 13 analysis binary sequence buffer 14 descrambler 16 comparator 17 descrambling output sequence buffer 18 updater 19 irreducible polynomial list

Claims (8)

A decoding method for estimating the generator polynomial from a received binary sequence scrambled with an unknown generator polynomial,
One irreducible polynomial from the storage means in which all irreducible polynomials up to the order assumed in the binary sequence are stored in advance for the analyzed binary sequence that is the binary sequence received as the initial value A first step of descrambling using
A second step of calculating entropy of the analytic binary sequence and calculating each entropy of the descrambled output sequence descrambled in the first step and comparing them;
When the entropy of the descrambling output sequence is smaller than the entropy of the analysis binary sequence, the irreducible polynomial used in the descrambling of the first step is registered as a list at that time. A third step of registering the entropy of the descrambling output sequence as a minimum entropy Emin and updating the descrambling output sequence as the analysis binary sequence;
The first to third steps are repeated until all the irreducible polynomials stored in the storage means are used in the descrambling in the first step, and all the irreducible polynomials are used in the descrambling. A fourth step of multiplying an irreducible polynomial registered in the list at the time of being generated, and using the polynomial obtained by the multiplication as an estimation candidate for a generating polynomial of the binary sequence scrambler, A decoding method characterized by the above. A decoding method for estimating the generator polynomial from a received binary sequence scrambled with an unknown generator polynomial,
A first step of calculating entropy of the binary sequence;
A second step of performing descrambling of the binary sequence using one irreducible polynomial from storage means in which all irreducible polynomials up to the order assumed in the binary sequence are stored in advance;
A third step of calculating entropy of the output sequence descrambled in the second step;
A fourth step of comparing the entropies respectively calculated in the first step and the third step;
If the entropy calculated in the third step is smaller than the entropy calculated in the first step by the fourth step, then the third step is performed. The irreducible polynomial used in the descrambling in step 1 is registered as a list, the entropy calculated in the third step is registered as the minimum entropy Emin, and the descrambling output in which the entropy is calculated in the third step A fifth step of storing the series as an analytic binary series;
A sixth step of descrambling the analytic binary sequence stored in the fifth step using an irreducible polynomial that is not yet used among the irreducible polynomials stored in the storage unit;
A seventh step of calculating entropy of the output sequence descrambled in the sixth step;
An eighth step of comparing the minimum entropy Emin and the entropy calculated in the seventh step;
When the comparison result obtained by the eighth step is smaller than the minimum entropy Emin, the entropy calculated in the seventh step is used for descrambling in the sixth step. Registering the irreducible polynomial as a list, updating the entropy calculated in the seventh step as the minimum entropy Emin, and analyzing the descramble output sequence in which the entropy is calculated in the seventh step A ninth step of storing as a sequence;
The sixth to ninth steps are repeated until all of the irreducible polynomials stored in the storage means are used in descrambling, and all the irreducible polynomials are used in the descrambling list. And a tenth step of multiplying a registered irreducible polynomial by a power and using the polynomial obtained by the power as a candidate for estimation of a generator polynomial of the binary sequence scrambler. .   3. The decoding method according to claim 1, wherein the binary series is data wirelessly communicated with a digital amateur radio. A decoding apparatus for estimating the generator polynomial from a binary sequence scrambled with an unknown generator polynomial,
Storage means for storing in advance all irreducible polynomials up to the degree assumed in the binary series;
A descrambling means for performing descrambling using an irreducible polynomial from the storage means for the analysis binary series that is the binary series received as an initial value;
Entropy calculating means for calculating entropy of the analysis binary sequence and each entropy of the descrambling output sequence descrambled in the first step;
When comparing the entropy of the analysis binary sequence and the entropy of the descramble output sequence, when the entropy of the descramble output sequence is smaller than the entropy of the analysis binary sequence, At this time, the irreducible polynomial used in the descrambling means is registered as a list, the entropy of the descrambling output sequence is registered as the minimum entropy Emin, and the descrambling output sequence is updated as the analysis binary sequence Comparison / registration means,
The operations of the descrambling means, the entropy calculation means, and the comparison / registration means are repeated until all the irreducible polynomials stored in the storage means are used in the descrambling means. A control means for summing up the irreducible polynomials registered in the list at the time of use in scramble, and using the polynomial obtained by the summation as an estimation candidate of a generating polynomial of the binary sequence scrambler; A decoding device comprising: A decoding apparatus for estimating the generator polynomial from a binary sequence scrambled with an unknown generator polynomial,
Storage means in which all irreducible polynomials up to the order assumed in the binary series are stored in advance;
Buffer means for storing an analytical binary sequence whose initial value is the binary sequence;
Descrambling means for performing descrambling using one irreducible polynomial stored in the storage means and outputting a descrambling output series for the analytic binary series from the buffer means;
Entropy calculating means for calculating a first entropy of the analysis binary sequence and a second entropy of the descrambling output sequence, respectively.
Comparing means for comparing the first and second entropies calculated by the entropy calculating means;
When the comparison means obtains a comparison result in which the second entropy is smaller than the first entropy, the descrambling means when outputting the descrambling output sequence of the second entropy A list registration means for registering the irreducible polynomial used in step 1
Minimum entropy update registration means for updating and registering the second entropy as the minimum entropy Emin when the comparison means obtains a comparison result in which the second entropy is smaller than the first entropy; ,
When the comparison means obtains a comparison result in which the second entropy is smaller than the first entropy, the descrambling output sequence of the second entropy is updated as the analysis binary sequence. Analysis binary series update means;
The descramble means, entropy calculation means, comparison means, list registration means, minimum entropy until all of the irreducible polynomials stored in the storage means are used in the descram for the updated binary analysis sequence. The operations of the update registration means and the analysis binary series update means are repeated, and the irreducible polynomials registered in the list at the time when all the irreducible polynomials are used in descrambling are raised to the sum of the powers. And a control means for using the binary polynomial as a candidate for estimation of the generating polynomial of the binary sequence scrambler.   6. The decoding apparatus according to claim 4, wherein the binary series is data wirelessly communicated with a digital amateur radio. A decoding program for causing a computer to execute decoding for estimating the generator polynomial from a received binary sequence scrambled with an unknown generator polynomial,
In the computer,
One irreducible polynomial from the storage means in which all irreducible polynomials up to the order assumed in the binary sequence are stored in advance for the analyzed binary sequence that is the binary sequence received as the initial value A first step of descrambling using
A second step of calculating entropy of the analytic binary sequence and calculating each entropy of the descrambled output sequence descrambled in the first step and comparing them;
When the entropy of the descrambling output sequence is smaller than the entropy of the analysis binary sequence, the irreducible polynomial used in the descrambling of the first step is registered as a list at that time. A third step of registering the entropy of the descrambling output sequence as a minimum entropy Emin and updating the descrambling output sequence as the analysis binary sequence;
The first to third steps are repeated until all the irreducible polynomials stored in the storage means are used in the descrambling in the first step, and all the irreducible polynomials are used in the descrambling. And performing a fourth step of multiplying an irreducible polynomial registered in the list at the time of the summation, and using the polynomial obtained by the summation as an estimation candidate of a generating polynomial of the binary sequence scrambler A decryption program characterized in that From a received binary sequence scrambled with an unknown generator polynomial, a decoding program for causing a computer to execute decoding for estimating the generator polynomial,
In the computer,
A first step of calculating entropy of the binary sequence;
A second step of performing descrambling of the binary sequence using one irreducible polynomial from storage means in which all irreducible polynomials up to the order assumed in the binary sequence are stored in advance;
A third step of calculating entropy of the output sequence descrambled in the second step;
A fourth step of comparing the entropies respectively calculated in the first step and the third step;
If the entropy calculated in the third step is smaller than the entropy calculated in the first step by the fourth step, then the third step is performed. The irreducible polynomial used in the descrambling in step 1 is registered as a list, the entropy calculated in the third step is registered as the minimum entropy Emin, and the descrambling output in which the entropy is calculated in the third step A fifth step of storing the series as an analytic binary series;
A sixth step of descrambling the analytic binary sequence stored in the fifth step using an irreducible polynomial that is not yet used among the irreducible polynomials stored in the storage unit;
A seventh step of calculating entropy of the output sequence descrambled in the sixth step;
An eighth step of comparing the minimum entropy Emin and the entropy calculated in the seventh step;
When the comparison result obtained by the eighth step is smaller than the minimum entropy Emin, the entropy calculated in the seventh step is used for descrambling in the sixth step. Registering the irreducible polynomial as a list, updating the entropy calculated in the seventh step as the minimum entropy Emin, and analyzing the descramble output sequence in which the entropy is calculated in the seventh step A ninth step of storing as a sequence;
The sixth to ninth steps are repeated until all of the irreducible polynomials stored in the storage means are used in descrambling, and all the irreducible polynomials are used in the descrambling list. And performing a tenth step of multiplying a registered irreducible polynomial to a power, and using the polynomial obtained by the power as a candidate for estimating a generator polynomial of the binary sequence scrambler. program.

Images