Residual error probability estimation method for secure communication under guess decoding condition

Abstract

The invention belongs to the technical field of secure communication, and discloses a residual error probability estimation method for secure communication under a guess decoding condition, which comprises the following steps: generating a noise error pattern by using a GRAND algorithm and a receiving end SPDU, performing guess decoding on the receiving end SPDU, and calculating a guess SPDU sequence; calculating a syndrome of CRC coding, judging a guess decoding result according to the value of the syndrome, and calculating REP performance after guess decoding; and searching the minimum CRC signature length under the condition of the given maximum error correction capability M, so that the REP performance of CRC error detection is optimal. According to the method, on the basis of an IEC61784-3 international standard heavy residual error probability calculation mode, closed mathematical expressions of residual error probabilities corresponding to different maximum error correction capabilities M under the condition of guessing random additive noise decoding are deduced, and the residual error probability performance is improved at the cost of increasing the CRC signature length.

Description

Technical Field

[0001] The invention belongs to the technical field of secure communications, and in particular relates to a residual error probability estimation method for secure communications under guessed decoding conditions. Background Art

[0002] According to the IEC61784-3 protocol, under the black channel model, the framework of the secure communication layer is as follows: Figure 1 As shown. Assume that the errors in the transmission of binary digital information are symmetrical under black channel conditions. Under electromagnetic interference in industrial environments, the probability that any information bit 1 in the security information frame SPDU changes to 0 and 0 changes to 1 is P e Under electromagnetic interference conditions, a P e =10 -4 A bit error rate of 10 will cause a communication system to stop during data exchange. Under actual conditions, a pulse interference will cause multiple bit transmission errors. -4 The bit error rate P e In order to ensure that enough interference can be detected, the error detection mechanism should be able to ensure 10 -4 100 times more powerful detection capability, that is, when P e For 10 -2 When P is used, the residual error probability (REP) can be guaranteed to be sufficiently low. Therefore, IEC61784-3 stipulates that e =10 -2 Used for REP calculation.

[0003] Assume that the length of the security information data frame SPDU is n bits. According to the IEC61784-3 protocol, the probability of k bit errors in an n-bit channel noise is P n (k) Follows binomial distribution:

[0004]

[0005] When the n-bit security information frame SPDU is coded with CRC, the minimum Hamming weight of the CRC code is d, and the total number of all error bits can be detected to be less than d-1, then the upper limit residual error probability of the CRC is R UL (k) is calculated as follows:

[0006]

[0007] For a security information frame SPDU with a CRC signature length of r bits and a total length of n bits, let the minimum Hamming weight of the CRC codeword be d minIEC 61784-3 stipulates the total residual error probability R caused by channel noise CRC (P e ) The calculation formula is shown in formula (3):

[0008]

[0009] Formula (3) shows that:

[0010] 1) When the number of channel noise error bits k<d min When , the channel noise cannot be a legal CRC codeword, and the residual error probability is 0;

[0011] 2) When the number of channel noise error bits k ≥ d min When a channel noise sequence with k error bits is used, the residual error probability R rep (k) can be expressed as shown in formula (4):

[0012]

[0013] 3) Let M be the maximum number of error correction bits in GRAND decoding. When k>nM, the residual error probability R caused by a channel noise sequence with k error bits is rep (k) accounts for a very small proportion of the total residual error probability. For the convenience of calculation and derivation, equation (3) is further simplified to equation (5):

[0014]

[0015] According to the IEC 61784-3 standard, the sender uses CRC to sign the transmitted security information frame SPDU, and the receiver performs error detection and integrity detection on the SPDU to ensure that the residual error probability REP of the SPDU is lower than the given security level requirement. When the SPDU passes the CRC test, the SPDU is submitted to the upper application layer; if it fails the CRC test, the SPDU will be discarded and the sender will be notified to retransmit. The IEC61784-3 standard also requires that error correction processing is generally not recommended for CRC-encoded SPDUs.

[0016] With the development of theory and technology, the GRAND algorithm makes CRC error correction possible. After using the GRAND algorithm to correct CRC errors, the probability of retransmission of SPDU by the communication system can be greatly reduced, and the transmission delay can be reduced, which is very beneficial to the entire system. However, after using the GRAND algorithm for decoding, if the existing REP calculation method under the IEC61784-3 standard is continued to be used to calculate the residual error probability corresponding to different maximum error correction capabilities M, the REP performance will be significantly reduced. Therefore, it is necessary to study the REP calculation problem of SPDU under the condition of using GRAND error correction. Summary of the invention

[0017] To solve the above technical problems, the present invention provides a residual error probability estimation method for secure communication under guessed decoding conditions, and derives the residual error probabilities corresponding to different maximum error correction capabilities M under guessed random additive noise decoding conditions; and improves the residual error probability performance at the cost of increasing the CRC signature length.

[0018] The residual error probability estimation method for secure communication under guessed decoding conditions of the present invention comprises the following steps:

[0019] Step 1: The sender uses CRC to encode the SPDU, uses the GRAND algorithm, generates a noise error pattern for the receiver's SPDU, performs guess decoding on the receiver's SPDU, and calculates the guessed SPDU sequence;

[0020] Step 2, calculate the syndrome S of the CRC code, judge the guessed decoding result according to the value of the syndrome S, and calculate the REP after guessed decoding;

[0021] Step 3: Search for the minimum CRC signature length under the given maximum error correction capability M to achieve the best REP performance for CRC error detection.

[0022] Furthermore, in step 1, assuming that the length of the SPDU is n bits, the CRC-encoded SPDU at the transmitting end is X=x 1 x 2 …x i …x n , the channel noise is Z = z 1 z 2 …z i …z n , the receiving end SPDU is Y=y 1 y 2 …y i …y n , 1≤i≤n,x i ,y i ,z i Take values ​​in the binary symbol set {0,1}; the relationship between X, Z, and Y is as follows:

[0023]

[0024] in Represents modulo-2 addition.

[0025] Furthermore, the receiving end generates a noise error pattern E=e 1 e 2 …e i …e n, guess and decode the receiving end SPDU and calculate the guessed SPDU sequence As shown below:

[0026]

[0027] Further, in step 2, let the check polynomial of the CRC codeword be H, and calculate the syndrome S=s 1 s 2 …s j …s r , where r is the CRC signature length, 1≤j≤r, and T is the matrix transpose calculation symbol:

[0028]

[0029] When the syndrome S is not 0, it indicates that Z≠E, and the guess is incorrect. The receiver generates a new noise error pattern E and restarts the next round of guess decoding.

[0030] When the syndrome S is equal to 0, according to the syndrome S calculation formula, there are two states:

[0031] State 1) E = Z, It is a legal CRC codeword, and the guess decoding is successful;

[0032] Status 2) It is a legal CRC codeword. Although it passes the CRC error check, it is decoded incorrectly.

[0033] Calculate the REP performance after guessing the decoding.

[0034] Furthermore, let the minimum Hamming weight of the CRC codeword space be d min , the Hamming weight of the channel noise Z is H z , the Hamming weight of the generated noise error pattern E is H e , The Hamming weight is H ze ; When the arbitrary error correction capability of the GRAND algorithm is m bits, 0≤m≤M, M is the maximum error correction capability, and the SPDU passes the CRC error detection, the residual error probability As shown below:

[0035]

[0036] Where M is the maximum error correction capability, 0≤m〈0-M;

[0037] When m=0, SPDU only performs error detection without speculative decoding.

[0038] Furthermore, when CRC error detection is passed, the total REP consists of two parts:

[0039] 1) When 0≤H z ≤M, 0≤m≤M, guess that the decoding is successful, the corresponding residual error probability The weighted average The calculation is as follows:

[0040]

[0041] 2) When M<H z When the maximum error correction capability is exceeded, the SPDU cannot be correctly guessed and decoded, but the corresponding residual error probability is for:

[0042]

[0043] Total residual error probability for:

[0044]

[0045] When M=0, the maximum error correction capability is 0, and SPDU only performs error detection.

[0046] The beneficial effects of the present invention are:

[0047] 1) Based on the calculation method of the residual error probability of the IEC61784-3 international standard, the present invention derives the closed mathematical expression of the residual error probability corresponding to different maximum error correction capabilities M under the condition of guessing random additive noise decoding; it provides a reliable mathematical method for calculating the residual error probability when the GRAND algorithm is used for SPDU secure communication;

[0048] 2) Using the GRAND algorithm for secure communication will greatly reduce the residual error probability performance; the present invention uses traditional CRC error detection as a reference benchmark and increases the CRC signature length to improve the residual error probability performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a schematic diagram of the black channel model structure of the IEC61784-3 standard;

[0050] Figure 2 It is a schematic diagram of REP performance comparison under the conditions of SPDU length of 128 bits and different maximum error correction capability M values;

[0051] Figure 3 It is a schematic diagram of REP performance comparison corresponding to different maximum error correction capabilities M when the SPDU length is 32 to 640 bits;

[0052] Figure 4Is the minimum length of the CRC signature Search process;

[0053] Figure 5 is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0054] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments in conjunction with the accompanying drawings.

[0055] like Figure 5 As shown, the residual error probability estimation method for secure communication under guessed decoding conditions of the present invention comprises the following steps:

[0056] Step 1: The sender uses CRC to encode the SPDU, uses the GRAND algorithm, generates a noise error pattern for the receiver's SPDU, performs guess decoding on the receiver's SPDU, and calculates the guessed SPDU sequence;

[0057] Step 2, calculate the syndrome S of the CRC code, judge the guessed decoding result according to the value of the syndrome S, and calculate the REP after guessed decoding;

[0058] Step 3: Search for the minimum CRC signature length under the given maximum error correction capability M to achieve the best REP performance for CRC error detection.

[0059] In step 1, let the CRC-encoded SPDU of the sender be X=x 1 x 2 …x i …x n , the channel noise is Z = z 1 z 2 …z i …z n , the receiving end SPDU is Y=y 1 y 2 …y i …y n , 1≤i≤n,x i ,y i ,z i The value is in the binary symbol set {0,1}. The relationship between X, Z, and Y is shown in equation (6), where Represents modulo-2 addition.

[0060]

[0061] According to the GRAND algorithm, the receiving end generates a noise error pattern E = e 1 e 2 …e i …e n, guess and decode the receiving end SPDU and calculate the guessed SPDU sequence As shown in formula (7).

[0062]

[0063] Assume that the check polynomial of the CRC codeword is H, and calculate the syndrome S=s 1 s 2 …s f …s r , where r is the CRC signature length, 1≤f≤r:

[0064]

[0065] When the syndrome S is not 0, it means that Z≠E, the guess is incorrect, and the receiver generates a new noise error pattern E and returns to formula (7) to start the next round of guess decoding. When the syndrome S is equal to 0, it can be seen from formula (8) that there are two cases:

[0066] 1) E = Z, It is a legal CRC code word, and the guess decoding is successful.

[0067] 2) It is a legal CRC codeword. Although it passes the CRC error detection, it is decoded incorrectly.

[0068] When the second situation occurs, it is called missed detection, which is the reason for the residual error probability REP. In order to examine the residual error probability under GRAND decoding conditions, it is necessary to modify equation (5) to calculate the REP performance after guess decoding.

[0069] According to the IEC61784-3 standard, the error bit "1" in the channel noise Z follows the binomial distribution of formula (1). When GRAND is used for guess decoding, the noise error pattern generator at the receiving end generates the corresponding noise error pattern E from high to low according to the distribution probability of the error bit "1", which is equivalent to the Hamming weight of E. e Assume that the Hamming weight of the noise sequence Z is d z , then d z The value of follows the binomial distribution of formula (1). Let the minimum Hamming weight of the CRC codeword space be d min , Under the condition that GRAND’s error correction capability is m bits, the residual error probability caused by guessing decoding is analyzed.

[0070] Without loss of generality, when the error correction capability is less than m and the SPDU fails the CRC error detection, it can be seen that the Hamming weight of the channel noise Z is z≥m, and there are no residual errors. When the error correction capability is m, the calculation of the residual error probability when the SPDU passes the CRC error detection is investigated.

[0071] When the error correction capability is m, the Hamming weight of the generated noise error pattern E is H e =The number of m is When doing guess decoding, Hamming weight ze Yes e +1 = m + 1 possibilities. The Hamming weight is of The number is Where j = 0, 1, ..., m. Since m ≤ d z ≤nM, we can know:

[0072]

[0073] And only when H ze ≥d min There may be a residual error probability only when , equation (9) can be written as equation (10):

[0074]

[0075] Considering Formula (10) can be transformed into z To express, that is:

[0076] max(d min -(2j-m),m)≤H z ≤(nM) (11)

[0077] Therefore, from equations (4) and (5), we can deduce the residual error probability introduced by CRC error detection when the error correction capability is m and the guess decoding is successful: As shown in formula (12):

[0078]

[0079] Formula (12) gives the unified residual error probability calculation formula of the guess decoding algorithm under the condition of any error correction capability m, 0≤m≤M. When m=0, it is equivalent to generating a noise error pattern E with a Hamming weight of 0. The calculated residual error probability is The result is the same as that calculated by equation (5). This is equivalent to SPDU only doing error detection without guessing decoding. Equation (5) is a special case of equation (12).

[0080] Assume that the GRAND algorithm is used to decode the CRC-encoded SPDU, and the maximum error correction capability is M. When the number of error bits in the transmitted SPDU is equal to the Hamming weight of the channel noise Z, H z When it exceeds M and fails to pass the CRC error detection, the receiver discards the SPDU and notifies the sender to resend. When it passes the CRC error detection, the total REP consists of two parts:

[0081] 1) When 0≤H z ≤M, 0≤m≤M, can be guessed and decoded, the corresponding residual error probability The weighted average The calculation is as follows:

[0082]

[0083] 2) When M<H z When the maximum error correction capability is exceeded, the SPDU cannot be correctly guessed and decoded (but it may still pass the CRC error detection). According to formula (5), the corresponding residual error probability is for:

[0084]

[0085] Total residual error probability for:

[0086]

[0087] When M=0, the maximum error correction capability is 0, which is equivalent to SPDU only performing error detection. The calculation result of formula (15) is equal to formula (5); therefore, formula (5) is equivalent to a special case of formula (15).

[0088] Assume that the CRC signature length r is 24 bits, the SPDU length is n = 128 bits, and under different maximum error correction capabilities M, corresponding to different P e The residual error probability REP curve is as follows Figure 2 As shown, Figure 2 (a) is a schematic diagram for comparing the residual error probability REP of SPUD under different M values; Figure 2 (b) is Figure 2 A partial enlarged schematic diagram in (a).

[0089] Fixed P e and the value of the CRC signature length r, according to IEC61784-3, the minimum Hamming weight d under different SPDU lengths min The values ​​are 6, 4 and 2 respectively. e =10 -2, CRC signature length 24 bits, SPDU length 32 to 640 bits. Corresponding to different maximum error correction capabilities M, the performance comparison of REP, such as Figure 3 shown.

[0090] Figure 2 and 3 The comparison shows that the GRAND algorithm greatly reduces the REP performance. A detailed analysis of formulas (5) and (15) shows that choosing a longer CRC signature length r will achieve better REP performance. A method of increasing the CRC signature length r is proposed to offset the REP performance degradation caused by the GRAND algorithm at the cost of reducing the SPDU code rate and transmission efficiency.

[0091] Based on the given SPDU length n and CRC signature length r, search for the minimum CRC signature length that can achieve CRC error detection REP performance under the given maximum error correction capability M. search The process is as follows Figure 4 shown.

[0092] In P e =10 -2 , Under the condition that the CRC signature length of the traditional CRC error detection mechanism is 24 bits, different M values ​​correspond to different SPDU lengths n, Figure 4 Process Search The values ​​are shown in Table 1.

[0093] Table 1 Search value

[0094] n 32 96 160 224 288 352 416 480 576 640 M＝0 24 24 24 24 24 24 24 24 24 24 M＝1 29 30 30 30 30 30 29 29 28 27 M＝2 34 37 38 38 37 38 38 38 38 37 M＝3 38 43 41 43 44 45 45 46 46 46 M＝4 38 44 44 47 48 50 52 53 54 54 M＝5 38 44 46 50 53 55 57 59 60 61 M＝6 38 44 47 52 56 59 62 64 66 68 M＝7 38 44 48 54 59 63 66 69 72 74 M＝8 38 44 48 55 61 66 70 73 77 79

[0095] The above description is only a preferred embodiment of the present invention and is not intended to be a further limitation of the present invention. All equivalent changes made using the contents of the present specification and drawings are within the protection scope of the present invention.

Claims

1. A method for estimating residual error probability of secure communication under guess decoding conditions, characterized in that: The following steps are involved: Step 1: The sender uses CRC to encode the SPDU, uses the GRAND algorithm, generates a noise error pattern for the receiver's SPDU, performs guess decoding on the receiver's SPDU, and calculates the guessed SPDU sequence; Step 2, calculate the syndrome S of the CRC code, judge the guessed decoding result according to the value of the syndrome S, and calculate the REP after guessed decoding; Step 3: Search for the minimum CRC signature length under the given maximum error correction capability M to achieve the best REP performance for CRC error detection.

2. The residual error probability estimation method for secure communication under guessed decoding conditions according to claim 1, characterized in that: In step 1, assuming that the length of the SPDU is n bits, the CRC-encoded SPDU at the sender is X = x1 x2…x i …x n , the channel noise is Z = z1 z2…z i …z n , the receiving end SPDU is Y=y1 y2…y i …y n , 1≤i≤n,x i ,y i ,z i Take values ​​in the binary symbol set {0,1}; the relationship between X, Z, and Y is as follows: in Represents modulo-2 addition.

3. The residual error probability estimation method for secure communication under guessed decoding conditions according to claim 2, characterized in that: The receiving end generates a noise error pattern E = e1 e2…e i …e n , guess and decode the receiving end SPDU and calculate the guessed SPDU sequence As shown below:

4. The residual error probability estimation method for secure communication under guessed decoding conditions according to claim 3, characterized in that: In step 2, let the check polynomial of the CRC codeword be H, and calculate the syndrome S = s1 s2…s f …s r , where r is the CRC signature length, 1≤f≤r, and T is the matrix transpose calculation symbol: When the syndrome S is not 0, it indicates that Z≠E, and the guess is incorrect. The receiver generates a new noise error pattern E and restarts the next round of guess decoding. When the syndrome S is equal to 0, according to the syndrome S calculation formula, there are two states: State 1) E = Z, It is a legal CRC codeword, and the guess decoding is successful; Status 2) It is a legal CRC codeword. Although it passes the CRC error check, it is decoded incorrectly. Calculate the REP performance after guessing the decoding.

5. The residual error probability estimation method for secure communication under guessed decoding conditions according to claim 4, characterized in that: Assume that the minimum Hamming weight of the CRC codeword space is d min , the Hamming weight of the channel noise Z is H z , the Hamming weight of the generated noise error pattern E is H e , The Hamming weight is H ze ; When the arbitrary error correction capability of the GRAND algorithm is m bits, 0≤m≤M, M is the maximum error correction capability, and the SPDU passes the CRC error detection, the residual error probability As shown below: When m=0, SPDU only performs error detection without speculative decoding.

6. The residual error probability estimation method for secure communication under guessed decoding conditions according to claim 5, characterized in that: When CRC error detection is passed, the total REP consists of two parts: 1) When 0≤H z ≤M, 0≤m≤M, guess that the decoding is successful, the corresponding residual error probability The weighted average The calculation is as follows: 2) When M<H z When the maximum error correction capability is exceeded, the SPDU cannot be correctly guessed and decoded, but the corresponding residual error probability is for: Total residual error probability for: When M=0, the maximum error correction capability is 0, and SPDU only performs error detection.

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