CN103944712B - Method for generating MBE-SSP (Multi Band Excitation-Service Switching Point) control code sequence - Google Patents

Abstract

The invention discloses a method for generating an MBE-SSP control code sequence: step 1, allocation and negotiation stage; step 2, initial key sequence generation: Alice sends the initial value x ₀ and parameter value μ into the chaotic system, and iterates N times to get N real numbers, and select n real numbers X _1a , X _2a ,...,X _na from them, and perform binary processing on X _1a , X _2a ,...,X _na respectively to generate binary initial encryption key sequence S _0a ; step 3, generation of verification code sequence and control code sequence; step 4, transmission and authentication of verification code sequence; step 5, process of shifting and cyclically generating discarded codewords in control code sequence. The invention utilizes the extreme sensitivity of the chaotic system to the initial state and parameters and the good randomness of the chaotic sequence to generate the initial key sequence, obtains the check code sequence and the control code sequence through grouping, XOR, and extraction, and then transmits the check code through the quantum channel sequence to ensure the legitimacy of both parties in communication and the validity of the control code sequence.

Description

A method for generating MBE-SSP control code sequence

technical field

The invention belongs to the field of quantum secure communication, and in particular relates to a method for generating an MBE-SSP control code sequence. The method includes a method for generating a control code sequence based on chaos and quantum characteristics and a control code sequence cyclic discarding algorithm.

Background technique

Quantum communication is an important research direction in quantum information science. It has developed rapidly in the past two decades and provides a new way of thinking for secure communication systems. Key distribution and quantum secret sharing are two important research directions, which have made important progress in theory and experiment, and have broad application prospects.

Document 1 "Chen Pan. Theoretical Research on Quantum Key Distribution and Quantum Secret Sharing [D]. Tsinghua University, 2006." discloses a Measuring basis encryption-six states protocol, Abbreviated as MBE-SSP, three different measurement bases are selected through the control code. In the case of no noise and no eavesdropping, the communication efficiency can reach 100%, and for the eavesdropper, it is necessary to select one of the three measurement bases. , the hit probability is only 13, so the scheme is not only highly efficient but also safe. However, it needs to be carried out on the premise that the control code sequence is strictly confidential, and the control code sequence generation method of this scheme is single, and the length of the key sequence generated under the action of the control code sequence is a fixed value, so it often needs to be used repeatedly in practical applications. Control code sequence, there is a risk of leakage in the control code sequence; Document 2 "Zhao Long. Research on Quantum Key Distribution and Quantum Signature Theory [D]. Northwest University, 2012." ) method of obtaining the control code sequence, there is an irreconcilable contradiction between its length and the safety factor, the higher the safety factor, the shorter the length of the control code sequence, the more it needs to be reused, and this will cause more information leak. The scheme enhances the security of the control code sequence through the grouping XOR method of the control code sequence, but the length of the transmitted key sequence is still a fixed value, the frequency of repeated use of the control code sequence is high, and there is a high risk of leakage.

Contents of the invention

Aiming at the defects or deficiencies in the above-mentioned prior art, the present invention proposes a method for generating MBE-SSP control code sequences. some problems.

A kind of MBE-SSP control code sequence generation method, specifically comprises the steps:

Step 1, allocation and negotiation phase: the sender Alice and the receiver Bob obtain the shared initial value x ₀ through the trusted certification center CA; Alice and Bob obtain the parameter value μ, the number of iterations N and Initial key sequence length n;

Step 2. Initial key sequence generation: Alice sends the initial value x ₀ and parameter value μ into the chaotic system, and iterates N times to get N real numbers, and selects n real numbers X _1a , X _2a ,..., X _na ; Binarize X _1a , X _2a ,...,X _na respectively to generate binary initial key sequence S _0a ; at the same time, Bob sends the initial value x ₀ and parameter value μ into the same Chaotic system, and iterate N times to get N real numbers, and select n real numbers X _1b , X _2b ,...,X _nb from the N real numbers in the same way as Alice, and set X _1b , X _2b ,... .,X _nb performs the same binarization process as X _1a , X _2a ,...,X _na to generate a binary initial key sequence S _0b ;

Step 3, check code sequence and control code sequence generation: Alice generates the check code sequence S _1a and control code sequence S _2a from the initial key sequence S _0a through grouping, XOR and extraction processing; meanwhile, Bob also passes Alice In the same way, the verification code sequence S _1b and the control code sequence S _2b are generated from the initial key sequence S _0b ; the sequences S _2a and S _2b are used as the control code sequences for communication between Alice and Bob;

Step 4. Transmission and authentication of the verification code sequence: Alice transmits the verification code sequence S _1a to Bob through the quantum channel; Bob compares the received verification code sequence S _1a with the verification code sequence S _1b generated in step 3, and sends The comparison result is fed back to Alice; when S _1a and S _1b are the same, it is considered that the control code sequence S _2a is the same as the control code sequence S _2b ; both the control code sequence S _2a and the control code sequence S _2b are recorded as the control code sequence K;

Step 5, the process of generating discarded codewords by shifting and cyclically shifting the control code sequence: both Alice and Bob select the measurement base sequence through the control code sequence K to generate a key sequence; in the process of generating the key sequence, if the required key sequence length If it is greater than the length of the measurement base sequence controlled by the control code sequence K, the control code sequence K is shifted and cyclically discarded to generate different control code sequences for use.

Further, in the step 1, the initial value x ₀ ∈[-1,1].

Further, in the step 1, the parameter value of the chaotic system μ∈[1.42, 2], the initial key sequence length n is an even number, and n<N.

Further, the initial value x ₀ =0.8835, the parameter value μ=1.92, the number of iterations N=500, and the initial key length n=20.

Further, in the step 2, the chaotic system selected by Alice and Bob is Logistic mapping, $x_{i+1}=f\left(x_i\right)=1-{\mathrm{\&mu;x}}_i^2,$ x _i ∈ [-1,1], μ ∈ [1.42, 2].

Further, in the step 2, the operation of the binarization process: set a threshold k, when a certain real value in the initial key is greater than k, it is mapped to 1, when a certain real value in the initial key When the real value is less than or equal to k, the mapping is 0; the specific form is as follows:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; k</span>}\end{array}\right.$

In the formula, y _i is a binary value, x _i is a real value, and i represents the serial number of the real number in the initial key.

Further, in the step 3, the specific steps of Alice generating the verification code sequence S _1a and the control code sequence S _2a from the initial key sequence S _0a through grouping, XOR and extraction processing are as follows:

Divide the binary codewords in the initial key sequence S _0a into two groups in turn, and perform XOR operation on the two binary codewords in each group respectively to obtain the sequence S _1a ; then the initial key sequence S _0a Perform extraction to obtain sequence S _2a , extraction rule: when a certain bit in sequence S _1a is 1, then extract the second bit in the two binary code words corresponding to the bit; when a certain bit in S _1a is 0 , then extract the first bit in the two binary code words corresponding to the bit; use the sequence S _2a as the control code sequence for communication between Alice and Bob, and use the sequence S _1a as the check code sequence.

Further, in the step 4, the quantum channel in the step 4 adopts the HKH98 protocol.

Further, in the step 5, the control code sequence K shift cycle discarding algorithm is as follows:

The combination of the first bit and the second bit codeword of the control code sequence K is used as the combination to be discarded. After discarding, when the control code sequence needs to be used again, the first bit of the control code sequence K is shifted to the last bit and The remaining bits are moved forward sequentially to obtain a new control code sequence K ₁ ; the combination of the first and second codewords of the new control code sequence K ₁ is the combination to be discarded; when the control code sequence needs to be used again, sequentially By analogy, the first bit of the previous control code sequence is shifted to the last bit and the remaining bits are shifted forward sequentially to obtain a new control code sequence.

The invention utilizes the extreme sensitivity of the chaotic system to the initial state and parameters and the good randomness of the chaotic sequence to generate the initial key sequence, obtains the check code sequence and the control code sequence through grouping, XOR, and extraction, and then transmits the check code through the quantum channel sequence to ensure the legitimacy of both parties in communication and the validity of the control code sequence. When the length of the key sequence is greater than the length of the measurement base sequence controlled by the control code sequence, the present invention adopts a shift cycle discarding algorithm for the control code sequence, so that the combinations discarded when the control code sequence is used for many times are all different, and the control code The sequence itself is constantly changing, and the corresponding measurement base sequence is also constantly changing. Compared with the solutions described in Document 1 and Document 2, the control code sequence generated in the present invention is not transmitted in the channel, so the eavesdropping party will not be able to obtain valid information. At the same time, different control code sequences are generated by shifting and cyclically discarding, so that a longer key sequence can be transmitted with a certain length of control code sequence without repetition, which reduces the frequency of repeated control code sequences and reduces the risk of information leakage. risk; at the same time, it avoids the irreconcilable contradiction between the length of the control code sequence obtained through other quantum key distribution protocols and the safety factor in the prior art. In the present invention, when the length of the control code sequence is L and the number of cycles is M, then the control code sequence has M kinds of changes.

Description of drawings

FIG. 1 is a schematic diagram of the allocation and negotiation phase of step 1.

The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments.

detailed description

MBE-SSP control code sequence generation method of the present invention, comprises the following steps:

Step 1. Allocation and negotiation phase: As shown in Figure 1, the sender Alice and the receiver Bob obtain the shared initial value x ₀ (x ₀ ∈ [-1,1]); Alice and Bob obtain the parameter value μ(μ∈[1.42,2]) of the chaotic system, the number of iterations N and the length of the initial key sequence n through quantum channel negotiation, where n is an even number, And n<N.

For example: set the initial value x ₀ =0.8835, the parameter value μ=1.92, the number of iterations N=500, and the initial key length n=20; the quantum channel adopts the BB84 protocol;

Step 2. Initial key sequence generation: Alice sends the initial value x ₀ and parameter value μ into the chaotic system, and iterates N times to get N real numbers, and selects n real numbers X _1a , X _2a ,..., X _na , perform binary processing on X _1a , X _2a ,...,X _na respectively to generate a binary initial key sequence S _0a ; at the same time, Bob sends the initial value x ₀ and parameter value μ into the same Chaotic system, and iterate N times to get N real numbers, and select n real numbers X _1b , X _2b ,...,X _nb from these N real numbers in the same way as Alice, and set X _1b , X _2b ,... ,X _nb performs the same binarization process as X _1a , X _2a ,...,X _na to generate a binary initial key sequence S _0b ;

For example: the chaotic system chosen by Alice and Bob is Logistic mapping, μ∈(0,2], x _i ∈[-1,1]. When μ∈[1.42,2], the system is in a state of chaos.

The operation of the above-mentioned binarization process is as follows: set a threshold k=0, when a certain real value in the initial key is greater than k, it is mapped to 1; when a certain real value in the initial key is less than or equal to k, mapped to 0. The specific form is expressed as follows:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; k</span>}\end{array}\right.$

In the formula, y _i is a binary value, x _i is a real value, and i represents the serial number of the real number in the initial key. Assume that the initial key sequences S _0a and S _0b generated by Alice and Bob are both 01010000101101101110.

Step 3. Generation of verification code sequence and control code sequence: Alice generates verification code sequence S _1a and control code sequence S _2a from the initial key sequence S _0a through grouping, XOR and extraction processing; the specific steps are as follows:

Divide the binary codewords in the initial key sequence S _0a into two groups in turn, and perform XOR operation on the two binary codewords in each group respectively to obtain the sequence S _1a ; then the initial key sequence S _0a Perform extraction to obtain sequence S _2a , extraction rule: when a certain bit in sequence S _1a is 1, then extract the second bit in the two binary code words corresponding to the bit; when a certain bit in S _1a is 0 , then extract the first bit in the two binary code words of the corresponding group; the sequence S _2a is used as the control code sequence for communication between Alice and Bob, and the sequence S _1a is used as the check code sequence;

For example, when the generated initial key sequence S _0a is 01010000101101101110, S _0a is grouped into: 01 0100 00 10 11 01 10 11 10; the two binary code words in each group are subjected to XOR operation to obtain the sequence S _1a is 1100101101; and then extract the binary sequence S _0a according to the above extraction rules for the sequence S _2a . For example, the first bit of the sequence S _1a is 1, which corresponds to the first group 01 in the binary sequence S _0a , then the second bit 1 in the corresponding group is extracted, and after such sequential extraction, the obtained sequence S _2a is 1100011010;

At the same time, Bob also generates the verification code sequence S _1b and the control code sequence S _2b from the initial key sequence S _0b through the same method as Alice (that is, grouping, XOR and extraction processing); the sequence S _2b is used as the key between Alice and Bob. Inter-communication control code sequence;

The check code sequence is obtained by grouping XOR of the initial sequence, and the control code sequence is obtained by extracting the initial key sequence through its corresponding check code sequence. As long as the check code sequences of Alice and Bob are consistent, then the control code sequences of Alice and Bob It should be consistent.

Step 4, transmission and authentication of the verification code sequence: Alice transmits the verification code sequence S _1a to Bob through the quantum channel; in the present invention, the quantum channel in step 4 adopts the HKH98 protocol; Bob transfers the received verification code sequence S _1a to Step 3 The generated verification code sequence S _1b is compared, and the comparison result is fed back to Alice; when S _1a and S _1b are the same, both the control code sequence S _2a and S _2b are considered to be valid, and the control code sequence S _2a is consistent with the control code The sequence S _2b is the same; the control code sequence S _2a and the control code sequence S _2b are both recorded as the control code sequence K; in the present invention, the check code sequence S _1a is transmitted through the HKH98 protocol.

Step 5, the process of generating discarded codewords by shifting and cyclically shifting the control code sequence: both Alice and Bob select the measurement base sequence through the control code sequence K to generate a key sequence; in the process of generating the key sequence, if the required key sequence length It is longer than the length of the measurement base sequence controlled by the control code sequence K. In order to reduce the frequency of repeated use of the fixed control code sequence K, the control code sequence K is shifted and cyclically discarded to generate different control code sequences. The control code sequence K shift cycle discarding algorithm is as follows:

The combination of the first bit and the second bit codeword of the control code sequence K is used as the combination to be discarded. After discarding, when the control code sequence needs to be used again, the first bit of the control code sequence K is shifted to the last bit and The remaining bits are moved forward in turn to obtain a new control code K ₁ ; the combination of the first and second codewords of the new control code K ₁ is the combination to be discarded; when the control code sequence needs to be used again, and so on, That is, the first bit of the previous control code sequence is shifted to the last bit and the remaining bits are shifted forward in sequence to obtain a new control code sequence.

For example, when the control code sequence K is 1100011010, the first bit is 1, and the second bit is also 1, then the discarded codeword combination is 11; after discarding, the remaining control code sequence K' is 00011010, which is defined by {00, 01,10} three groups of code words are combined, and the corresponding relationship between them and the measurement base is set as: 00 corresponds to , 01 corresponds to , 10 corresponds, then the order of the measurement bases controlled by the control code K' is When the control code sequence needs to be used again, the first bit of the control code sequence K is shifted to the last bit, and the second bit is shifted to the first bit to obtain a new control code sequence K ₁ is 1000110101; at this time, its first bit is 1, the second bit is 0, then the discarded codeword combination is 10; after discarding, the remaining control code sequence K ₁ ′ is 00110101; the control code sequence K ₁ ′ is composed of {00,01,11} three groups of codewords are formed, and the corresponding relationship between them and the corresponding measurement base is set as: 00 corresponds to , 01 corresponds to , 11 corresponds to . Then the sequence of measurement bases controlled by the control code K ₁ ′ is

Following is the security analysis that the scheme of the present invention is carried out:

The method of the present invention utilizes the chaotic system and Logistic mapping, and needs to provide initial values and chaotic parameters to Alice and Bob, where the initial value _x0 is obtained through a trusted authentication center CA, and the setting and iteration of parameters μ The times N and the initial key length n are negotiated by Alice and Bob. Among them, security issues may appear in the following two stages:

1. Allocation and negotiation phase (step 1). If the CA is unreliable, the effective information that the CA can obtain is only x ₀ , and the parameters μ, N, and n of the chaotic system cannot be obtained. In order to obtain the S _0a and S _0b sequences, the CA can only eavesdrop on the negotiation phase that he does not participate in. At that time, his status was the same as that of other eavesdroppers. The communication parameters are negotiated through the quantum channel, and the security can be guaranteed by the Heisenberg uncertainty principle and the quantum non-cloning theorem. And because the chaotic system is extremely sensitive to parameters, even if the parameters are slightly different, the iterated real value sequence will be completely different, so step 1 can effectively prevent unreliable CA and other eavesdroppers from eavesdropping, to ensure S _0a and S _0b is safe.

2. Check code sequence transmission stage (step 4). The function of S _1a is to prove the legitimacy of Alice’s identity, and to ensure the consistency of control code sequences S _2a and S _2b . Alice needs to transmit S _1a to Bob using the HKH98 protocol. If there is eavesdropping, under the guarantee of quantum uncertainty and non-cloning principles, the eavesdropping behavior will be easily detected by both communication parties; if Eve can obtain information, it is only S _1a . Part of the information not exceeding 1/3, for Eve, this information is not valid information, because S _0a is segmented, XORed, and extracted to obtain the check code sequence S _1a and the control code sequence S _2a , S _1a The generation process of is irreversible, that is, it is easy to obtain S _1a from S _0a , and then obtain S _2a according to S _1a , but in the case of obtaining S _1a , neither S _0a nor S _2a can be deduced. Therefore, even if S _1a partially leaks, S _2a will not be endangered. Therefore, Eve cannot deduce S _0a from the partial information of S _1a , and therefore cannot deduce S _2a . So this stage is also safe.

Claims (8)

1. a kind of based on six state measurement bases encryption quantum-key distribution mbe-ssp control code method for generating sequence it is characterised in that Specifically include following steps:

Step 1, distribution and negotiation phase: it is shared that sender alice and recipient bob passes through reliable authentication center ca acquisition Initial value x₀；Alice and bob is consulted by quantum channel, obtains parameter value μ, the iterations n of chaos system and initially close Key sequence length n；

Step 2, initial key sequence generate: the initial value x that alice will share₀Send into chaos system with parameter value μ, and iteration n Secondary, obtain n real number, and therefrom choose n real number x_1a, x_2a,...,x_na；By x_1a, x_2a,...,x_naCarry out respectively at binaryzation Reason, generates binary system initial key sequence s_0a；Meanwhile, the initial value x that bob will share₀Identical with alice with parameter value μ feeding Chaos system, and iteration obtains n real number for n time, and with choosing n real number from this n real number with alice identical mode x_1b, x_2b,...,x_nb, by x_1b, x_2b,...,x_nbCarry out and x_1a, x_2a,...,x_naIdentical binary conversion treatment, generates at the beginning of binary system Beginning key sequence s_0b；

Step 3, check code sequence and control code sequence generate: alice passes through packet, XOR and extraction and processes, from initial key Sequence s_0aMiddle generation check code sequence s_1aWith control code sequence s_2a；Meanwhile, bob is also by the method same with alice, from first Beginning key sequence s_0bMiddle generation check code sequence s_1bWith control code sequence s_2b；Sequence s_2a、s_2bAs logical between alice and bob The control code sequence of letter；

Step 4, the transmission of check code sequence and certification: alice are by check code sequence s_1aBob is sent to by quantum channel；Bob will Check code sequence s receiving_1aCheck code sequence s generating with step 3_1bCompare, and comparison result is fed back to alice；Work as s_1aWith s_1bIt is believed that control code sequence s when identical_2aWith control code sequence s_2bIdentical；By control code sequence s_2aAnd Control code sequence s_2bAll it is designated as control code sequence k；

Step 5, the circulation generation of control code sequential shift are abandoned code word process: alice and bob and are all selected by control code sequence k Measurement basic sequence, generates key sequence；In key sequence generating process, if required key sequence length is more than controlled The measurement base sequence length that code sequence k controls, then abandon algorithm using control code sequence k shift cycle and generate different control codes Sequence is in case use；

Wherein, described control code sequence k shift cycle is abandoned algorithm and is referred to:

Using first of control code sequence k and second code word combination as combination to be abandoned, after abandoning, when needing again During secondary use control code sequence, the first of control code sequence k is moved to its last position and remaining bit moves forward successively, obtains New control code k₁；New control code k₁First and the second bit word be combined as combination to be abandoned；When need again During using control code sequence, the like, it is to be moved to the first of the control code sequence of last time its last position and will remain Remaining position moves forward successively, obtains new control code sequence.

2. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 1, described Shared initial value x₀∈[-1,1].

3. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 1, described Parameter value μ ∈ [1.42,2] of chaos system, initial key sequence length n is even number, and n ＜ n.

4. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that described shared initial value x₀ =0.8835, parameter value μ=1.92, iterations n=500, initial key length n=20.

5. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 2, alice The chaos system selecting with bob maps for logistic,x_i∈ [- 1,1], μ ∈ [1.42,2].

6. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 2, described The operation of binary conversion treatment: set threshold value k, when certain real number value in initial key is more than k, be mapped as 1, when initial When certain real number value in key is less than or equal to k, it is mapped as 0；Concrete form is expressed as follows:

$y_i=f\left(x_i\right)=\left\{\begin{array}{cc}0& x_i\&le;k\\ 1& x_i>k\end{array}\right.$

In formula, y_iFor binary numeral, x_iFor real number value, i represents the sequence number of the real number in initial key.

7. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 3, described Alice passes through packet, XOR and extraction and processes, from initial key sequence s_0aMiddle generation check code sequence s_1aWith control code sequence s_2aSpecifically comprise the following steps that

By initial key sequence s_0aIn binary code word be divided into one group successively two-by-two, and respectively by two binary systems in every group Code word carries out XOR, obtains sequence s_1a；Again to initial key sequence s_0aExtracted, obtained sequence s_2a, decimation rule: When sequence s_1aIn a certain position when being 1, then extract the second in two binary code words of this corresponding group；Work as s_1aIn a certain When position is for 0, then extract first in two binary code words of this corresponding group；By sequence s_2aBetween alice and bob The control code sequence of communication, by sequence s_1aAs check code sequence.

8. mbe-ssp control code method for generating sequence as claimed in claim 1 is it is characterised in that in described step 4, described The quantum channel of step 4 adopts hkh98 agreement.