CN1773906B - Magic square signature method for true or false identification - Google Patents
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- CN1773906B CN1773906B CN 200410046922 CN200410046922A CN1773906B CN 1773906 B CN1773906 B CN 1773906B CN 200410046922 CN200410046922 CN 200410046922 CN 200410046922 A CN200410046922 A CN 200410046922A CN 1773906 B CN1773906 B CN 1773906B
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Abstract
A method of using magic square signature to identify true or false of status includes generating a magic square for each article, adding elements of generated magic square on elements of signature magic square to achieve model for obtaining a signature matrix and using this matrix as identification data of article status, sending signature matrix to identifying device with signature magic square for calculating model difference of said matrix to signature magic square and verifying whether matrix is magic square or not, confirming that status having signature matrix is true or otherwise it isfalse if matrix is magic square.
Description
Technical field
The present invention relates to a kind of magic square endorsement method that the identity true and false is differentiated that is used for, be meant a kind of ostensible identity two-way dynamic confirming method of log-on message that constitutes by magic square signature, encryption and shuffling method especially, and a kind of encryption algorithm and all ostensible magic square digital anti-counterfeit method of database.
Technical background
Authentication is the primary link in the network information security system, is the basis of ecommerce and E-Government.The General Principle of authentication is to be verified some specific information that Fang Suoneng provides or to have some special computing capability and corresponding information or ability that authentication is held compare.The method of network ID authentication has a lot, the most frequently used a kind of be that user account number and password are combined, with account number identification " who are you ", use password authentification " whom you are really " more earlier.This identity identifying method is simple to operate, but dangerous, and account number and password are stolen easily.At present safer identity identifying method is the inquiry of adopting " one-time pad " password technology/reply a formula access token identity identifying method.Its authentication principles is as follows: the user holds the authentication card of a certain special function programming, the copy of corresponding this special function of preservation of certificate server.When the user logined host computer system, how the host asks certificate server verified the user, and certificate server informs that main frame verifies to inquire about/to reply asynchronous mode, and informed the inquiry random number of checking this time.Main frame will be inquired about random number and pass to user terminal, and the user calculates its response with this random number as the input value of its special function, and this response is sent to main frame.Main frame is passed response back certificate server, and with compare by the result that the copy of special function calculates according to same inquiry random number, if two numbers equate then can confirm that the user is a validated user.Special function in the verification process generally adopts hash function or cryptographic algorithm to realize that as the DES algorithm, each user has same enciphering algorithm module but its key is unique.Therefore, the transfer process of inquiry random number is ciphering process, adopts the fail safe of the inquiry of symmetric encipherment algorithm/reply formula access token the same with the fail safe of encryption key.Although DES is an extremely complicated algorithm of a kind of ciphering process, owing to the exhaustive number of times to the DES cipher key attacks is 2
56=72,057,594,037,927,936, under the computing technique condition of current develop rapidly, just can finish exhaustive attack in the short period to DES; Based on the contextual algorithms of DES internal work, NSA can decode DES in 3 to 5 minutes in addition.In addition, if grasped a large amount of plaintexts and ciphertext, the expert of NSA can obtain the key of being correlated with at an easy rate.Therefore, the fail safe of the system of this employing DES algorithm also is difficult to meet the demands.Modern common key cryptosystem can solve some shortcomings of Private Key Cryptosystem preferably, and as the public key encryption transmission of business cipher key, wherein typical case's representative is exactly RSA.But there is following shortcoming in the RSA common key cryptosystem: it is pretty troublesome 1) to produce key, is subjected to the restriction of prime number generating technique, thereby is difficult to accomplish one-time pad; 2) block length is too big, and for guaranteeing fail safe, block length will cause the computing cost too high more than 600bits at least, and especially speed is slower, than the slow several magnitude of symmetric cryptographic algorithm; And along with the development of big several decomposition techniques, this length is also increasing, and encryption efficiency also will descend, and is unfavorable for the standardization of data format; 3) existence is at selection ciphertext only attack method and the public modulus attack method of RSA; 4) though PKI can disclose, changed by the people easily, the affirmation of PKI is needed the Verification System of complexity.More worrying is that people can decompose the big integer of more than 140 decimal digit at present.
In the applicant's the patent formerly " magic square identity two-way identification and cipher key delivery integral method " with one at random magic square evenly be divided into two complementary defective matrixes randomly, be stored in certificate server and the authentification of user card as log-on message and authentication information respectively, can constitute a magic square digital phase-locking.Safety was sent to the other side after the authentication both sides evenly shuffled the defective matrix at random, and can both sides all confirm the other side to recover magic square.The key tuple can repeatedly be selected from magic square at random by a side, and its position vector is passed to the other side, to recovering the key tuple in view of the above.Magic square identity two-way identification and cipher key transmitting process combine together, then cipher key delivery success of authentication success, and vice versa.Though the magic square identity authentication method is safe and reliable and efficient is high, client enrollment information can not disclose.
The applicant is formerly in the patent " magic square digital anti-counterfeit method ", for each commodity distributes an exclusive number according to the order of sequence and produces one the five above magic square in rank at random.This magic square through an element be 0 or 1 the square formation of shuffling the at random unfinished magic square that is divided into two complementations (M1, M2), the numeral among unfinished magic square M1 and the M2 constitutes a true and false effect vector V2 according to the order of sequence, and is stored in false proof data center; The matrix of shuffling is converted into the security code of decimal number as this commercial product identification; For commodity are made the label that contains commercial product identification numbering and security code, and security code is covered; The user delivers to true and false verification center by input unit with goods number and security code, recovers magic square with this.If can recover magic square and belong to inquiry first, then be genuine piece, otherwise be false.This magic square digital anti-counterfeit method has that encryption algorithm can disclose, false proof database can disclose, independent, the two-way advantage such as false proof, easy to implement of anti-fake code, but there is the local correlations of internal data without the magic square shuffling method of displacement, and can produces privately without the anti-fake code of magic square signature.
Summary of the invention
The objective of the invention is to propose a kind of magic square endorsement method that the identity true and false is differentiated that is used for.
Another object of the present invention provides the ostensible magic square identity two-way dynamic confirming method of a kind of log-on message.
A further object of the present invention provides a kind of magic square digital anti-counterfeit method, this magic square digital anti-counterfeit method has that algorithm can disclose, database can disclose, anti-fake code is independent, can two-way false proof, anti-collusion from both within and without fraud etc. plurality of advantages.
For achieving the above object, the present invention is used for the magic square endorsement method that the identity true and false is differentiated, may further comprise the steps:
1) magic square more than n rank of random configuration is as signature magic square D, and signature magic square D maintains secrecy n 〉=5;
2) produce n rank magic square M at random according to article characteristics information, magic square M is at random carried out mould n with the element step-by-step of signature magic square D
2+ 1 He obtains a signature matrix H, and this signature matrix H is as the identifying information of article identity;
3) matrix H of will signing is passed in the identification equipment that has signature magic square D, the mould difference matrix M of compute signature matrix H and signature magic square D
*
4) validation matrix M
*Whether be magic square, if M
*Be magic square, the article identity that then has the matrix H of signing is true, otherwise is false.
Above-mentioned magic square endorsement method, in the described step (2), the signature matrix H is replaced as displacement signature matrix W according to magic square permutation table P, and displacement signature matrix W is as the identifying information of article identity; To replace the signature matrix W in the step (3) and pass in the identification equipment that has signature magic square D and permutation table P, matrix W is inverted according to permutation table P and changes the signature matrix H into, and the signature matrix H is carried out mould n with signature magic square D step-by-step again
2+ 1 difference obtains matrix M
*
The ostensible magic square identity two-way dynamic confirming method of a kind of log-on message comprises the steps:
1) user's registration step: (fixing and maintain secrecy signature magic square D and permutation table P)
A1, registrar produce a n rank magic square M at random for the registered user;
A2, registrar are two complementary unfinished magic square M with the even random division of magic square M
1With unfinished magic square M
2, unfinished magic square M wherein
1And M
2Middle defective locations fills out 0, unfinished magic square M
2Be stored in the authentification of user card;
A3, unfinished magic square M
1With signature magic square D step-by-step addition delivery n
2+ 1 obtains mould and matrix H, again mould and matrix H is obtained matrix M S by permutation table P displacement
1
A4, with matrix M S
1Be stored in the ostensible authentication database or hold for the user as user's registration information.
2) certificate server is confirmed registered user's step:
B1, user log-in authentication server;
B2, certificate server produce even a shuffle matrix B and pass to the user of 0-1 at random;
B3, the user matrix B input authentication card of will shuffling;
B4, authentication card according to the matrix B of shuffling by shuffling algorithm with unfinished magic square M
2Convert vectorial V to, and pass V back user;
B5, user pass to certificate server with vectorial V;
B6, certificate server are with user's enrollment status information MS
1, vectorial V passes to calibrating chip with the corresponding matrix B of shuffling;
B7, calibrating chip are according to permutation table P and signature magic square D decrypted user enrollment status information MS
1Obtain unfinished magic square
M
1Shuffle recovery algorithms according to unfinished magic square M by unfinished magic square then
1, the vectorial V and the matrix B composite matrix M that shuffles
*Last validation matrix M
*Magic square character whether satisfy, and will verify that the result passes to certificate server.Above-mentioned magic square identity two-way dynamic confirming method comprises that also the user confirms the step of registrar:
C1, certificate server send an authentication request information to the user, promptly require the user to produce an even 0-1 matrix B of shuffling at random
1
C2, user produce an even 0-1 matrix B of shuffling at random
1And pass to certificate server in response;
C3, the certificate server matrix B of will shuffling
1Be sent to the proof of identity chip;
C4, proof of identity chip are according to shuffling matrix B
1With decrypted user enrollment status information MS
1Back gained defective matrix M
1Shuffle into vectorial V
1, and with vectorial V
1Send certificate server back to;
C5, certificate server are with vectorial V
1Be sent to the user;
C6, user are with vectorial V
1With the matrix B of shuffling
1The input authentication card;
C7, authentication card will represent the unfinished magic square M of subscriber identity information according to the unfinished magic square recovery algorithms of shuffling
2, vectorial V
1
With the matrix B of shuffling
1Synthetic complete matrix M
* 1At last, verify this matrix
M * 1 Magic square character whether satisfy, and will verify that the result returns the user.
In above-mentioned affirmation registered user's the step, step b4 step b4
*Replace, simultaneously, step b7 step b7
*Replace: b4
*: authentication card with the original matrix B of shuffling as the initial state of cellular automaton, and the matrix B of this time being shuffled more than three steps of forward direction operation
*Then according to shuffling matrix B
*By shuffling algorithm with unfinished magic square M
2Convert vectorial V to, and pass V back user;
B7
*: calibrating chip is according to permutation table P and signature magic square D decrypted user enrollment status information MS
1Obtain unfinished magic square M
1With the original matrix B of shuffling as the initial state of cellular automaton, and operation and step b4 forward
*In the identical step number matrix B of this time being shuffled
*Then, by the recovery algorithms of shuffling according to unfinished magic square M
1, the vectorial V and the matrix B of shuffling
*Synthetic complete matrix M
*At last, verify this matrix M
*Magic square character whether satisfy, and will verify that the result returns the user.
Above-mentioned user confirms in the step of registrar, step c4 step c4
*Replace, simultaneously, step c7 step c7
*Replace::
C4
*: the proof of identity chip is with the original matrix B of shuffling
1As the initial state of cellular automaton, and the matrix B of this time being shuffled more than three steps of forward direction operation
* 1Then according to shuffling matrix B
* 1With decrypted user enrollment status information MS
1Back gained defective matrix M
1Shuffle into vectorial V
1, and with vectorial V
1Send certificate server back to;
C7
*: the authentication card is with the matrix B of shuffling
1As the initial state of cellular automaton, and operation and step c4 forward
*The identical step number matrix B of this time being shuffled
* 1Then, by the recovery algorithms of shuffling according to unfinished magic square M
2, vectorial V
1With the matrix B of shuffling
* 1Synthetic complete matrix M
* 1At last, verify this matrix M
* 1Magic square character whether satisfy, and will verify that the result returns the user.
A kind of magic square digital anti-counterfeit method may further comprise the steps:
D1, be that each commodity produces a uniqueness identity code N according to the order of sequence;
D2, produce more than one 5 rank at random magic square M and one the 0-1 matrix S of shuffling at random for each commodity N, by from left to right, the matrix S of will shuffling of order from top to bottom is converted into binary number, and then be converted to a decimal system number, as the security code V of this commercial product identification
1
D3, matrix S is directly cut apart Matrix C as the magic square that produces two-way check card to shuffle;
D4, cut apart at random according to cutting apart Matrix C that magic square M obtains unfinished magic square M
1, unfinished magic square M
1In digital correspondence cut apart respective element 1 in the Matrix C, then with unfinished magic square M
1Be printed as two-way check card, and identity code N is printed on the card;
D5, replace with magic square permutation table P
At randomMagic square M obtains permutation matrix W;
D6, permutation matrix W is divided into two complementary defective permutation matrix (W according to the matrix S of shuffling
1, W
2), the defective matrix W
1The middle numeral and the matrix of shuffling
SMiddle respective element 1 correspondence, the defective matrix W
2The middle numeral and the matrix of shuffling
SMiddle respective element 0 correspondence;
D7, by from left to right, order from top to bottom is the defective matrix W
1In numeral defective matrix M complementary with it
2In numeral line up two row according to the order of sequence, the verification of a security code of end to end then formation vector V
2With commercial product identification sign indicating number N and verification vector V
2Be stored in the false proof data center;
D8, on commodity, make and contain commercial product identification sign indicating number N and security code V
1Label, and with security code V
1Cover.
In the above-mentioned magic square digital anti-counterfeit method, adopt signature magic square D, magic square permutation table P and irreversible cellular automaton fixing and that maintain secrecy, steps d 3 usefulness steps d 3
*Replace steps d 5 usefulness steps d 5
*Replace, promptly
D3
*, be the initial condition of irreversible cellular automaton, iteration forward with the matrix S of shuffling
3Obtain magic square more than step and cut apart Matrix C;
D5
*, with the signature magic square D magic square M at random that signs, obtain the matrix H of signing; With magic square permutation table P displacement signature matrix H, obtain displacement signature matrix W again.
The advantage that the ostensible magic square identity two-way dynamic confirming method of this log-on message is had:
1) guaranteed that by the magic square mould with the magic square encryption technology that the magic square displacement combines user's registration information can disclose, and has overcome the catastrophic results that authentication database is divulged a secret and may be caused in the existing authentication method;
2) the dynamic identity authentication method of " one-time pad " can prevent to reuse out-of-date authentication information, has improved authenticating safety;
3) magic square identity authentication protocol and algorithm can be realized in open network: matrix can not be derived unencryption identity information M before with the dynamic credentials that the vector of shuffling is formed by shuffling
1With the identity information M in authentication (intelligence) card
2
Even by the mode of wiretaping, it is right with the vector of shuffling no matter to collect the matrix of how much shuffling, and also can not derive identity information M
1With M
2.
4) authentication protocol and algorithm all can disclose, and signature magic square and permutation table are solidificated in the proof of identity the core of the card sheet;
5) irreversibility of cellular automaton can prevent to design attack pattern in advance, has improved the fail safe of authentication;
6) the magic square identity identifying algorithm is simple, is convenient to logic chip and realizes that cost is low;
7) magic square identity authentication protocol and efficiency of algorithm height can avoid authenticating the treatment effeciency bottleneck problem in rush hour.
This magic square digital anti-counterfeit method has following advantage:
1) encryption algorithm is open: magic square is replaced, shuffles and signature technology guarantees that algorithm can disclose.
2) database can disclose: magic square is shuffled and is guaranteed not calculate security code by check code with replacement technique, and promptly expose signature magic square and permutation table (key) still can not calculated security code by check code; The magic square signature technology is guaranteed can't insert legal check code privately;
3) anti-fake code is independent: anti-fake code is at random independently, obtains its corresponding security code by the check code of every pair of anti-fake code and all must independently crack.If want to calculate its corresponding security code, adopt 100 the highest PC combined calculation of present dominant frequency on average to need for 9 years by a check code.
4) realize two-way false proof: system can verify commodity true and false, simultaneously the true and false that the user also can the verification Antiforge system;
5) nucleus module solidifies: signature magic square and permutation table are stored in the Flash chip, and core algorithm is solidified into fpga chip, guarantees to read, and is not only safe and reliable but also efficient; The final lawful authority of anti-fake code is concentrated to modifiable PCI coding card initialization password, and lawful authority hardwareization has been stopped the occupational crime behavior that false proof central task personnel insert illegal false proof number privately;
6) central authorization coding: the each anti-fake code number that generates of coded system must carry out the remote central mandate by authorization identifying system, utilize magic square identity two-way dynamic authentication and cellular automaton principle, can be so that any coded system can only be produced the anti-fake code of authorized quantity, and the anti-fake code between the different enterprise can not be used with.
7) coding checkout is simple: only need simple add operation, consumer and computer all can be verified the true and false, but ordinary PC per second verification 10,000 times;
Description of drawings
Accompanying drawing 1: complementary unfinished magic square is filled principle.
Accompanying drawing 2: magic square mould and decomposition principle at random.
Accompanying drawing 3: complementary defective signature matrix principle.
Accompanying drawing 4: magic square permutation table.
Accompanying drawing 5: magic square encrypt and decrypt process.
Accompanying drawing 6: the magic square recovery principle of shuffling.
Accompanying drawing 7: defective shuffle matrix process.
Accompanying drawing 8: defective shuffle matrix recovery process.
Accompanying drawing 9: cellular automaton is that initial state obtains the matrix S of shuffling with the matrix S of shuffling
*
Accompanying drawing 10: magic square M, the matrix S of shuffling at random
*, unfinished magic square M
1With complementary unfinished magic square M
2
Accompanying drawing 11: be stored in signature magic square D and permutation table P in the chip.
Accompanying drawing 12: registration magic square M (Alice), the unfinished magic square M of user Alice
1(Alice) with complementary unfinished magic square M
2(Alice).
Accompanying drawing 13: encrypt M
1(Alice) obtain MS
1(Alice).
Accompanying drawing 14: server is confirmed the process of user Alice identity.
Accompanying drawing 15: user Alice confirms the process of server identity.
Accompanying drawing 16: impediment magic square M
2(Alice) the process of shuffling.
Accompanying drawing 17:Alice enrollment status information MS
1(Alice) decrypting process.。
Accompanying drawing 18: impediment magic square M
2(Alice) the recovery process of shuffling.
Accompanying drawing 19: registration unfinished magic square M
1(Alice) the process of shuffling.
Accompanying drawing 20: registration unfinished magic square M
1(Alice) recovery process of shuffling.
Accompanying drawing 22: (Web t) is the initial state matrix B of newly being shuffled to cellular automaton with B
*(Web, t).
Accompanying drawing 22: (Alice t) is the initial state matrix B of newly being shuffled to cellular automaton with B
*(Alice, t).
Accompanying drawing 23: magic square M, the matrix S of shuffling and security code conversion at random.
Accompanying drawing 24: cellular automaton is that initial state obtains magic square and cuts apart Matrix C with the matrix S of shuffling.
Accompanying drawing 25: magic square M, magic square are cut apart Matrix C and unfinished magic square M at random
1
Accompanying drawing 26: magic square M, signature magic square D, signature matrix H and displacement signature matrix W at random.
Accompanying drawing 27: displacement signature matrix W, the matrix S of shuffling, defective matrix W
1With complementary defective matrix W
2
Accompanying drawing 28: by the defective matrix W
1With complementary defective matrix W
2Form verification vector V
2
Accompanying drawing 29: two-way check digit (complementary unfinished magic square M
2) obtain flow process.
Embodiment
Unfinished magic square is filled principle: with the even random division of the magic square of a random configuration is two complementary unfinished magic squares, also there is not effective unified calculation method at present in theory, make and recover second half digital position by only containing half digital unfinished magic square, make it still to constitute a magic square, vice versa.We claim that this problem is that unfinished magic square is filled problem, and this problem is a disclosed mathematics difficult problem, as shown in Figure 1.Usually, wherein any one unfinished magic square is as lock if incite somebody to action, and another then can be used as corresponding key, and the two is locked and key each other.Can not push away " key " accordingly by " lock ", can not push away " lock " accordingly by " key ", " lock " can disclose.7 rank magic squares can construct 10
34The magic square digital phase-locking, when known " lock ", the exhaustive number of times of corresponding " key " be 25! ≈ 1.55 * 10
25
Magic square mould and principle: with two n rank element step-by-step addition delivery n of magic square at random
2+ 1 obtains a mould n
2Natural matrix in+1, judge this matrix whether be two n rank at random the magic square sum on calculating, be undecidable; Usually, with the matrix element step-by-step addition of the n rank magic square of k 〉=2 random configuration delivery n again
2+ 1, obtain a mould n
2Natural matrix in+1, judge this matrix whether can be decomposed into k n rank at random the magic square sum in calculating, be undecidable.This principle can be applicable to fields such as key management, authentication, multipart identification authentication, micropayments and digital code anti-false, and has security intensity height, verification efficiency height, is easy to advantages such as logic chip realization.Illustrate, as shown in Figure 2,, on calculating, can not and be decomposed into magic square 1 and magic square 2 at random at random the magic square mould if only know magic square mould and matrix at random.
Directly obtain the magic square signature technology by magic square mould and principle.Magic square of random configuration is as covert signature magic square (being equivalent to signature private key), arbitrary magic square at random and this signature magic square mould and obtain afterwards one the signature matrix, this signature matrix must be a magic square with the mould difference of signature magic square, with this can the certifying signature matrix the true and false.Whether can judge the magic square at random of being signed by side's generation by the true and false of certifying signature matrix, but not other party is forged.Usually, the signature matrix of magic square is unique, does not promptly have two different magic squares, and its signature matrix of same relatively signature magic square equates.The magic square signature technology also can be called the magic square encryption technology.
Can further unfinished magic square filling problem be extended to defective signature matrix by the magic square signature technology and fill problem.A signature matrix is taken out numeral about half at random, be difficult to release second half numeral of being taken out, make it still to constitute a legal signature matrix by half remaining numeral.The filling problem that can be known defective signature matrix by the uniqueness of signature matrix also is unique, promptly can not have two groups of different numerals, makes it all to constitute the legitimate signature matrix with half known numeral.As shown in Figure 3.
Magic square principle,displacement: design a matrix element permutation table one to one, with each element map in n * n matrix to another matrix of equal scale on the new element position, no longer be in colleague or same column or same diagonal after making element on any two colleagues in the original matrix or same column or the same diagonal mapped, this replacement process is called the magic square displacement, and wherein permutation table is called the magic square permutation table.
What is called is permutation table one to one, as shown in Figure 4.Be exemplified below, one 6 * 6 matrix element is mapped as another matrix element of 6 * 6, wherein, (i, j) expression is with the capable and j row crossover location of i in the extremely new matrix of the element map on the relevant position in the original matrix,, be mapped in the new matrix on the 5th row and the 1st row crossover location the i.e. element on the 0th row and the 0 row crossover location of upper left corner element in the original matrix as upper left corner element (5,1) expression, so analogize, mapping one by one, none repetition claims this magic square replacement process for just replacing.If with certain binary element in the permutation table (i, j) be interpreted as the capable element map that lists with j of i in the matrix to the new matrix this binary element (i, j) on the position, then this magic square replacement process is called decommutation.Therefore, same magic square permutation table promptly can be used as just replacing and also can be used as decommutation, and the two is inverse process each other.
If magic square is used replacement process, can make between the magic square digital element and lose correlation.
Magic square encrypt and decrypt principle: as shown in Figure 5, fix a magic square and magic square permutation table as encryption key, magic square carries out mould and obtains the matrix of signing arbitrary magic square (expressly) that constitutes at random with being somebody's turn to do fixedly earlier, the matrix of should signing is again replaced by permutation table, obtain a character matrix (ciphertext), this process is called the magic square ciphering process, and corresponding inverse process is called the magic square decrypting process.Though known what to magic square (expressly) at random and its encrypted result (ciphertext), on calculating, be difficult to derive its fixing signature magic square and permutation table.The magic square encryption principle can be used for fields such as network ID authentication, access control and micropayments.
The principle of shuffling: but randomly draw wherein about half numeral according to the order of sequence the Serial No. in order from n of one group of verification with inner mathematical relationship, line up the set of number sequence sequentially, and this sequence placed after the last Serial No., constitute a new Serial No., claim the regrouping process of this Serial No. to be the process of shuffling at random, the reorganization Serial No. is called the result that shuffles, and the scheme of wherein evenly randomly drawing numeral according to the order of sequence can be by the 0-1 of n unit binary representation, and is referred to as the scheme of shuffling.But be impossible recover former check digit sequence in order only, but the result that shuffles only can directly revert to former check digit sequence in order by the scheme of shuffling by the result that shuffles, the principle of shuffling of Here it is Serial No..
The magic square recovery principle of shuffling: construct n rank magic square M at random, by a certain open permutation table P with this at random magic square be replaced as another random matrix X; The evenly 0-1 matrix S (this matrix of shuffling can be converted into a decimal number) of shuffling at random of a n * n of structure, matrix will be divided into two complementary defective matrixes, one of them defective matrix X by the random matrix X that displacement obtains according to shuffling
1In numeral corresponding with respective element 1 in the matrix of shuffling, another complementary defective matrix X
2In numeral corresponding with respective element 0 in the matrix of shuffling; Again two complementary defective matrixes being converted into length according to the order of sequence is n
2Digital vectors V.The magic square permutation table P that promptly exposes is n by length
2Digital vectors V be difficult to recover the former M of magic square at random, just be difficult to derive the matrix S of shuffling calculating by digital vectors V.As shown in Figure 6, be that the digital vectors V of 36 elements and permutation table P are difficult to derive magic square M or complementary defective shuffle matrix of the matrix S of shuffling and recovery algorithms at random on calculating by length: establishing size is two complementary defective matrix M for the matrix M of N * n by even random division
1With M
2, the length of vectorial V is n
2, each element is initialized as 0 among the V, the matrix of evenly shuffling at random
b
Ij∈ 0,1}.
As shown in Figure 7, defective matrix M
2The basic process of the transfer algorithm of shuffling be, at first according to the order of sequence will the M corresponding with element among the B 1
2In nonzero digit write incoming vector V, then according to the order of sequence will the M corresponding with element among the B 0
2Middle nonzero digit is write incoming vector V, and gained vector V is the result that shuffles, and can be expressed as:
Suppose that 6 * 6 matrix M is split into two parts M
1With M
2, from upper left corner element, by from left to right, rule from top to bottom is until lower right corner element, order will the M corresponding with element among the B 1
2In nonzero digit write among the incoming vector V, obtain vectorial V=(27,6,11,1,26,10,17,35,31,3,34,19,21,2,15,13,7,24,22,0,0,0 ..., 0); Then, from upper left corner element, by from left to right, rule from top to bottom is until lower right corner element, according to the order of sequence will the M corresponding with element among the B 0
2In nonzero digit, tightly write among the incoming vector V by current vector pointer, V. as a result obtains shuffling
The recovery algorithms of shuffling of defective matrix is the inverse process of shuffling algorithm, as shown in Figure 8, and M wherein
1Be equivalent to " key " in this inverse operation process.The recovery algorithms of shuffling is according to shuffling result vector V, the matrix B of shuffling and complementary defective matrix M
1Recover original matrix M, can be expressed as:
The basic process of the recovery algorithms of shuffling is, at first recovers the matrix numeral corresponding with element 1 in the matrix B of shuffling, and from upper left corner element, by from left to right, rule from top to down is until lower right corner element, considers the M corresponding with element 1 among the B respectively
1In element, if this element non-zero is then put and is recovered that the relevant position is this numeral in the matrix M; Otherwise, put and recover that the relevant position is a currentElement among the vectorial V in the matrix M, the pointer of vectorial V advances one simultaneously, so repeatedly until the lower right corner of B element.Then, vectorial V is from current pointer, recovers the matrix element corresponding with element 0 among the B, promptly from upper left corner element, and by from left to right, rule from top to down is until lower right corner element, the corresponding M of element 0 among consideration and the B respectively
1In element, if this element non-zero is then put and is recovered that the relevant position is this numeral in the matrix; Otherwise, put and recover that the relevant position is a currentElement among the vectorial V in the matrix M, the pointer of vectorial V advances one simultaneously, so repeatedly until the lower right corner of B element, obtains original matrix M at last.
When matrix M during for magic square at random, complementary defective shuffle matrix and recovery algorithms can be used for based on the dynamic identity authentication technology of magic square at random.
Cellular automaton: cellular automaton is the general parallel computational model that is proposed in the late period forties in last century by Ulam and Von Neumann.The cell of cellular automaton and the interactive relationship of its neighborhood make the local cells state spatially to propagate in time, and these characteristics make cellular automaton show very complicated macroscopical temporal-spatial evolution behavior.Usually, the global state of a cellular automaton may have more than one initial status, just has more than one global state and be transferred to this state by step mapping under same cellular automaton rule.Usually, cellular automaton is irreversible, promptly can not release its initial status to state by the back.
As shown in Figure 9, the matrix S of shuffling can be regarded the global state of cellular automaton as, if by a certain cellular automaton rule this is shuffled matrix iteration operation number step (k step) forward, obtains a new matrix S of shuffling
*According to the irreversibility of cellular automaton, even under the condition that discloses this cellular automaton rule, by the matrix S of shuffling
*It is the matrix S of shuffling that impossible derive its preposition k step.
As shown in figure 10, utilize the matrix S of shuffling, push away the k step before by the matrix S of shuffling according to a certain fixed cell automaton rule then and obtain the new matrix S of shuffling displacement signature shuffle matrix
*, by the new matrix S of shuffling
*Cut apart magic square M at random as cutting apart Matrix C, obtain complementary unfinished magic square M
1With M
2, can realize bi-directional verification.
The present invention is used for an embodiment of authentication
Suppose must carry out the bidirectional identification dynamic authentication between user Alice and the certificate server, D is the signature magic square, and P is the magic square permutation table, and as shown in figure 11, signature magic square and permutation table are stored in the proof of identity chip.
The registration step of user Alice is as follows:
A1, registrar are example for registered user Alice produces the above magic square M (Alice) in one 5 rank at random with 6 rank;
A2, registrar evenly are divided into two complementary unfinished magic square M at random with M (Alice)
1(Alice) and M
2(Alice), wherein the defective element fills out 0; M
2(Alice) direct proof of identity information as Alice deposits in authentication (intelligence) card, and the authentication card is with the PIN code protection, as shown in figure 12;
A3, unfinished magic square M
1(Alice) with signature magic square D step-by-step addition delivery (n
2+ 1) obtains mould and matrix H, again mould and matrix H are obtained permutation matrix MS by permutation table P displacement
1(Alice), as shown in figure 13;
A4, with MS
1(Alice) as user's enrollment status information stores in ostensible certificate server database, also can hold by user oneself.
Certificate server confirms that the process of user Alice identity is as follows, as shown in figure 14:
B1, user Alice login authentication server;
B2, certificate server produce one evenly at random the 0-1 matrix B (Web, t) and pass to user Alice;
B3, user Alice are with B (Web, t) input authentication card;
(Web t) presses defective shuffle matrix algorithm with unfinished magic square M according to the matrix B of shuffling for b4, authentication card
2(Alice) convert to Ciphering Key V (Alice, t), and with V (Alice t) passes user Alice back, as shown in figure 15;
(Alice t) passes to certificate server with vectorial V for b5, user Alice;
B6, certificate server are with MS
1(Alice), V (Alice, t) with shuffle accordingly that (Web t) passes to calibrating chip to matrix B together;
B7, calibrating chip are according to permutation table P and signature magic square D deciphering MS
1(Alice) obtain unfinished magic square M
1(Alice), as shown in figure 16; Then according to defective shuffle matrix recovery algorithms with M
1(Alice), (Alice is t) with B (Web, t) composite matrix M for V
*, as shown in figure 17; Last validation matrix M
*Magic square character whether satisfy, and will verify that the result passes to certificate server.
User Alice confirms that the process of certificate server identity is as follows, as shown in figure 18:
C1, certificate server send an authentication request information to user Alice, promptly require user Alice produce one evenly at random 0-1 shuffle matrix B (Alice, t);
C2, user Alice produce one evenly at random 0-1 shuffle matrix B (Alice, t) and pass to certificate server in response;
(Alice t) is sent to calibrating chip with B for c3, certificate server;
(Alice t) will decipher MS according to B for c4, calibrating chip
1(Alice) back gained unfinished magic square M
1(Alice) by defective shuffle matrix algorithm convert to Ciphering Key V (Web, t), and with V (Web t) sends certificate server back to, as shown in figure 19;
(Web t) is sent to user Alice with V for c5, certificate server;
(Web is t) with shuffle matrix B (Alice, t) input authentication card with vectorial V for c6, user Alice;
C7, authentication block according to defective shuffle matrix recovery algorithms M
2(Alice), (Web is t) with B (Alice, t) synthetic complete matrix M for V
*, as shown in figure 20; At last, verify this matrix M
*Magic square character whether satisfy, and will verify that the result returns user Alice.
Among the step b4 and b7 of the foregoing description, (We b, t) as initial state, and forward direction iteration three goes on foot the matrix B of newly being shuffled to available same cellular automaton with B
*(Web, t), as shown in figure 21, again with the matrix B of newly shuffling
*(Web t) shuffles; Among step c4 and the c7, (Alice, t) as initial state, and forward direction iteration three goes on foot the matrix B of newly being shuffled to available same cellular automaton with B
*(Alice, t), as shown in figure 22, again with the matrix B of newly shuffling
*(Alice t) shuffles.According to the irreversibility of cellular automaton, even disclosing under the condition of this cellular automaton, by the matrix B of shuffling
*(Web, t) be impossible derive its preposition matrix B of shuffling (Web, t), by the matrix B of shuffling
*(Alice also is impossible derive its preposition matrix B of shuffling (Alice t), thereby can prevent that the design formula in advance that may carry out this magic square identity two-way dynamic confirming method from attacking t).
The present invention is used for an embodiment of digital code anti-false
At first constructing one 5 D of magic square at random more than the rank as the signature magic square, and generate a permutation table P at random as the magic square permutation table, as shown in figure 11, is example with 6 rank magic squares.Signature magic square D and permutation table P are solidificated in the Flash storage chip of PCI coding card and check card.
Commodity digital anti-counterfeit method may further comprise the steps:
D1, according to the order of sequence for each commodity produces a uniqueness identity code N, as N=2789502342;
D2, produce more than one 5 rank at random the evenly 0-1 matrix S of shuffling at random of magic square M and for each commodity N, by from left to right, the matrix S of will shuffling of order from top to bottom is converted into binary number, be converted to a decimal system number 23564019279 again, as the security code V of this commercial product identification
1, as shown in figure 23;
D3, with the matrix S of shuffling as the initial condition of irreversible cellular automaton, iteration k=3 obtains magic square more than the step and cuts apart Matrix C forward, as shown in figure 24; (CAM can disclose, as CAM=01010101 ... 010101)
D4, cut apart magic square M and obtain unfinished magic square M according to cutting apart Matrix C
1, unfinished magic square M
1In digital correspondence cut apart respective element 1 in the Matrix C, then with M
1Be printed as two-way check card, and identity code N is printed on the card, as shown in figure 25;
D5, magic square M is at random signed, obtain the matrix H of signing, with magic square permutation table P the signature matrix H is replaced again, obtain displacement signature matrix W, as shown in figure 26 with signature magic square D; This process is finished in coding pci card FPGA;
D6, will replace the signature matrix W according to the matrix S of shuffling and be divided into two complementary defectives displacements matrix (W that sign
1With W
2), the defective matrix W
1Middle numeral is corresponding with respective element 1 in the matrix of shuffling, the defective matrix W
2Middle numeral is corresponding with respective element 0 in the matrix of shuffling, as shown in figure 27;
D7, by from left to right, order from top to bottom is the defective matrix W
1In numeral defective matrix M complementary with it
2In numeral constitute true and false verification vector V according to the order of sequence
2: 35,35,29,16,20,34,11,4,15,15,36,33,30,16,16,18,33,23,28,26,1,31,35,15,32,3,3,36,3,2,0,21,9,7,13,19; With commercial product identification sign indicating number N and corresponding verification vector V
2Be stored in the false proof data center, as shown in figure 28;
D8, on commodity, make and contain commercial product identification sign indicating number N and security code V
1Label, and with security code V
1Cover.
The commodity true and false query script: the user passes through phone, note and website with commercial product identification sign indicating number N on the commodity and security code V
1Deliver to true and false verification center, true and false verification center is taken out corresponding true and false verification vector V according to commercial product identification sign indicating number N from false proof database
2, utilize security code V
1With true and false verification vector V
2Recover displacement signature matrix W, according to magic square permutation table P and signature magic square D displacement signature matrix W is carried out decommutation again and mould subtracts, obtain matrix M
*(this process realizes in the PCI check card); If M
*Being the inquiry first of magic square and genus, then is genuine piece, simultaneously according to security code V
1Obtain magic square split-matrix C by cellular automaton, obtain unfinished magic square M on the two-way check card by magic square M and magic square split-matrix C
1Complementary unfinished magic square M
2, at last with complementary unfinished magic square M
2Numeral pass to the user according to the order of sequence; Otherwise, if M
*Be not magic square, then commodity are false product.True and false verification with obtain two-way check digit M
2Flow process as shown in figure 29.
Claims (8)
1. one kind is used for the magic square endorsement method that the identity true and false is differentiated, it is characterized in that, may further comprise the steps:
1) magic square more than n rank of random configuration is as signature magic square D, and signature magic square D maintains secrecy n 〉=5;
2) produce n rank magic square M at random according to article characteristics information, magic square M is at random carried out mould n with the element step-by-step of signature magic square D
2+ 1 He obtains a signature matrix H, and this signature matrix H is as the identifying information of article identity;
3) matrix H of will signing is passed in the identification equipment that has signature magic square D, the mould difference matrix M of compute signature matrix H and signature magic square D
*
4) checking mould difference matrix M
*Whether be magic square, if mould difference matrix M
*Be magic square, the article identity that then has the matrix H of signing is true, otherwise is false.
2. a kind of magic square endorsement method that the identity true and false is differentiated that is used for according to claim 1 is characterized in that:
In the described step (2), the signature matrix H is replaced as displacement signature matrix W according to matrix permutation table P, and displacement signature matrix W is as the identifying information of article identity;
To replace the signature matrix W in the step (3) and pass in the identification equipment that has signature magic square D and permutation table P, displacement signature matrix W is inverted according to permutation table P and changes the signature matrix H into, and the signature matrix H is carried out mould n with signature magic square D step-by-step again
2+ 1 difference obtains mould difference matrix M
*
3. the ostensible magic square identity two-way dynamic confirming method of log-on message is characterized in that, may further comprise the steps:
1) user's registration step:
A1, registrar produce a n rank magic square M at random for the registered user;
A2, registrar are two complementary unfinished magic square M with the even random division of magic square M
1With unfinished magic square M
2, unfinished magic square M wherein
1And M
2Middle defective locations fills out 0, unfinished magic square M
2Be stored in the authentification of user card;
A3, unfinished magic square M
1With signature magic square D step-by-step addition delivery n
2+ 1 obtains mould and matrix H, again mould and matrix H is obtained matrix M S by permutation table P displacement
1
A4, with matrix M S
1Hold in ostensible authentication database or for the user as user's enrollment status information stores;
2) certificate server is confirmed registered user's step:
B1, user log-in authentication server;
B2, certificate server produce even a shuffle matrix B and pass to the user of 0-1 at random;
B3, the user matrix B input authentication card of will shuffling;
B4, authentication card according to the matrix B of shuffling by shuffling algorithm with unfinished magic square M
2Convert vectorial V to, and pass vectorial V back user;
B5, user pass to certificate server with vectorial V;
B6, certificate server are with user's enrollment status information MS
1, vectorial V passes to calibrating chip with the corresponding matrix B of shuffling;
B7, calibrating chip are according to permutation table P and signature magic square D decrypted user enrollment status information MS
1Obtain unfinished magic square M
1Shuffle recovery algorithms according to unfinished magic square M by unfinished magic square then
1, the vectorial V and the matrix B composite matrix M that shuffles
*Last validation matrix M
*Magic square character whether satisfy, and will verify that the result passes to certificate server.
4. the ostensible magic square identity two-way dynamic confirming method of a kind of log-on message according to claim 3 is characterized in that: comprise that also the user confirms the step of registrar:
C1, certificate server send an authentication request information to the user, require the user to produce an even 0-1 matrix B of shuffling at random
1
C2, user produce an even 0-1 matrix B of shuffling at random
1And pass to certificate server in response;
C3, the certificate server matrix B of will shuffling
1Be sent to the proof of identity chip;
C4, proof of identity chip are according to shuffling matrix B
1With decrypted user enrollment status information MS
1Back gained defective matrix M
1Shuffle into vectorial V
1, and with vectorial V
1Send certificate server back to;
C5, certificate server are with vectorial V
1Be sent to the user;
C6, user are with vectorial V
1With the matrix B of shuffling
1The input authentication card;
C7, authentication card will represent the unfinished magic square M of subscriber identity information according to the unfinished magic square recovery algorithms of shuffling
2, vectorial V
1With the matrix B of shuffling
1Synthetic complete matrix M
* 1At last, verify this matrix M
* 1Magic square character whether satisfy, and will verify that the result returns the user.
5. the ostensible magic square identity two-way dynamic confirming method of a kind of log-on message according to claim 3 is characterized in that:
Step b4 b4
*Step replaces:
B4
*: authentication card with the original matrix B of shuffling as the initial state of cellular automaton, and the matrix B of this time being shuffled more than three steps of forward direction operation
*Then according to shuffling matrix B
*By shuffling algorithm with unfinished magic square M
2Convert vectorial V to, and pass vectorial V back user;
Simultaneously, step b7 then uses b7
*Step replaces:
B7
*: calibrating chip is according to permutation table P and signature magic square D decrypted user enrollment status information MS
1Obtain unfinished magic square M
1With the original matrix B of shuffling as the initial state of cellular automaton, and operation and step b4 forward
*In the identical step number matrix B of this time being shuffled
*Then, by the recovery algorithms of shuffling according to unfinished magic square M
1, the vectorial V and the matrix B of shuffling
*Synthetic complete matrix M
*At last, verify this matrix M
*Magic square character whether satisfy, and will verify that the result returns the user.
6. the ostensible magic square identity two-way dynamic confirming method of a kind of log-on message according to claim 4 is characterized in that:
Step c4 c4
*Step replaces:
C4
*: the proof of identity chip is with the original matrix B of shuffling
1As the initial state of cellular automaton, and the matrix B of this time being shuffled more than three steps of forward direction operation
* 1Then according to shuffling matrix B
* 1With decrypted user enrollment status information MS
1Back gained defective matrix M
1Shuffle into vectorial V
1, and with vectorial V
1Send certificate server back to;
Simultaneously, step c7 then uses c7
*Step replaces:
C7
*: the authentication card is with the matrix B of shuffling
1As the initial state of cellular automaton, and operation and step c4 forward
*In the identical step number matrix B of this time being shuffled
* 1Then, by the recovery algorithms of shuffling according to unfinished magic square M
2, vectorial V
1With the matrix B of shuffling
* 1Synthetic complete matrix M
* 1At last, verify this matrix M
* 1Magic square character whether satisfy, and will verify that the result returns the user.
7. magic square digital anti-counterfeit method may further comprise the steps:
D1, be that each commodity produces a uniqueness identity code N according to the order of sequence;
D2, produce more than one 5 rank at random magic square M and one the 0-1 matrix S of shuffling at random for each commodity N, by from left to right, the matrix S of will shuffling of order from top to bottom is converted into binary number, and then be converted to a decimal system number, as the security code V of this commercial product identification
1
D3, matrix S is directly cut apart Matrix C as the magic square that produces two-way check card to shuffle;
D4, cut apart at random according to cutting apart Matrix C that magic square M obtains unfinished magic square M
1, unfinished magic square M
1In digital correspondence cut apart respective element 1 in the Matrix C, then with unfinished magic square M
1Be printed as two-way check card, and identity code N is printed on the card;
D5, replace magic square M at random, obtain permutation matrix W with magic square permutation table P;
D6, permutation matrix W is divided into two complementary defective permutation matrix W according to the matrix S of shuffling
1, W
2, defective permutation matrix W
1Middle numeral is corresponding with respective element 1 in the matrix S of shuffling, defective permutation matrix W
2Middle numeral is corresponding with respective element 0 in the matrix S of shuffling;
D7, by from left to right, order from top to bottom is defective permutation matrix W
1In numeral defective permutation matrix complementary W with it
2In numeral line up two row according to the order of sequence, the verification of a security code of end to end then formation vector V
2With commercial product identification sign indicating number N and verification vector V
2Be stored in the false proof data center;
D8, on commodity, make and contain commercial product identification sign indicating number N and security code V
1Label, and with security code V
1Cover.
8. magic square digital anti-counterfeit method according to claim 7 is characterized in that: adopt signature magic square D and permutation table P and irreversible cellular automaton fixing and that maintain secrecy, steps d 3 is used d3
*Replace, steps d 5 is used d5
*Replace, promptly
D3
*, be the initial condition of irreversible cellular automaton with the matrix S of shuffling, iteration obtains magic square more than 3 steps and cuts apart Matrix C forward;
D5
*, with the signature magic square D magic square M at random that signs, obtain the matrix H of signing; With magic square permutation table P displacement signature matrix H, obtain permutation matrix W again.
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| CN1471258A (en) * | 2002-07-24 | 2004-01-28 | 涛 谢 | Integration method for magic square identity two-way identification and key transmission |
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