CN110278072A - One kind 16 takes turns SM4-128/128 whitepack password implementation method - Google Patents
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
- H04L9/0631—Substitution permutation network [SPN], i.e. cipher composed of a number of stages or rounds each involving linear and nonlinear transformations, e.g. AES algorithms
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Abstract
In an unsafe environment; binary system, the key in reading memory and the program that cryptanalysis person can be run by tracing program execute the modes such as intermediate result, static analysis to implement the attack to algorithm and key, and whitepack cryptographic algorithm can protect key under this dangerous environment.The invention discloses one kind 16 to take turns SM4-128/128 whitepack password implementation method, describes the new model that SM4 cryptographic algorithm is improved when encryption round number is 16 wheel, which improves structure, that is, Encryption Algorithm iterative process of round function；A kind of improved SM4 whitepack cryptographic algorithm is proposed, entire encryption and decryption process can be converted into the form for calculating the affine transformation and look-up table that randomly select.Its principle is the internal state of input, output scrambling and coding hidden algorithm, and key is embedded in look-up table in a compiled manner, while reducing look-up table scale using matrix in block form.
Description
Technical Field
The invention belongs to the technical field of information security, and particularly relates to an improved SM4 white box password implementation method. The invention also relates to a new mode of the encryption algorithm, in which the plaintext block is 128 bits or even larger when the number of encryption rounds of the SM4 algorithm is 16.
Background
At present, it is widely believed that public cryptographic algorithms can provide corresponding security assurance under the condition that a secret key is guaranteed, and the running environment of the cryptographic algorithms is not necessarily enough security. In an insecure environment, a cryptanalyst may implement attacks on algorithms and keys by tracking the binary of program execution, reading keys in memory and program execution intermediate results, static analysis, and the like. This attack environment is called white-box attack environment, and it assumes that the attacker has full control capability on the device terminal, and can observe and change the internal data when the program runs. The white-box attack environment is a model that is well adapted today when information technology is rapidly evolving.
In 2002, Chow et al pioneered the first white-box AES scheme and the first white-box DES scheme by representing a function by a look-up table (i.e., traversing the input of the function, storing the output values of the function to form the look-up table, thereby hiding the internal information of the function), embedding a key into the look-up table, and protecting the look-up table using random bijections (Chow et al, random bijections are coding). With the continuous expansion of the application field of white-box passwords and the continuous increase of scenes, the design of the white-box passwords has very important safety significance.
The SM4 cryptographic algorithm (original name SMs4) is a commercial block cipher standard published by the commercial cipher management office in china, and is widely used for encryption of wireless local area network products. The standard SM4 algorithm has a packet length and a key length of 128 bits, adopts a 32-round nonlinear iterative structure for encryption and decryption, and has a similar algorithm structure to that of the encryption algorithm except that the round keys are used in the reverse order.
Patent document 1 (publication No. CN106452729, published 2017, 02, 22) provides an encryption method based on a white-box cipher based on random permutation, and the main principle is that by introducing an input confusion function P, a random permutation S and an output confusion function Q, more information can not be obtained except for a look-up table, so that the security of running an encryption algorithm on an untrusted terminal is ensured. However, from the principle analysis, the output confusion of each round and the input confusion of the next round are reciprocal, and when the adjacent lookup tables are combined, the confusion effects are mutually cancelled.
Patent document 2 (publication number: CN108270550A, published 2018, 07/10) proposes a safe and efficient white-box implementation method and device based on SM4 algorithm, and the main principle is to introduce n 32-bit random numbers to protect a lookup table, so that the generation efficiency of a white-box decryption lookup table is high, and the storage space required by a terminal is low. However, in the actual use process, the process of sending the lookup table and the random number is easily intercepted by a cryptanalyst, and the random number is difficult to protect by a server and a terminal in a white-box attack environment.
Patent document 3 (publication No. CN108809626A, published 2018, 11/13/h) proposes a white-box SM4 cryptographic algorithm scheme and system, and the main principle is to improve the key expansion algorithm, i.e. the generation process of round keys, to a certain extent, change the key grouping from 128 bits to 192 bits, and reduce the table lookup size by using a block matrix in the white-box scheme and then perform splicing, thereby reducing the number of table lookup. In this method, the number of iterations limits the encryption efficiency to be improved.
The above inventions have some disadvantages through analysis of the above three patent documents. The complex internal codes which can be mutually offset cannot effectively improve the security of the white-box cryptographic algorithm, and the random number introduced in the white-box attack environment is not safe and reliable enough. Moreover, practical problems need to be considered in the design of the scheme, and the balance between space and efficiency is considered as far as possible. In order to meet the high-standard security requirements of various fields, the SM4 white-box encryption algorithm is applied to more working environments, and is very necessary to design a safe and efficient SM4 white-box encryption algorithm capable of resisting white-box attacks.
Disclosure of Invention
Aiming at the above requirements of the SM4 algorithm and overcoming the defects of the prior art, the invention provides a new mode of an improved SM4 cryptographic algorithm with 16 encryption rounds, and simultaneously, an improved design of a white-box algorithm is carried out. The white-box SM4 encryption algorithm here is similar in structure to the white-box SM4 decryption algorithm, and the lookup table structure used is the same, except for the order in which the keys are used.
In the scheme provided by the invention, a new mode is adopted, the mode improves the structure of the round function, namely the iteration process of the encryption algorithm to a certain extent according to the design principle, so that each round of the round function generates two intermediate variables, the encryption process of 32 rounds is reduced to 16 rounds, and the overall calculation efficiency of the algorithm is improved. Two improved designs are carried out on the white-box cryptographic algorithm, firstly, scrambling codes are added before the first round of input and after the last round of output, and external codes are carried out after internal codes are carried out, so as to ensure the integrity and the usability of the white-box cryptographic algorithm, wherein the codes of the scheme are all in a reversible affine transformation mode; secondly, the difference between the ith round of output scrambling codes and the (i + 1) th round of input scrambling codes is a constant, the constants of each round are randomly selected and cannot be obtained from a lookup table, and through calculation, the scrambling codes are added after the last round of output, and the interference constants are offset together, so that the output ciphertext of the improved SM4 white-box cryptographic algorithm is consistent with the output ciphertext of the new mode of the improved SM4 cryptographic algorithm;
the invention has the advantages that:
1. a new mode of the 16-round SM4-128/128 cryptographic algorithm is provided. By improving the iteration process of the standard SM4 algorithm, two intermediate variables are generated in each round of functions, the encryption process of 32 rounds is reduced to 16 rounds, and a new mode of the 16 rounds of SM4-128/128 cryptographic algorithms is obtained.
2. A16-round SM4-128/128 white-box cryptographic algorithm scheme and system are provided. The whole implementation process of the improved SM4 white-box cryptographic implementation method is based on an improved SM4 cryptographic algorithm new mode, adopts a form of combination of affine transformation and a lookup table, and performs external coding while performing internal coding, so that a 16-round SM4-128/128 white-box cryptographic algorithm scheme and system are constructed.
3. The execution efficiency is high, and the occupied space is small. The existing SM4 white-box algorithm has a large number of matrix multiplication operations, and the algorithm operation process of the invention mainly comprises reversible affine transformation and a lookup table, and is relatively faster. The whole algorithm has 16 rounds of iteration processes, and the input and output scrambling code parts before the first round and after the last round are reversible affine transformation from 4 bits to 32 bits; each round is divided into three parts, the first part comprises 2 affine transformations from 32 bits to 32 bits, the second part comprises 4 lookup tables from 8 bits to 32 bits, and the third part comprises 4 affine transformations from 32 bits to 32 bits; therefore, the 16-round SM4-128/128 white-box password implementation method provided by the invention occupies a small space for program execution.
The scheme provided by the invention needs to perform 64 times of table lookup, 48 times of exclusive-or operation and 104 times of affine transformation when the encryption algorithm is executed once. The method has obvious advantages in storage space and execution speed.
4. The safety is high. The main purpose of the white-box cryptographic algorithm design is to prevent an attacker from extracting keys from the execution of the cryptographic algorithm in a white-box attack environment. The invention hides the key information in the lookup table and adds the external code, so that the input code and the output code randomly selected by the lookup table are difficult to break and recover, and the key information can not be easily obtained by an attacker.
The security of the white-box cryptographic algorithm mainly looks at the complexity of separating out a secret key from a lookup table or recovering an input/output code. By calculating the existing white-box safety index: the white box diversity and the white box mixing degree, the 16-round SM4-128/128 white box password implementation method provided by the invention is safe. Through analysis, the scheme provided by the invention can resist BGE attack, and an attacker is difficult to deduce the input/output scrambling codes and the key information from an affine transformation or a lookup table.
Drawings
FIG. 1 is a 16 round SM4-128/128 cryptographic algorithm operation process;
FIG. 2 is a flow chart of the operation of 16 rounds of cryptographic algorithms SM4-128/128 encryption round functions;
FIG. 3 is an overall structure of a modified SM4 white-box cryptographic algorithm;
fig. 4 is a first part of a modified SM4 white-box cryptographic algorithm;
fig. 5 is a second part of a modified SM4 white-box cryptographic algorithm;
fig. 6 is a third part of the modified SM4 white-box cryptographic algorithm.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings, without in any way limiting the scope of the invention.
The scheme provided by the invention is improved based on an SM4 cryptographic algorithm. The improved SM4 cryptographic algorithm is still an iterative cryptographic algorithm and consists of an encryption and decryption algorithm and a key expansion algorithm, the plaintext length and the key length are both 128 bits, and the initial plaintext is subjected to 16 iterative operations and 1 reverse order transformation R to calculate a 128-bit ciphertext.
Step one, as shown in fig. two, two intermediate variables are generated for each round of round function in the iterative operation process, namely
Wherein,is a bit XOR symbol, Xj(j 0, 1.. times.32) are 32-bit values, which are intermediate variables generated by iterative operation of 128-bit plain texts;
(1) synthesis of the substitution T:the method is reversible transformation, and is formed by compounding nonlinear transformation tau and linear transformation L, namely T (·) ═ L (tau (·));
(2) the nonlinear transformation τ is composed of 4 parallel S-boxes, with the input beingOutput is asThen (b)0，b1，b2，b3)＝τ(A)＝(Sbox(a0)，Sbox(a1)，Sbox(a2)，Sbox(a3) S-boxes are consistent with the standard SM4 algorithm;
(3) the output of the non-linear transformation τ is the input of the linear transformation L, given as inputOutput is asThen
(4)Generated by the key expansion algorithm in the standard SM4 cryptographic algorithm, in the new mode, 16 round keys (rk) are used0，rk1，...，rk15) And (6) performing operation.
Step two, as shown in the figure one, after 16 rounds of iterative operation, the ciphertext is output through reverse order transformation, namely
(Y0，Y1，Y2，Y3)＝R(X32，X33，X34，X35)＝(X35，X34，X33，X32)
Wherein, the reverse order transformation R is defined as: r (A)0，A1，A2，A3)＝(A3，A2，A1，A0)，
The generation of the sub-keys of the scheme depends on the key expansion operation of the standard SM4 cryptographic algorithm, the cryptographic algorithm in the new mode of the improved SM4 cryptographic algorithm has 16 rounds of iterative operations, so that 16 sub-keys are needed to be operated, and the key expansion operation of the standard SM4 cryptographic algorithm generates 1 sub-key in one round, so that 16 rounds of key expansion operation are needed. The encryption key isFor 128 bits, round keysIs 32 bits.
The generation steps of the round key are as follows:
wherein FK ═ FK (FK)0，FK1，FK2，FK3) Being a system parameter of the standard SM4 cryptographic algorithm, CK ═ (CK)0，CK1，…，CK15) Is a fixed parameter of the standard SM4 cryptographic algorithm, where FKi(i＝0，...，3)、CKi(i ═ 0.,. 15) is 32 bits. The T 'transform is substantially the same as the T transform in the round function in the encryption algorithm, with the difference in changing the linear transform L to L':
the decryption transformation and the encryption transformation are the same in structure when decrypting, and only the use sequence of the round keys is opposite. The use sequence of the round key in encryption is (rk)0，rk1，...，rk15) The use sequence of round keys in decryption is (rk)15，rk30，...，rk0)。
A16-round SM4-128/128 white-box password implementation method is white-box based on the new mode of the improved SM4 password algorithm. The SM4 white-box encryption algorithm and the SM4 white-box decryption algorithm still have the same structure, and the used lookup table has the same structure, except for the sequence of using the keys, which is not described in detail for the decryption algorithm process.
The whole implementation process of the SM4 white-box cryptographic algorithm provided by the invention can be converted into the form of calculating affine transformation and a lookup table to obtain 128-bit data (X)0，X1，X2，X3) As plain text input, after external scrambling coding and 16 rounds of transformation, the plain text is subjected to reverse order transformation, and finally 128-bit cipher text (Y) is output0，Y1，Y2，Y3) (ii) a In the 16-wheel transformation, the ith (i is more than or equal to 0 and less than or equal to 15) wheel transformation is provided with 4 32-bit numerical values X'2i，X′2i+1，X′2i+2，X′2i+3As input, 2 32-bit numerical values X 'are output'2i+4，X′2i+5。
As shown in fig. 3, the modified SM4 white-box cipher algorithm adds scrambling codes both before the first round and after the last round. For an incoming 128-bit plaintext block (X)0，X1，X2，X3) All using 32 th order invertible matrix PiMixing to obtain X'i＝Pi·Xi(i-0, 1, 2, 3) as the input of the round function, and the output X 'is generated through 16 rounds of conversion'32，X′33，X′34，X′35Using a 32 th order invertible matrix PiCarry out scrambling coding, namelyThen carrying out reverse order transformation R once to obtain X35，X34，X33，X32I.e. ciphertext blocks. The codes of the scheme are all reversible affine transformation forms, and the mathematical expression is as follows:wherein P represents an affine transformation,/[ P ]]Is an invertible matrix, is the linear part of P, cp]Is in the form of a column vector and is a constant term for P. And P isi(i ═ 0, 1, 2, 3) to X 'of the first partial pair of the front four wheels'iThe input scrambling of (i-0, 1, 2, 3) is cancelled,and third portion of the last four wheels to X'iThe output scrambling of (i 32, 33, 34, 35) and the accumulated 16 round constants cancel out.
In the scheme 16 provided by the invention, each round function in round transformation is divided into three parts, affine transformation is used as input scrambling code and output scrambling code to hide each internal state of SM4 algorithm, a lookup table is used to realize transformation function T, and key information contained in T is hidden by encoding input and output values of the lookup table. No ith wheel conversion input 4 32-bit numerical values X'2i，X′2i+1，X′2i+2，X′2i+3Outputs a 32-bit value X'2i+4，X′2i+5(ii) a The process of the scheme is divided into three parts.
As shown in fig. 4, the first part: calculating X, wherein the known scheme adopts a network coding mode and firstly inputs X 'to the ith wheel'2i+2，X′2i+3And performing preprocessing, eliminating a part of output scrambling codes in the previous round of transformation, and then performing coding. The first calculation process can be expressed as: namely, it isA hereini+jIs a 32 × 32 invertible matrix over GF (2), ai+jIs a constant of 32 bits; ei＝diag(E′i0，E′i1，E′i2，E′i3)，E′i0、E′i1、E′i2、E′i3An 8-bit to 8-bit reversible affine transformation, all over GF (2); due to Pi+jAnd EiAre all randomly selected and kept secret, only by storingThereby translating into a 32-bit to 32-bit compound affine transformation.
As shown in fig. 5, the second part: and coding the original T transformation to form a lookup table, and hiding the secret key in the lookup table. In each round of the algorithm, the keys are combined with the S-boxes, i.e. the round keys are scattered and hidden in the look-up table.
Wherein,l represents the linear transformation of the T transform in the SM4 algorithm, as two 32 × 32 matrices over GF (2); ei0，Ei1，Ei2，Ei3An 8-bit to 8-bit reversible affine transform over GF (2) as input code for the look-up table; q2iIs a 32-bit to 32-bit reversible affine transform that is encoded as the output of a look-up table.
As shown in fig. 6, the third part: calculating X'2i+4，X′2i+5。Namely, it isNamely, it isThe scheme adopts a networked coding mode, firstly eliminates a part of output scrambling codes in the previous round of transformation, and then carries out calculation coding.
The difference between the output scrambling code of the ith round and the input scrambling code of the (i + 1) th round in the improved SM4 white-box cryptographic algorithm is a constant which is randomly selected and cannot be obtained from a lookup table, and the scrambling code is added after the last round of output, so that the constants can be selectively offset, and the output ciphertext of the improved SM4 white-box cryptographic algorithm and the output ciphertext of the new mode of the improved SM4 cryptographic algorithm have two possibilities of sameness.
Claims (7)
1. A16-round SM4-128/128 white-box cipher realization method is characterized in that a new improved SM4 cipher algorithm mode with 16 encryption rounds is described, the mode improves the structure of a round function, namely an iterative process of an encryption algorithm, according to a design principle, inputs 128 bits of plaintext m, and takes 32 bits as a packet length, namely the packet lengthPlaintext m is subjected to 16 rounds of iterative operation and 1 time of inverse operationSequence transformation to obtain 128-bit cipher text
2. The improved SM4 new mode of cryptographic algorithm of claim 1, wherein two intermediate variables are generated per round of function during the iterative operation, namely:
wherein,is a bit XOR symbol, Xj(j 0, 1.. times.32) are 32-bit values, which are intermediate variables generated by iterative operation of 128-bit plain texts;
(1) synthetic replacementThe method is reversible transformation, and is formed by compounding nonlinear transformation tau and linear transformation L, namely T (·) ═ L (tau (·));
(2) the nonlinear transformation τ is composed of 4 parallel S-boxes, with the input beingOutput is asThen (b)0，b1，b2，b3)＝τ(A)＝(Sbox(a0)，Sbox(a1)，Sbox(a2)，Sbox(a3))；
(3) The output of the non-linear transformation τ is the input of the linear transformation L, given as inputOutput is asThen
(4)Generated by a key expansion algorithm in a standard SM4 cryptographic algorithm, and only the first 16 round keys (rk) are used in the new mode0，rk1，...，rk15) And (6) performing operation.
3. The improved SM4 new mode of cipher algorithm according to claim 1, wherein the idea is not only applicable to the case that the block length/key length is 128 bits/128 bits, but also to the case that the plaintext length and key length are larger, such as 128 bits/256 bits and 256 bits/256 bits.
4. A16-round SM4-128/128 white-box cipher realization method is characterized in that an improved SM4 white-box cipher realization method is provided, and the whole realization process can be converted into a form of calculating affine transformation and a lookup table to obtain 128-bit data (X)0，X1，X2，X3) As plain text input, after external scrambling coding and 16 rounds of transformation, the plain text is subjected to reverse order transformation, and finally 128-bit cipher text (Y) is output0，Y1，Y2，Y3) (ii) a In the 16-wheel transformation, the ith (i is more than or equal to 0 and less than or equal to 15) wheel transformation is provided with 4 32-bit numerical values X'2i，X′2i+1，X′2i+2，X′2i+3As input, 2 32-ratio outputsSpecial numerical value X'2i+4，X′2i+5。
5. The improved SM4 white-box cipher implementation method of claim 4, wherein scrambling codes are added before and after round-robin, i.e. before the first round of input and after the last round of output, and outer coding is performed while inner coding is performed to ensure integrity and usability of the white-box algorithm; the codes of the scheme are all reversible affine transformation forms, and the mathematical expression is as follows:wherein P represents an affine transformation,/[ P ]]Is an invertible matrix, is the linear part of P, cp]Is in the form of a column vector and is a constant term for P. Therefore, can be represented by X'i＝Pi·Xi(i＝0，1，2，3)；。
6. The improved SM4 white-box cipher implementation method of claim 4, wherein the ith round of transformation inputs 4 32-bit numerical values X'2i，X′2i+1，X′2i+2，X′2i+3Outputs 2 32-bit values X'2i+4，X′2i+5(ii) a The process of the scheme is divided into three parts.
Wherein the first part: calculate X is Ei＝diag(E′i0，E′i1，E′i2，E′13)，E′i0、E′i1、E′i2、E′i3All 8-bit to 8-bit reversible copies over GF (2)Performing emission transformation; in the scheme, a networked coding mode is adopted, and the input X 'to the ith wheel is firstly input'2i+2，X′2i+3Decoding processing is carried out, a part of output scrambling codes in the previous round of transformation is eliminated, and then the output scrambling codes are carried out;
a second part:
wherein,
and coding the original T transformation to form a lookup table, and hiding the secret key in the lookup table. In each round of the algorithm, the keys are combined with the S-boxes, i.e. the round keys are scattered and hidden in the look-up table.
And a third part: calculating X'2i+4，X′2i+5。Namely, it isNamely, it isThe scheme adopts a networked coding mode, firstly eliminates a part of output scrambling codes in the previous round of transformation, and then carries out calculation coding.
7. The method for implementing the improved SM4 white-box cipher as claimed in claim 4, wherein the i-th round output scrambling code and the i + 1-th round input scrambling code differ by a constant which is randomly selected and not obtained from the lookup table, and the scrambling code is added after the last round of output, and the constants can be selectively cancelled, so that there are two possibilities that the output cipher text of the improved SM4 white-box cipher algorithm is identical to the output cipher text of the new mode of the improved SM4 cipher algorithm.
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