CN113938273B - Symmetric encryption method and system capable of resisting quantitative parallel computing attack - Google Patents

Symmetric encryption method and system capable of resisting quantitative parallel computing attack Download PDF

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CN113938273B
CN113938273B CN202111164387.0A CN202111164387A CN113938273B CN 113938273 B CN113938273 B CN 113938273B CN 202111164387 A CN202111164387 A CN 202111164387A CN 113938273 B CN113938273 B CN 113938273B
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byte
mod
box
coding
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CN113938273A (en
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王杰林
廖亦凡
高金定
周浪
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Hunan Yaosheng Communication Technology Co ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H04L63/0435—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply symmetric encryption, i.e. same key used for encryption and decryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/50—Reducing energy consumption in communication networks in wire-line communication networks, e.g. low power modes or reduced link rate

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  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • General Engineering & Computer Science (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)

Abstract

The invention discloses a symmetrical encryption method and a system capable of resisting an attack of quantitative parallel computing, wherein the method comprises the following steps: the S box array is generated by exclusive OR logic operation of the password sequence and the two-dimensional table, and has extremely high safety intensity; in addition, the round function which jointly generates the nonlinear weighting coefficient through the S box array and the password sequence is applied to the process of coding the weighted probability model, and is independent of the sequence data to be encrypted, the linear correlation and algebraic relation of the data to be encrypted can not be used as reference factors for cracking by the method, so that high-strength data encryption is realized; before coding the sequence X to be coded, pre-coding u random sequences Q, so that the security of data encryption is improved; and the cipher text is obtained by exclusive OR operation of bytes in the coding result and bytes in the S box, and the S box is dynamically generated by the password sequence and the two-dimensional table during decoding, so that the safety of the coding result is improved. In conclusion, the method and the device realize good lossless compression effect, have high-strength data encryption, and can resist quantum parallel computing attack.

Description

Symmetric encryption method and system capable of resisting quantitative parallel computing attack
Technical Field
The invention relates to the technical field of data coding, in particular to a symmetric encryption method and a system capable of resisting an attack of quantitative parallel computing.
Background
Lossless compression algorithms (entropy coding) have been widely used in the technical fields of communication, storage, etc., and common lossless compression algorithms include run-length coding, dictionary coding, huffman coding, arithmetic coding (section coding), etc. The symmetric encryption algorithm is used as a core tool of information security, and is also widely applied to the fields of communication, transaction, payment, data desensitization and the like, and common symmetric encryption algorithms include DES (Data Encryption Standard ), AES (Advanced Encryption Standard, advanced encryption standard), blowfish (a symmetric encryption block algorithm) and the like.
In order to realize high-strength encryption symmetric encryption and have good compression effect, a coding scheme of 'Jielin code' is proposed at present, and the scheme realizes high-strength encryption symmetric encryption and has lossless compression effect. But this approach still suffers from deficiencies in terms of resistance to quantum parallel computing attacks (quantum parallel computation).
Disclosure of Invention
The present invention aims to at least solve the technical problems existing in the prior art. Therefore, the invention provides a symmetric encryption method and a system capable of resisting quantum parallel computing attack, which can realize good lossless compression effect, have high-strength data encryption and can resist quantum parallel computing attack.
The first aspect of the present invention provides a symmetric encryption method capable of resisting an attack of an massively parallel computing, which is applied to an encoding end, and includes the following steps:
step S101, a password sequence B with a sequence length L, a sequence X to be coded with a sequence length n and a random sequence Q with a sequence length u are obtained;
step S103, calculating an S box array:
step S1031, randomly generating T 2 Storing the non-repeated integer values into a two-dimensional table of T, and entering step S1033 when n+u is more than or equal to L;
step S1033, obtaining f (j) from the two-dimensional table; wherein j represents a statistical variable and an initial value of j is 0, and f (j) represents a j-th byte in the two-dimensional table;
step S1035, when j<T 2 In the time-course of which the first and second contact surfaces,and j=j+1, and jump to step S1033 until j is equal to or greater than T 2 When it entersStep S105; wherein S [ j ]]Representing the j-th byte in the S-box array, said +.>Representing exclusive or logic operations;
step S105, connecting the random sequence Q and the sequence X to be coded in series to obtain a binary sequence Z;
step S107, encoding the binary sequence Z based on a weighted probability model and the S-box array:
step S1071, obtaining the ith byte X in the binary sequence Z i And the ith mod L byte B (i mod L) and the L- (ith mod L) byte B (L- (i mod L)) in the cryptographic sequence B, i representing a statistical variable and an initial value of i being 0;
step S1073, calculate The X is i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to xT+y;
step S1077, calculating a nonlinear round function r (i); wherein,s represents an integer of 6 or more;
step S1079, coding the binary sequence Z based on the weighted probability model and the nonlinear round function r (i) to obtain a coding result;
step S109, performing exclusive OR logic operation on the coding result and the S box array to obtain ciphertext;
step S110, the ciphertext is sent to a decoding end.
In a second aspect of the present invention, there is provided a symmetric encryption system capable of combating an massively parallel computing attack, comprising:
the data acquisition unit is used for acquiring a password sequence B with a sequence length L, a sequence X to be coded with a sequence length n and a random sequence Q with a sequence length u;
an S-box calculation unit for calculating an S-box array by:
step S1031, randomly generating T 2 Storing the non-repeated integer values into a two-dimensional table of T, and entering step S1033 when n+u is more than or equal to L;
step S1033, obtaining f (j) from the two-dimensional table; wherein j represents a statistical variable and an initial value of j is 0, and f (j) represents a j-th byte in the two-dimensional table;
step S1035, when j<T 2 In the time-course of which the first and second contact surfaces,and j=j+1, and jump to step S1033 until j is equal to or greater than T 2 At this time, the process advances to step S105; wherein S [ j ]]Representing the j-th byte in the S-box array, said +.>Representing exclusive or logic operations;
the data serial unit is used for connecting the random sequence Q and the sequence X to be coded in series to obtain a binary sequence Z;
a data encoding unit for encoding the binary sequence Z based on a weighted probability model and the S-box array by:
step S1071, obtaining the ith byte X in the binary sequence Z i And the ith mod L byte B (i mod L) and the L- (ith mod L) byte B (L- (i mod L)) in the cryptographic sequence B, i representing a statistical variable and an initial value of i being 0;
step S1073, calculate The X is i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to xT+y;
step S1077, calculating a nonlinear round function r (i); wherein,
s represents an integer of 6 or more;
the ciphertext generating unit is used for carrying out exclusive OR logic operation on the encoding result and the S box array to obtain ciphertext;
and the ciphertext sending unit is used for sending the ciphertext to the decoding end.
In a third aspect of the method, an electronic device is provided comprising at least one control processor and a memory for communicatively coupling with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the symmetric encryption method described above that is resistant to the quantitative parallel computing attack.
In a fourth aspect of the method, a computer readable storage medium is provided: the computer-readable storage medium stores computer-executable instructions for causing a computer to perform the symmetric encryption method described above that is resistant to quantitative parallel computing attacks.
In the symmetric encryption method capable of resisting the attack of the parallel computation of the quantity, the random sequence Q and the sequence X to be encoded are obtained in the step S105, so that the sequence X to be encoded is encoded, and simultaneously u random sequences Q are required to be encoded, the sequence X is unknown because the random sequence Q is unknown, the length of the encoded sequence is increased, and L n+u There are 256 3(n+u) A possible value. The byte in the coding result obtained in the step S1079 and the byte in the S box are exclusive-or operated to obtain ciphertext, when in decoding, the S box is dynamically generated by a password sequence and a two-dimensional table, and the password sequence is unknown, so that the S box and (x, y) cannot be usedThe result of the encoding is unknown. In step S1035, the S box array is generated by performing exclusive-or logic operation on the password sequence and the two-dimensional table, and has extremely high security intensity; in step S1035, the round function for generating the nonlinear weighting coefficient by the S-box array and the cipher sequence is applied to the process of weighted probability model coding, and is independent of the sequence data to be encrypted, so that the linear correlation and algebraic relation of the data to be encrypted cannot be used as the reference factors for cracking in the method, and high-strength data encryption is realized. In summary, the symmetric encryption method capable of resisting the quantum parallel computing attack provided by the embodiment achieves a good lossless compression effect, has high-strength data encryption, and can also resist the quantum parallel computing attack.
It is to be understood that the advantages of the second to fourth aspects compared with the related art are the same as those of the first aspect compared with the related art, and reference may be made to the related description in the first aspect, which is not repeated herein.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic diagram of the operation process of the code 010 of the weighted probability model provided by the invention;
FIG. 2 is a flow chart of a symmetric encryption method for resisting an attack of an quantitative parallel computing according to an embodiment of the present invention;
fig. 3 is a schematic flowchart of step S109 according to an embodiment of the present invention;
fig. 4 is a schematic flowchart of step S1079 according to an embodiment of the present invention;
FIG. 5 is a flowchart of a symmetric encryption method for resisting an attack of an quantum parallel computing according to another embodiment of the present invention;
FIG. 6 is a schematic diagram of a two-dimensional table according to one embodiment of the present invention;
fig. 7 is a schematic structural diagram of a symmetric encryption system capable of resisting an attack of an quantum parallel computing according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
Before describing the embodiments of the present application, the principles of the present application are described, and mainly include weighted probability model coding, lossless decoding proof of weighted probability model coding, and simple description of weighted probability model information entropy. It should be noted that the general knowledge of "jerry code" is used herein, and thus only the principle related to the inventive concept will be briefly described:
first, weighted probability model coding;
signaling source sequence x= (X) 1 ,X2,…,X i ,…,X n ) Is a discrete sequence of a finite number of values or a few possible values, X i E a= {0,1,2, …, k }. There is then a probability space for everything in a:
since the random process must be transferred to a certain symbol, at any time there is:
thus, arbitrary symbol X i The distribution function of (2) is:
wherein, p (0) is less than or equal to F (x) is less than or equal to 1, and s is less than or equal to A.
Definition 1: let discrete random variable X, X epsilonA= {0,1, …, k }, P { x=a } = P (a) (a e a), the weighted probability mass function isp (a) is a probability mass function, 0.ltoreq.p (a). Ltoreq.1, r is a weight coefficient (also called weighting coefficient according to the relevant scheme), and:
F(a)＝∑ i≤a p(i) (2)
if F (a, r) satisfies F (a, r) =f (a), F (a, r) is referred to as a weighted cumulative distribution function, abbreviated as a weighted distribution function. Obviously, the weighted probability sum of all symbols is
Let the discrete source sequence x= (X) 1 ,X 2 ,…,X n )，X i E A, and let F (X i -1)＝F(X i )-p(X i ) The weighted distribution function of the sequence X is denoted as F (X, r). When n=1:
F(X,r)＝rF(X 1 -1)+rp(X 1 )
when n=2:
F(X,r)＝rF(X 1 -1)+r 2 F(X 2 -1)p(X 1 )+r 2 p(X 1 )p(X 2 )
when n=3:
F(X,r)＝rF(X 1 -1)+r 2 F(X 2 -1)p(X 1 )+r 3 F(X 3 -1)p(X 1 )p(X 2 )+r 3 p(X 1 )p(X 2 )p(X 3 )
order theAnalogize to obtain:
the set of weighted distribution functions satisfying equation (3) is defined as a weighted probability model, abbreviated as weighted model, denoted as { F (X, r) }.If X i E a= {0,1}, then { F (X, r) } is called a binary weighted model. And (3) making:
H n ＝F(X,r) (4)
L n ＝H n -R n (6)
wherein X is i E a, n=1, 2, …. When r=1:
h is obtainable from (4), (5) and (6) n =f (X, 1), i.e., section coding (arithmetic coding) is a lossless coding method based on a weighted distribution function when r=1.
Due to X i Must take the value of A, so p (X i )>0. Obviously, the interval columns of (4), (5) and (6) [ L ] i ，H i ) Is the variable X of the source sequence X at time i (i=0, 1,2, …, n) i Corresponding interval subscripts, R i ＝H i -L i Is the length of the interval. R is set to i=0 according to formulas (4), (5) and (6) 0 ＝H 0 ＝1，L 0 =0, so i=1, 2, …, n-time weighted probability model coding operation is:
it should be noted that the formula (8) includes the above three formulas, and the weighted probability model coding operation is performed on the source sequence X by the formula (8), L n Is a real number and is the result of weighted probability model coding. L (L) n Binary sequences are obtained by means of binary conversion. Taking binary sequence as an example, let 0<r.ltoreq.1 and 3 symbols of the sequence X starting from the i+1 position are 0,1,0. The coding operation of the weighted probability model according to equation (8) is shown in fig. 1.
According to FIG. 1, if H i+3 >H i+1 Cause section [ H i+1 ，H i+3 )∈[H i+1 ，H i+1 +R i+1 ) And [ H ] i+1 ,H i R i ) Corresponding to symbol 1, the (i+1) th symbol 0 may be incorrectly decoded as symbol 1. If H i+3 ≤H i+1 Then [ L ] i+3 ,H i+3 )∈[L i+1 ，H i+1 ). As in [ L ] of FIG. 1 i+1 ，H i+1 ) Corresponds uniquely to symbol 0, so that symbol 0 at the i+1 position is L i+3 Correctly decoded, and symbols 1 and 0 at positions i+2 and i+3 can also be correctly decoded. When 0 is<When r is less than or equal to 1, [ L ] is present at any time i+1 ,H i+1 )∈[L i ,H i ) Can be decoded losslessly.
Lossless decoding evidence of second and weighted probability model coding;
theorem 2, weighted model satisfies:
1)L n <H n ∧L n <H n-1 ∧...∧L n <H 1 through L n The sequence Q can be completely restored;
2)lim n→∞ (H n -L n ) =0, i.e. convergence;
3)lim n→∞ H n ＝L n i.e. uniqueness.
Proof 1): according to formula (8), L n As a monotonic non-decreasing function if and only if L n ∈[L n ,H n )∧L n ∈[L n-1 ,H n-1 )∧...∧L n ∈[L 1 ,H 1 ) When in use, cause [ L ] i ,H i ) (i=1, 2, …, n) and variable X i Is the only mapping relation, so when L n ∈[L i ,H i ) (i=1, 2, …, n) gives a unique symbol X i Thereby obtaining the source sequence X, L n <H n ∧L n <H n-1 ∧...∧L n <H 1 。
Proof 2): according to formula (5), 0<r is less than or equal to 1 and 0 is less than or equal to p (X) i ) Is less than or equal to 1, when the source sequence X= { X i P (a) =1, r when r=1 and =a } n ＝1，L n →F(a,r)＝H n Thus H n -L n And 0. When 0 is<p(X i )<1 and 0<r is less than or equal to 1 and 0<rp(X i )<1，R n 0, due to H n -L n ＝R n Therefore H n -L n And 0. Therefore, lim at n → infinity l→∞ (H l -L l )＝lim l→∞ R l =0, the weighted probability model is convergent.
Proof 3): { L n The expression "is a strictly monotonically non-decreasing and upper-bound array, defined by monotonically defined conditions, provided with lim n→∞ L n =ζ, and ζ+.gtoreq.L n . Because lim n→∞ (H n -L n ) =0, so lim n→∞ L n ＝lim n→∞ H n ζ=l, so ζ=l n ，lim n→∞ H n ＝ξ＝ n And L is n Is unique.
Thirdly, weighting a probability model information entropy;
let the discrete memory-free source sequence X= (X) 1 ，X 2 ，…，X n )(X i E a, a= {0,1,2, …, k }), when r=1,defined by shannon information entropy, the entropy of X is:
when r.noteq.1, define a probabilityRandom variable X of (2) i The self information amount of (a) is:
I(X i )＝-log k+1 p(X i ) (10)
set { X } i In =a } (i=1, 2, …, n, a e a) there is c a And a. When the value of r is determined, the total information amount of the source sequence X is:
the information amount per symbol is then averaged:
definition 3: let H (X, r) be:
according to definition 3, when the value of r is determined, the binary length encoded by the weighted probability model is nH (X, r) in bits (bit).
In the related scheme, the coding scheme of the Jielin code realizes high-strength encryption symmetric encryption and has lossless compression effect. However, this scheme still has a disadvantage in resisting quantum parallel computing attack (quantum parallel computation), and there is room for improvement.
An example section;
referring to fig. 2 to 6, an embodiment of the present invention provides a symmetric encryption method capable of resisting an attack of an quantum parallel computing, which is applied to an encoding end, and the encoding end is not limited in this embodiment, and may be any terminal having a computing function, for example, a computer, and the encryption method includes the following steps:
step S101, a password sequence B with a sequence length L, a sequence X to be coded with a sequence length n and a random sequence Q with a sequence length u are obtained.
Step S103, calculating an S box array:
step S1031, randomly generating T 2 And storing the non-repeated integer values into a two-dimensional table of T, and when n+u is more than or equal to L, entering step S1033.
Step S1033, obtaining f (j) from the two-dimensional table; where j represents a statistical variable and the initial value of j is 0, and f (j) represents the j-th byte in the two-dimensional table.
Step S1035, when j<T 2 In the time-course of which the first and second contact surfaces,and j=j+1, and jump to step S1033 until j is equal to or greater than T 2 At this time, the process advances to step S105; wherein S [ j ]]Represents the j-th byte in the S-box array, < >>Representing an exclusive or logical operation.
Step S105, the random sequence Q and the sequence X to be coded are connected in series to obtain a binary sequence Z.
Step S107, a binary sequence Z is encoded based on a weighted probability model and an S-box array:
step S1071, obtaining the ith byte X in the binary sequence Z i And the ith mod L byte B (i mod L) and the L- (i mod L) th byte B (L- (i mod L)) in the cipher sequence B, i representing a statistical variable and an initial value of i being 0;
step S1073, calculate X i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to xT+y;
step S1077, calculating a nonlinear round function r (i); wherein,
s represents an integer of 6 or more;
step S1079, the binary sequence Z is encoded based on the weighted probability model and the nonlinear round function r (i), and an encoding result is obtained.
And step 109, performing exclusive OR logic operation on the coding result and the S box array to obtain ciphertext.
Step S110, the ciphertext is sent to a decoding end.
The following explanation and security analysis of the principles related to the above steps S101 to S109 are performed by specific examples:
in step S101, the cipher sequence B mainly plays a role of calculating S box and calculating nonlinear round function in the subsequent step, the sequence to be encoded X is also called plaintext sequence, and the random sequence Q is mainly encrypted in combination with the sequence to be encoded X in the subsequent step to increase the security of data encryption.
According to the jerry code, the weight coefficient r of the sequence X to be coded can be obtained by the above formula (8), and if r does not change with i (i=1, 2, …, n), r is called a static weight coefficient; if r varies with i, then r is referred to as the dynamic weighting factor, denoted r (i). The weighted probability model can be coded lossless when 0<r.ltoreq.1 according to the above-mentioned theorem 2, and can be coded when r.fwdarw.1 according to the above-mentioned definition 3, -log r.fwdarw.0, then H (X, r). Fwdarw.H (X). Obviously, based on the dynamic weighting coefficient r (i), the weighted probability model coding method can reach information entropy when 0<r (i) is less than or equal to 1 and r (i) to 1. Since r (i) is related to the sequence number i of the current symbol and to the encoding operation of each symbol, the definition of the key is complied with. Since the dynamic weighting coefficients r (i) are suitable for constructing nonlinear round functions, r (i) is defined as a weighted probability model symmetric encryption key. The weighted distribution function based on the dynamic weight coefficient r (i) is:
because of 0<r(i)<1 and 0.ltoreq.p (X) j ) F (X, r) which is not less than 0 and not more than 1 can be obtained easily<1, obtaining unique real number L after coding n ，L n Can be converted into a sequence Y of m bytes. Then:
the common DES, AES, blowfish symmetric encryption algorithm uses nonlinear byte substitution and round functions (chaotic map) to eliminate the linear correlation, commonly referred to as S-boxes. Unlike the S box provided by the related scheme, the present embodiment constructs the S box in steps S1031 to S1035:
the cipher sequence input in this embodiment is L bytes, where let L be greater than or equal to 6, to improve security, n is the number of bytes of the sequence X to be encoded, and B (j) is the j (j=1, 2, …, L) byte value of the cipher sequence, i.e., B j =0, 1, …,255. When n is<When L, B (j) is calculated by the following formula, each byte in the cipher sequence can effectively act on the weighting coefficient, so that l=n exists.
In step S1031 of this embodiment, T is randomly generated 2 (let t=16 here, ensure a balance of computational complexity and high security) the non-repeated values of 0 to 255 are stored in a two-dimensional table of T, as shown in fig. 6, it being noted that the two-dimensional table of fig. 6 is represented by 16-ary integer. In the present embodiment, T (t=1, 2, …, T 2 ) The calculation method of the byte value S (t) comprises the following steps:
f (t) is the value of the t-th byte in the two-dimensional table. Obviously, if only the two-dimensional table is known and the code sequence B is unknown, then S (t) is not known and only the correct code sequence is used to derive the correct coordinates and S box.
The values in the S-box after the calculation of equation (15) may have the same values, and the byte substitution of the AES-like cannot be achieved. Let the byte value of coordinates (x, y) in the S box be g (x, y), the calculation formula of x and y is:
after concatenating the random sequence Q and the sequence X to be encoded and obtaining the binary sequence Z in step S105, X in formula (16) i An ith byte value for sequence Z; this isPlease note that the distinction is "X i "means.
In step S1077, the nonlinear round function of r (i) is defined as:
wherein,is a subscript of the cryptographic sequence. The actual value of s is equal to or greater than 6, and s=7 can be selected according to the operation precision of the computer. The larger s, the closer r (i) is to 1, so the weighted probability model coding method can approach the information entropy, because r (i) →1, -log r→0, and H (X, r) →h (X). Because r (i) is the ith symbol X i R in coding i And weight coefficients of iterative operation, namely:
L i ＝L i-1 +R i-1 r(i)F(X i -1) (18)
it should be noted that equation (18) includes two equations, the weight coefficient round function available from (18) is calculated by R i And L i And iterating, wherein the iteration times are n. Formulas (16) and (17) are such that r (i), r (i+1) and r (i-1) do not have a linear relationship becauseAnd g (x, y) e {0,1, …,255}, so ∈ -> When s determines that the set R has 65536 real values, the probability that R (i) takes any real value in the set R is +.>When X and Y are known, L is known because Y is known n Is known, so L 1 ，L 2 ，…，L n-1 There is a trend that is less than L n And is close to L n Is a value of (2). There are 65536 possible values for r (1). p (X) 1 ) And F (X) 1 -1) is known and R 0 ＝1，L 0 =0, from formula (18) L 1 Is related to r (1) only, so L 1 There are 65536 possible values, find out that is less than L n And is close to L n Is a value of (2). Also due to X 2 Known then p (X 2 ) And F (X) 2 -1) is known, then L 1 And L 2 At the same time satisfy less than L n And is close to L n Further reduction in the number of possible values of (c) makes it easy to approximate or calculate the code sequence. If X 1 Unknown, since p (0), p (1), …, p (255) are known, F (X) 1 -1) there are 256 possible values (when X 1 F (-1) =0 when=0. Since there are 65536 possible values for r (1), r (1) and F (X) 1 -1) are mutually independent variables, so L 1 There are 256 3 A possible value. If X 1 And X 2 Unknown, F (X) 2 -1) there are 256 possible values and r (2) there are 65536 possible values. Due to L 2 ＝L 1 +R 0 r(1)p(X 1 )r(2)F(X 2 -1), so only r (1), p (X) need to be considered 1 ) R (2) and F (X) 2 -1) four mutually independent variables, L being obtainable 2 There are 256 6 A possible value. But when Y is known, by L 1 And L 2 Whether or not "less than L" is satisfied n And is close to L n "remove invalid values". If Y is unknown, L 1 And L 2 Loss of critical conditions "less than L n And is close to L n ". Analogize to L n There are 256 3n A possible value. The probability of attack is analyzed, and the weighted model coding has lossless compression effect, so that the probability of each symbol of the sequence X is not variable.
Compared with the existing Jielin code scheme, the symmetric encryption method capable of resisting the quantitative parallel computing attack has the following beneficial effects:
since step S105 will followThe machine sequence Q and the sequence X to be coded are connected in series to obtain a binary sequence Z. Before coding the plaintext sequence (i.e. the sequence X to be coded), u random bytes are coded in advance, and because the random bytes are unknown, X is unknown, the length of the coded sequence is increased, L n+u There are 256 3(n+u) A possible value. The cipher text is obtained by exclusive-or operation of the bytes in the encoding result obtained in step S1079 and the bytes in the S box, and the S box is dynamically generated from the cipher sequence and the two-dimensional table during decoding, and the S box sum (, y) is unknown because the cipher is unknown, so the encoding result is unknown. In step S1035, the calculation method of each byte in the S box is as follows: according to the security analysis, the S box array is generated by exclusive OR logic operation of the password sequence and the two-dimensional table, so that the S box array has extremely high security intensity; in step S1035, the round function for generating the nonlinear weighting coefficient by the S-box array and the cipher sequence is applied to the process of weighted probability model coding, and is independent of the sequence data to be encrypted, so that the linear correlation and algebraic relation of the data to be encrypted cannot be used as the reference factors for cracking in the method of the embodiment, and high-strength data encryption is realized.
In summary, the symmetric encryption method capable of resisting the quantum parallel computing attack provided by the embodiment achieves a good lossless compression effect, has high-strength data encryption, and can also resist the quantum parallel computing attack. The method is simple and easy to realize by hardware, can be widely applied to communication, storage and security systems, for example, a part of file data with higher security needs to be transmitted between an encoding end and a decoding end, so that the method can be used for encryption, and the encrypted ciphertext has lossless compression effect, high-strength data encryption and can resist quantum parallel computing attack. However, it should be noted that the method of the present embodiment does not limit the use scenario of the sequence to be encoded and the ciphertext, and the above examples should not limit the protection scope of the present invention.
Based on the above embodiment, step S109 specifically includes the steps of:
step S1091, converting the encoding result into a sequence Y with a sequence length of m.
Step S1093, obtaining the ith byte value Y in the sequence Y i 。
Step S1095, when i<In the m-time period, the total number of the components,and i=i+1, and jump to step S1093 until ciphertext is obtained when i is greater than or equal to m.
The coding result is converted into a sequence Y, and the byte in the sequence Y and the byte in the S box are exclusive-or operated to obtain the ciphertext, so that the compression ratio is not influenced because the sequence Y is the coded byte sequence. When decoding ciphertext, the S-box is dynamically generated by the password sequence B and the two-dimensional table, and the password is unknown, so the S-box and (x, Y) are unknown, and the sequence Y is unknown.
Based on the above embodiment, step S1079 specifically includes the steps of:
step S1079a, calculating weighted probabilityAnd->Where p represents the probability of byte 0 in the sequence X to be encoded.
Step S1079b, if X i ＝0，If X i ＝0，/> Wherein R is i 、R i-1 、R i 、R i-1 Represents the coding variable, R 0 ＝1，L 0 ＝0。
Step S1079c, i=i+1, if i < n, jump to step S1079a, if i is not less than n, obtain the encoding result.
The present embodiment specifically refines the specific procedure of step S1079.
Based on the above embodiment, in step S103, the method further includes the steps of:
step S1032a, when n+u<L and i<In the case of n + u,where i represents a statistical variable and the initial value of i is 0.
Step S1032b, i=i+1, and step S1032a is skipped until i is equal to or greater than n+u, and step S1033 is performed.
The purpose of this embodiment is: when n+u<L and i<n+u, B (j) is passed through So that each byte in the cryptographic sequence can be effectively used as a weighting factor.
As a preferred embodiment, there is provided a symmetric encryption method capable of resisting an attack of an massively parallel computing, the encryption method specifically including the steps of:
the step of encoding the byte sequence X with the length of n by adopting a weighted probability model is as follows, wherein L (L is more than or equal to 6) byte sequences B are input, B (i) is the ith byte of the sequence B.
Initializing parameters, L 0 ←0，H 0 ←R 0 ←1，i←j←0；X 0 ＝0；
Step (2) defining S box array S [ T ] 2 ]；
Step (3) counting the number c of the symbols 0 of the sequence X,
step (4) randomly generating a byte sequence Q with the length of u (u is more than or equal to 16);
step (5) n≡n+u;
step (6), when n is more than or equal to L, turning to step (9);
step (7) when i<n is time ofi++1, repeating step (7);
step (8) i≡0, l≡n;
step (9) looking up a two-dimensional table according to j to obtain f (j);
step (10) when j<T 2 In the time-course of which the first and second contact surfaces,and j++1, repeating steps (9) to (10);
step (11) connecting Q (front) and X (rear) in series to obtain a binary sequence Z;
step (12) obtaining the ith byte value X of the sequence Z i ；
Step (13) acquires the cipher (i mod L) th byte value B (i mod L) and the L- (i mod L) th byte B (L- (i mod L));
step (14) calculates x and y,
step (15) obtaining g (x, y) according to xT+y checking S box;
step (16) of calculating r (i) according to the above formula (17);
step (17) calculating a weighted probabilityAnd->
Step (18) if X i ＝0，Otherwise->
Step (19) i≡i+1, if i < n, repeating steps (12) to (19);
step (20) of preparing L n Converting into a byte sequence Y, and marking the length of Y as m, i < 0 >;
step (21) obtaining the ith byte value Y of the sequence Y i ；
Step (22) when i<In the m-time period, the total number of the components,i≡i+1, repeating the steps (21) and (22);
step (23) outputs Y, m, n, c, u, and the encoding is finished.
In addition, a decoding method corresponding to a symmetric encryption method capable of resisting the quantitative parallel computing attack is provided, which is specifically as follows:
coding a byte sequence X ith symbol X based on (8) i . When X is i When=0, F (0-1, r) =rf (-1), becauseSo F (-1) =0.
When X is i When =a and a=1, 2, …, k:
according to the above theorem 2, the lossless decoding condition is L n ∈[L n ,H n )∧L n ∈[L n-1 ,H n-1 )∧...∧L n ∈[L 1 ,H 1 ) Region(s)M [ L ] i ,H i ) And symbol X i One-to-one mapping. If L i ≥L i-1 +R i-1 X at F (a-1, r) i =a, thus decode X i Time, order
H(a)＝L i-1 +R i-1 F(a-1)
Then L is n X is greater than or equal to H (a) i ＝a。
The method comprises the steps of setting M bytes in an input password byte sequence B', obtaining Y, M, n, c and u by a decoding end, and decoding a binary information source sequence X based on a weighted probability model, wherein the steps are as follows:
initializing parameters, L 0 ←0，R 0 ←1，H←1，i←j←0；X 0 ＝0；
Step (2) calculates the probability of symbol 0,
step (3) defining S box array S [ T ] 2 ]；
Step (4), when n is more than or equal to M, turning to step (7);
step (5) when i<n is time ofi++1, repeat (5);
step (6) i≡0, m≡n;
step (7), looking up a two-dimensional table according to j to obtain f (j);
step (8) when j<T 2 In the time-course of which the first and second contact surfaces,and j++1, repeating steps (7) to (8);
step (9) obtaining the ith byte value Y of the sequence Y i ；
Step (10) when i<In the m-time period, the total number of the components,i≡i+1, repeating the steps (9) and (10);
step (11) converting byte sequence Y into L n ，i←0；
Step (12) acquires the cipher (i mod L) th byte value B '(i mod L) and L- (i mod L) th byte B' (L- (i mod L));
step (13) of calculating x and y,
step (14) obtaining g (x, y) according to xT+y checking S box;
step (15) calculating r (i) according to formula (17);
step (16) calculating the weighted probability of all symbolsWherein a = 0,1,2, …, k;
step (17) of calculating a weighted distribution function H (a), H (a) ≡L of all symbols i +R i F (a-1), wherein a = 0,1,2, …, k;
step (18) if L n Not less than H (a), the ith symbol is X i ＝a，L i ←L i +R i F(a-1)，
Step (19) i≡i+1, if i < n, repeating steps (12) to (19);
step (20) removes the first u bytes, ending decoding.
The security analysis for the above preferred embodiment is as follows:
the code byte sequence B 'is input during decoding, and M numbers of B' are used. Obviously, lossless coding is possible when B' =b and m=l.
When B 'noteqb and m=l, or B' noteqb and M noteq L, decoding step (7) looks up the two-dimensional table to find the error of f (j), then the S-box value obtained in step (8) is wrong, and the sequences Y obtained in steps (9) and (10) are wrong, then L in step (11) n Errors. Since g (x, y) is wrong in step (14), r (i) is wrong in step (15), thus stepIn steps (16) (17) (18)And H (a) errors, and the symbol X cannot be determined because the first u random bytes are unknown i Whether the decoding is correct. />
The encoding and decoding process is based on a password sequence and a dynamically generated S-box, and r (i) is calculated based on a random S-box and random coordinates (x, y) for weighted probability model encoding, independent of the data to be encrypted. Therefore, the linear correlation and algebraic relation of the data to be encrypted cannot be used as the reference factors for cracking by the method of the embodiment. Although the two-dimensional table is known, the S-box is unknown, and the random coordinates (x, y) are unknown, the S-box or coordinates (x, y) cannot be derived based on the two-dimensional table. Based on the analysis, under the condition of unknown passwords, the probability of accurately decoding the first u bytes is thatWhen X is known, 256 is first performed 3u A traversal based on X 1 The analysis of the byte information of the password is started. However, since the sequence Y is unknown, L n Can not be regarded as L in decoding i Since it is impossible to determine whether or not the byte information of the cipher is estimated correctly, the cipher information cannot be obtained at the time of linear decoding. It can be derived that the method of the present embodiment is safe.
Referring to fig. 7, an embodiment of the present application provides a symmetric encryption system capable of resisting an attack of an quantum parallel computing, including a data acquisition unit 100, an S-box computing unit 200, a data concatenation unit 300, a data encoding unit 400, a ciphertext generating unit 500, and a ciphertext transmitting unit 600, wherein:
the data acquisition unit 100 is configured to acquire a code sequence B with a sequence length L, a sequence X to be encoded with a sequence length n, and a random sequence Q with a sequence length u;
the S-box calculation unit 200 is configured to calculate an S-box array by:
step S1031, randomly generating T 2 Storing the non-repeated integer values into a two-dimensional table of T, and entering step S1033 when n+u is more than or equal to L;
step S1033, obtaining f (j) from the two-dimensional table; wherein j represents a statistical variable and an initial value of j is 0, and f (j) represents a j-th byte in the two-dimensional table;
step S1035, when j<T 2 In the time-course of which the first and second contact surfaces,and j=j+1, and jump to step S1033 until j is equal to or greater than T 2 At this time, the process advances to step S105; wherein S [ j ]]Represents the j-th byte in the S-box array, < >>Representing exclusive or logic operations;
the data concatenation unit 300 is used for concatenating the random sequence Q and the sequence to be encoded X to obtain a binary sequence Z;
the data encoding unit 400 is configured to encode the binary sequence Z based on the weighted probability model and the S-box array by:
step S1071, obtaining the ith byte X in the binary sequence Z i And the ith mod L byte B (i mod L) and the L- (i mod L) th byte B (L- (i mod L)) in the cipher sequence B, i representing a statistical variable and an initial value of i being 0;
step S1073, calculate X i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to xT+y;
step S1077, calculating a nonlinear round function r (i); wherein,
s represents an integer of 6 or more;
the ciphertext generating unit 500 is configured to perform exclusive-or logic operation on the encoding result and the S-box array to obtain ciphertext;
ciphertext transmitting unit 600 may be configured to transmit ciphertext to the decoding side.
It should be noted that, the system embodiment provided in the present embodiment and the method embodiment described above are based on the same inventive concept, so that the relevant content of the method embodiment described above is also applicable to the system embodiment, and will not be described herein.
An embodiment of the application provides an electronic device; the electronic device may be any type of intelligent terminal, such as a mobile phone, tablet computer, personal computer, etc. Specifically, the electronic device includes: one or more control processors and memory, one control processor being the example. The control processor and the memory may be connected by a bus or other means, this example being by way of example a bus connection.
The memory is used as a non-transitory computer readable storage medium and can be used for storing non-transitory software programs, non-transitory computer executable programs and modules, such as program instructions/modules corresponding to the electronic device in the embodiment of the invention; the control processor implements the symmetric encryption method of the above method embodiments that can resist the quantitative parallel computing attack by running non-transitory software programs, instructions, and modules stored in memory. The memory may include a memory program area and a memory data area, wherein the memory program area may store an operating system, at least one application program required for a function; in addition, the memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory remotely located relative to the control processor, the remote memory being connectable to the electronic device via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof. The one or more modules are stored in the memory and when executed by the one or more control processors perform the symmetric encryption method of the method embodiments described above that is resistant to quantum parallel computing attacks.
Embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions that are executed by one or more control processors, for example, to cause the one or more control processors to perform the symmetric encryption method of the method embodiments described above that is resistant to an attack of quantitative parallel computation.
From the above description of embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented in software plus a general purpose hardware platform. Those skilled in the art will appreciate that all or part of the processes implementing the methods of the above embodiments may be implemented by a computer program for instructing relevant hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, may include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read Only Memory (ROM), a random access Memory (Random Access Memory, RAM), or the like.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims (8)

1. A symmetrical encryption method capable of resisting quantitative parallel computing attack is characterized by being applied to an encoding end and comprises the following steps:
step S101, a password sequence B with a sequence length L, a sequence X to be coded with a sequence length n and a random sequence Q with a sequence length u are obtained;
step S103, calculating an S box array:
step S1031, randomly generating T 2 Storing the non-repeated integer values into a two-dimensional table of T, and entering step S1033 when n+u is more than or equal to L; t=16;
step S1033, acquiring f (j) from a two-dimensional table according to j according to an extraction sequence of the two-dimensional table set in advance; wherein j represents a statistical variable and an initial value of j is 0, and f (j) represents a j-th byte in the two-dimensional table;
step S1035, when j<T 2 At the time S [ j ]]=b (j+1) mod L) ((j+1) mod L) f (j), and j=j+1, and jumps to step S1033 until j is equal to or greater than T 2 At this time, the process advances to step S105; wherein S [ j ]]Representing the j-th byte in the S-box array, wherein the bits represent exclusive OR logic operation; where B (j mod L) is the value of the j < th > mod L (j=1, 2, …, L) byte of the cipher sequence, mod is a modulo operation;
step S105, connecting the random sequence Q and the sequence X to be coded in series to obtain a binary sequence Z;
step S107, encoding the binary sequence Z based on a weighted probability model and the S-box array:
step S1071, obtaining the ith byte X in the binary sequence Z i And the ith mod L byte B (i mod L) and the L- (ith mod L) byte B (L- (i mod L)) in the cryptographic sequence B, i representing a statistical variable and an initial value of i being 0;
step S1073, calculate x= (X) i-1 ⊕B(i mod L))mod T,y＝(X i-1 B (L- (i mod L))) mod T, said X i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to x and y; the byte value of coordinates (x, y) in the S box is g (x, y);
step S1077, calculating a nonlinear round function r (i); wherein,s represents an integer of 6 or more;
step S1079, coding the binary sequence Z based on the weighted probability model and the nonlinear round function r (i) to obtain a coding result; the step S1079 specifically includes:
step S1079a, calculating weighted probabilityAnd-> Wherein, p represents the probability of byte 0 in the sequence X to be coded;
step S1079b, if X i ＝0，If X i ＝0，/> Wherein the R is i 、R i-1 、R i 、R i-1 Represents the coding variable, R 0 ＝1，L 0 ＝0；
Step S1079c, i=i+1, if i < n, jump to step S1079a, if i is not less than n, obtain the encoding result;
step S109, performing exclusive OR logic operation on the coding result and the S box array to obtain ciphertext; the step S109 specifically includes:
step S1091, converting the encoding result into a sequence Y with a sequence length of m;
step S1093, obtaining the ith byte value Y in the sequence Y i ；
Step S1095, when i<m is Y i ＝Y i ⊕S(imodT 2 ) And i=i+1, jumping to step S1093 until ciphertext is obtained when i is greater than or equal to m;
step S110, the ciphertext is sent to a decoding end.
2. The symmetric encryption method for combating quantitative parallel computing attacks according to claim 1, wherein the values in the two-dimensional table are 0 to 255.
3. The symmetric encryption method against the attack of the quantitative parallel computing according to claim 1, further comprising, in the step S103:
step S1032a, when n+u < L and i < n+u, B (i) =b (i) B (L-i); wherein i represents a statistical variable and the initial value of i is 0;
step S1032b, i=i+1, and step S1032a is skipped until i is equal to or greater than n+u, and step S1033 is entered.
4. The symmetric encryption method according to claim 1, wherein the binary sequence Z is obtained by concatenating the sequence to be encoded X after the random sequence Q in step S105.
5. The symmetric encryption method for resisting quantitative parallel computing attack according to claim 1, wherein L is equal to or greater than 6.
6. A symmetric encryption system operable against quantitative parallel computing attacks, comprising:
the data acquisition unit is used for acquiring a password sequence B with a sequence length L, a sequence X to be coded with a sequence length n and a random sequence Q with a sequence length u;
an S-box calculation unit for calculating an S-box array by:
step S1031, randomly generating T 2 Storing the non-repeated integer values into a two-dimensional table of T, and entering step S1033 when n+u is more than or equal to L; t=16;
step S1033, acquiring f (j) from a two-dimensional table according to j according to an extraction sequence of the two-dimensional table set in advance; wherein j represents a statistical variable and an initial value of j is 0, and f (j) represents a j-th byte in the two-dimensional table;
step S1035, when j<T 2 At the time S [ j ]]=b (jmodL)/(j+1) modL)/(f (j), and j=j+1, andjump to step S1033 until j is greater than or equal to T 2 At this time, the process advances to step S105; wherein S [ j ]]Representing the j-th byte in the S-box array, wherein the bits represent exclusive OR logic operation; where B (jmod L) is the value of the jmod L (j=1, 2, …, L) of the cipher sequence, mod is a modulo operation;
the data serial unit is used for connecting the random sequence Q and the sequence X to be coded in series to obtain a binary sequence Z;
a data encoding unit for encoding the binary sequence Z based on a weighted probability model and the S-box array by:
step S1071, obtaining the ith byte X in the binary sequence Z i And the imodL-th byte B (imodL) and the L- (imodL) -th byte B (L- (imodL)) in the cryptographic sequence B, i representing a statistical variable and the initial value of i being 0;
step S1073, calculate x= (X) i-1 ⊕B(imodL))modT,y＝(X i-1 B (L- (imodL))) mod T, said X i-1 Representing the i-1 th byte in the binary sequence Z;
step S1075, searching corresponding g (x, y) from the S box array according to x and y; the byte value of coordinates (x, y) in the S box is g (x, y);
step S1077, calculating a nonlinear round function r (i); wherein,s represents an integer of 6 or more;
step S1079, coding the binary sequence Z based on the weighted probability model and the nonlinear round function r (i) to obtain a coding result; the step S1079 specifically includes:
step S1079a, calculating weighted probabilityAnd-> Wherein, p represents the probability of byte 0 in the sequence X to be coded;
step S1079b, if X i ＝0，If X i ＝0，/> Wherein the R is i 、R i-1 、R i 、R i-1 Represents the coding variable, R 0 ＝1，L 0 ＝0；
Step S1079c, i=i+1, if i < n, jump to step S1079a, if i is not less than n, obtain the encoding result;
the ciphertext generating unit is used for carrying out exclusive OR logic operation on the encoding result and the S box array to obtain ciphertext; step S1091, converting the coding result into a sequence Y with a sequence length of m;
step S1093, obtaining the ith byte value Y in the sequence Y i ；
Step S1095, when i<m is Y i ＝Y i ⊕S(imodT 2 ) And i=i+1, jumping to step S1093 until ciphertext is obtained when i is greater than or equal to m;
and the ciphertext sending unit is used for sending the ciphertext to the decoding end.
7. An electronic device, characterized in that: comprising at least one control processor and a memory for communication connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the symmetric encryption method of any one of claims 1 to 5 that is resistant to an quantitative parallel computing attack.
8. A computer-readable storage medium, characterized by: the computer-readable storage medium stores computer-executable instructions for causing a computer to perform the symmetric encryption method of any one of claims 1 to 5 that is resistant to quantitative parallel computing attacks.
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