CN110058842B - Structure-variable pseudo-random number generation method and device - Google Patents
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Abstract
The invention relates to a structure variable pseudo-random number generation method, which comprises the following steps: acquiring an initial key, a primitive polynomial and an initialization vector; obtaining a first subsequence according to the primitive polynomial and the initialization vector; obtaining a second subsequence according to the initial key; obtaining a third subsequence according to the first subsequence and the second subsequence; and obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence. The method has variable structure, the lightweight algorithm is easy to realize by software and hardware, can resist relative attack, provides higher safety and flexibility for the generation of the pseudo random number, and the generated pseudo random sequence can be applied to a plurality of encryption applications.
Description
Technical Field
The invention belongs to the field of information security, and particularly relates to a structure-variable pseudo-random number generation method and device.
Background
The pseudo-random number is a periodic sequence with certain random characteristics, although not truly random, the generation speed is high, the implementation of software and hardware is easy, and the pseudo-random number is widely applied to important technical fields such as secret keys of communication, radar, navigation and cryptography, digital signatures, identity authentication and the like.
For example, a method of generating a pseudo-random number and a pseudo-random number generator, comprising: the method comprises the steps of obtaining a preset secret key, an initial vector, a seed and an encryption function, calling an SM4 algorithm and a 3DES algorithm by the encryption function, determining a generating function by combining the SM4 algorithm and the 3DES algorithm, and outputting a pseudo-random number according to the generating function, the secret key, the initial vector and the seed. As another example, another pseudo-random number generation apparatus and method uses two linear feedback shift registers with opposite shift directions to generate a random number of bits. For another example, a nonlinear pseudo-random sequence generator employs a linear feedback unit, a nonlinear feedback logic unit and a synthesis unit, wherein the linear feedback logic unit is correspondingly connected with a state output end of a shift register unit according to a primitive polynomial feedback function, and an output end of the linear feedback logic unit is connected with an input end of the synthesis unit. The input end of the nonlinear feedback logic unit is correspondingly connected with the state output end of the shift register unit according to the nonlinear characteristic function, the synthesis unit comprises an exclusive-OR gate, the input end of the synthesis unit is respectively connected with the output end of the linear feedback logic unit and the output end of the nonlinear feedback logic unit, the output end of the synthesis unit is connected with the input end of the shift register, and the generation method is simple.
However, the first method is not a lightweight algorithm and is not easily implemented in software and hardware. The second method only uses a linear feedback shift register, and the structure is not variable and cannot resist relevant attacks. The third method uses only one nonlinear feedback function, has a simple structure, and cannot be applied to various applications.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a pseudo random number generation method and apparatus with a variable structure. The technical problem to be solved by the invention is realized by the following technical scheme:
the embodiment of the invention provides a structure-variable pseudo random number generation method, which comprises the following steps:
acquiring an initial key, a primitive polynomial and an initialization vector;
obtaining a first subsequence according to the primitive polynomial and the initialization vector;
obtaining a second subsequence according to the initial key;
obtaining a third subsequence according to the first subsequence and the second subsequence;
obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence;
in one embodiment of the present invention, further comprising:
and repeatedly updating the first subsequence and the second subsequence to obtain the key stream.
In an embodiment of the present invention, obtaining the first subsequence according to the primitive polynomial and the initialization vector includes:
obtaining the structure of a linear feedback shift register according to the primitive polynomial;
obtaining a linear feedback shift register according to the structure of the linear feedback shift register;
and substituting the initialization vector into the linear feedback shift register to obtain the first subsequence.
In an embodiment of the present invention, obtaining the second subsequence based on the initial key sum includes:
obtaining the structure of a nonlinear feedback shift register according to the initial key;
obtaining a nonlinear feedback shift register according to the structure of the nonlinear feedback shift register;
and substituting the initial key into the nonlinear feedback shift register to obtain the second subsequence.
In an embodiment of the present invention, obtaining a third subsequence from the first subsequence and the second subsequence includes:
selecting a filtering function;
and substituting the first subsequence and the second subsequence into the filtering function to obtain a third subsequence.
In an embodiment of the present invention, obtaining a pseudo-random sequence according to the first subsequence, the second subsequence, and the third subsequence includes:
selecting an output function;
and substituting the first subsequence, the second subsequence and the third subsequence into the output function to obtain a pseudo-random sequence.
An embodiment of the present invention further provides a structure-variable pseudo random number generation apparatus, including:
the data acquisition module is used for acquiring an initial key, a primitive polynomial and an initialization vector;
a linear module, configured to obtain a first subsequence according to the primitive polynomial and the initialization vector;
the nonlinear module is used for obtaining a second subsequence according to the initial key;
a filtering module, configured to obtain a third subsequence according to the first subsequence and the second subsequence;
and the pseudo-random sequence generating module is used for obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence.
In one embodiment of the invention, the linear module comprises:
the structure generating unit is used for determining the structure of the linear feedback shift register according to the primitive polynomial;
the linear feedback shift register generating unit is used for obtaining a linear feedback shift register according to the structure of the linear feedback shift register;
and the first subsequence obtaining unit is used for substituting the initialization vector into the linear feedback shift register to obtain the first subsequence.
In one embodiment of the invention, the non-linear module comprises:
the structure generating unit is used for determining the structure of the nonlinear feedback shift register according to the initial key;
the nonlinear feedback shift register generating unit is used for obtaining a nonlinear feedback shift register according to the structure of the nonlinear feedback shift register;
and the second subsequence obtaining unit is used for substituting the initial key into the nonlinear feedback shift register to obtain the second subsequence.
In one embodiment of the invention, the filtration module comprises:
the function selection unit is used for selecting a filtering function;
and the third subsequence obtaining unit is used for substituting the first subsequence and the second subsequence into the filter function to obtain a third subsequence.
In one embodiment of the present invention, the pseudo random sequence generating module includes:
a function acquisition unit for acquiring an output function;
and the pseudo-random sequence acquisition unit is used for substituting the first subsequence, the second subsequence and the third subsequence into the output function to obtain a pseudo-random sequence.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention uses the small-sized nonlinear feedback shift register for cascade connection, can effectively reduce the use of logic devices and gates and exclusive-OR gates, belongs to a lightweight algorithm, and is easy to realize by software and hardware.
2. The algorithm structure of the invention uses the linear feedback shift register as the linear part to ensure that the period of the generated sequence is large enough, uses a plurality of nonlinear feedback shift register cascades of which the number and the length are controlled by a user key as the nonlinear part to achieve the aim of controlling the structure of the key, uses a Boolean function of high-order related immune order and balance in the filtering part, enhances the anti-attack property, provides higher safety and flexibility, and can apply the generated pseudorandom sequence to a plurality of encryption applications.
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FIG. 1 is a flow chart of a method for generating a pseudo random number with a variable structure according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for generating a structurally variable pseudo-random number according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a variable pseudo-random number generator according to an embodiment of the present invention;
fig. 4 is another schematic structural diagram of a structure-variable pseudo random number generator according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
This embodiment is implemented using a feedback shift register. Feedback shift registers, FSRs for short, are common devices for generating signals and sequences, and are largely classified into linear and nonlinear types according to the difference of feedback functions. A Linear Feedback Shift Register (LFSR) refers to a shift register in which a feedback function is a linear function, and the linear function of an output given by a previous state is reused as an input. The exclusive-or operation is the most common single-bit linear function: and carrying out exclusive OR operation on certain bits of the register to be used as input, and then carrying out integral shift on each bit in the register. A Nonlinear feedback shift register (NLFSR) is compared with a linear feedback shift register, and its feedback function is a Nonlinear function, which is similar to the linear feedback shift register in general circuit logic, except that the feedback logic of the NLFSR is composed of an exclusive or gate and an and gate, and only an exclusive or gate exists in the LFSR.
One embodiment of the present invention provides a method for generating a pseudo random number with a variable structure, which is mainly implemented according to the following steps, please refer to fig. 1 and fig. 2. FIG. 1 is a flow chart of a method for generating a pseudo random number with a variable structure according to an embodiment of the present invention; fig. 2 is another schematic flow chart of a structure-variable pseudo random number generation method according to an embodiment of the present invention.
An initial key, a primitive polynomial and an initialization vector are obtained.
The initial key plays a key role in the present invention, which determines the structure of the algorithm. The primitive polynomial is a necessary condition for generating the longest period linear feedback shift register, and vectors are initialized, so that the safety of an encryption algorithm can be greatly improved. In this embodiment, the initial key K is set to 128bits, and the primitive polynomial is: f. ofL(x)＝x128+x29+x27+x2+1, initialization IV is 128 bits.
And obtaining a first subsequence according to the primitive polynomial and the initialization vector.
The structure of the linear feedback shift register is 128 orders obtained from primitive polynomial. Substituting initialization vector IV into linear feedback shift register by { x0,x1,...,xn-1Denotes a 128-stage linear feedback shift register, x0Is connected to the non-linear feedback shift register by an exclusive or operation as an output. Let the register state at time t be (a)t,at+1,...,at+127) Correspondingly, the update function of the register is obtained as:
a number of status bits are extracted from a linear feedback shift register to obtain a first subsequence.
In this embodiment, the extracted 7 linear feedback shift register states are: { at+8,at+13,at+20,at+42,at+60,at+79,at+95}。
A second subsequence is derived from the initial key.
The initial key K is 128bits, each 16bits represents the length of the nonlinear feedback shift register, 80bits (0x1414241816) of the key are selected, and the structure of the obtained nonlinear feedback shift register adopts 5 small-sized nonlinear feedback shift registers in cascade connection and is set as { f0,f1,f2,f3,f4Length is 20,26,36,24,22, respectively, and total length is 128.
By
A non-linear feedback shift register is shown. And (3) placing the initial key K into a nonlinear feedback shift register, wherein the corresponding nonlinear feedback function is as follows:
referring to fig. 3, fig. 3 is a schematic structural diagram of a variable pseudo random number generator according to an embodiment of the present invention.
Updating a non-linear feedback shift register f4From the 3 inputs xor: first path is a non-linear feedback shift register f4Feedback of itself, the second path being a non-linear feedback shift register f0Output feedback of
The third path is the output x of the linear feedback shift register f0。
Setting the state of the nonlinear feedback shift register at the time t as follows:
thus, the nonlinear feedback shift register f4The update function of (a) is:
nonlinear feedback shift register f0,f1,f2,f3The feedback end is furtherThe feedback of the nonlinear feedback shift register and the output of the nonlinear feedback shift register cascaded at the previous stage are subjected to exclusive-or operation updating, and the updating function is as follows:
f3updating a function:
f2updating a function:
f1updating a function:
f0updating a function:
in this embodiment, let the state of the nonlinear feedback shift register at time t be
Extracting a state from each nonlinear feedback shift register, { b }t+10,bt+34,bt+55,bt+97,bt+121And obtaining a second subsequence.
In this embodiment, the extracted 7 linear feedback shift register states are: { at+8,at+13,at+20,at+42,at+60,at+79,at+95}。
And obtaining a third subsequence according to the first subsequence and the second subsequence.
Selecting a filter function H (x) as a 9-dimensional 3-order equalization Boolean function, which is defined as:
sending a slave linear feedback shiftThe first subsequence extracted from the memory and the second subsequence extracted from the non-linear feedback shift register are used as input arguments of the filter function, and the filter function input argument is { x }0,x1,x2,x3,x4,x5,x6,x7,x8}←{bt+34,at+8,at+13,at+20,bt+97,at+42,at+60,at+79,at+95Get the third subsequence through a filtering function.
And obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence.
Selecting an output function ztDefined as:
wherein,
where ω is {2,15,36,45,64,73,89}, it refers to the status bit, s, at the corresponding location in the nonlinear feedback shift registert+95Is a status bit in the linear feedback shift register. And substituting the first subsequence, the second subsequence and the third subsequence into an output function to obtain a pseudo-random sequence.
Due to the exclusive-or operation, the period of the pseudo-random sequence is not lower than that of the linear feedback shift register.
In the present embodiment, the number of the channels is { x }0,x1,...,xn-1Denotes a 128-stage linear feedback shift register, δkIndicating a shift of k registers to the left, hence delta1{x0,x1,...,xn-1Denotes a linear feedback shift register update once, x0Is connected to the non-linear feedback shift register by an exclusive or operation as an output.
The nonlinear feedback shift register is composed of N length N0,n1,…,nN-1The nonlinear feedback shift registers are cascade connected, and the output of the 1 st nonlinear feedback shift register is fed back to the Nth nonlinear feedback shift registerThe linear feedback shift register forms a ring.
The internal state of the nonlinear feedback shift register shifts the update register to the left,
the position state is used as output and transmitted to the cascaded nonlinear feedback shift register, the value calculated by the self nonlinear feedback function is exclusive-or updated with the output of the right end cascaded nonlinear feedback shift register to update the internal state of the right end register, fN-1Exclusive OR operation is carried out on the output of the linear module and the output of the 1 st nonlinear feedback shift register to update the position
The state of (1).
And the nonlinear feedback shift register and the linear feedback shift register are synchronously updated to continuously obtain a pseudorandom sequence to form a key stream.
The product of the star operations involved in the ring-like cascade connection and a class of NFSRs with the same cycle structure of reference A is expressed as: for any two Boolean functions f1(x0,x1,…,xn) And f2(x0,x1,…,xm) Is defined as:
f1*f2＝f1(f2(x0,…,xm),f2(x1,…,xm+1),…,f2(xn,…,xn+m))。
the cascade of 5 nonlinear feedback shift registers used in this embodiment is equivalent to a 128-step nonlinear feedback shift register, and the corresponding nonlinear function g (x) is easily expressed as:
g(x)＝f0*f1*f2*f3*f4
＝f0*f1*f2*h0(x0,…,x45)
＝f0*f1*h1(x0,…,x81)
＝f0*h2(x0,…,x107)
＝h3(x0,…,x127)
introduction function deltak(h (x)) means to add k to the subscript of the variable in the h (x) function.
g (x) h0(x0,…,x45)、h1(x0,…,x81)、h2(x0,…,x107)、h3(x0,…,x127) The concrete expression is as follows:
a nonlinear feedback function g (x), the register state at the time t is { s }t,…,st+128The corresponding update function:
the update function of g (x) obtains the following hardware implementation resources:
| exclusive-or gate | And gate | |
| h'0(st,…,st+45) | 23 | 13 |
| h’1(st,…,st+81) | 23*5+4＝119 | 13*5+1＝66 |
| h'2(st,…,st+107) | 119*6+5＝719 | 66*6+1＝397 |
| st+128 | 719*7+7＝5010 | 397*7+1＝2780 |
By 5 cascaded non-linear feedback shift registers f0,f1,f2,f3,f4The hardware implementation of the update function of 24 exclusive-or gates and 6 and gates is adopted, and hardware resources are greatly saved compared with the nonlinear function g (x) of the 128-order nonlinear feedback shift register.
An embodiment of the present invention also provides a structure-variable pseudo random number generation apparatus, including: the data acquisition module is used for acquiring an initial key, a primitive polynomial and an initialization vector; a linear module, configured to obtain a first subsequence according to the primitive polynomial and the initialization vector; the nonlinear module is used for obtaining a second subsequence according to the initial key; a filtering module, configured to obtain a third subsequence according to the first subsequence and the second subsequence; and the pseudo-random sequence generating module is used for obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence.
The above linear module includes: the structure generating unit is used for determining the structure of the linear feedback shift register according to the primitive polynomial; the linear feedback shift register generating unit is used for obtaining a linear feedback shift register according to the structure of the linear feedback shift register; and the first subsequence obtaining unit is used for substituting the initialization vector into the linear feedback shift register to obtain the first subsequence.
The nonlinear module includes: the structure generating unit is used for determining the structure of the nonlinear feedback shift register according to the initial key; the nonlinear feedback shift register generating unit is used for obtaining a nonlinear feedback shift register according to the structure of the nonlinear feedback shift register; and the second subsequence obtaining unit is used for substituting the initial key into the nonlinear feedback shift register to obtain the second subsequence.
The above-mentioned filtration module includes: the function selection unit is used for selecting a filtering function; and the third subsequence obtaining unit is used for substituting the first subsequence and the second subsequence into the filter function to obtain a third subsequence.
The pseudo random sequence generating module includes: a function acquisition unit for acquiring an output function;
and the pseudo-random sequence acquisition unit is used for substituting the first subsequence, the second subsequence and the third subsequence into the output function to obtain a pseudo-random sequence.
Fig. 3 and fig. 4 are schematic structural diagrams of a variable pseudo random number generator according to an embodiment of the present invention.
The invention provides a pseudo-random number generating method and device with a variable structure, wherein a cascaded nonlinear feedback shift register is adopted to replace a high-order nonlinear feedback shift register in a pseudo-random number generator, the use of a logic device and a gate and an exclusive-OR gate can be effectively reduced, and the Grain-like structure belongs to a lightweight algorithm and is easy to realize by software and hardware. In the specific use, the number and the length of the nonlinear feedback shift registers for cascade connection are selected by a user key, so that the purpose of controlling the structure by the key is achieved; the filtering module uses a balanced Boolean function with higher correlation immune order, can resist correlation attack and increase safety, and the generated high-performance pseudo-random number sequence can be applied to a plurality of encryption applications.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (6)
1. A method of generating a structurally variable pseudorandom number comprising:
acquiring an initial key, a primitive polynomial and an initialization vector;
obtaining a first subsequence according to the primitive polynomial and the initialization vector, including:
obtaining a first subsequence according to the primitive polynomial and the initialization vector, including:
determining the structure of a linear feedback shift register according to the primitive polynomial;
obtaining a linear feedback shift register according to the structure of the linear feedback shift register;
substituting the initialization vector into the linear feedback shift register to obtain the first subsequence;
obtaining a second subsequence according to the initial key; the method comprises the following steps:
determining the structure of a nonlinear feedback shift register according to the initial key; the nonlinear feedback shift register comprises a plurality of cascaded small-size nonlinear feedback shift registers, and the output of the 1 st small-size nonlinear feedback shift register is fed back to the Nth small-size nonlinear feedback shift register to form an annular structure;
obtaining a nonlinear feedback shift register according to the structure of the nonlinear feedback shift register;
substituting the initial key into the nonlinear feedback shift register to obtain the second subsequence;
obtaining a third subsequence according to the first subsequence and the second subsequence;
and obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence.
2. The method of claim 1, further comprising:
and repeatedly updating the first subsequence and the second subsequence to obtain the key stream.
3. The method of claim 1, wherein obtaining a third subsequence from the first subsequence and the second subsequence comprises:
selecting a filtering function;
and substituting the first subsequence and the second subsequence into the filtering function to obtain a third subsequence.
4. The method of claim 1, wherein obtaining a pseudo-random sequence from the first subsequence, the second subsequence, and the third subsequence comprises:
selecting an output function;
and substituting the first subsequence, the second subsequence and the third subsequence into the output function to obtain a pseudo-random sequence.
5. A variable structure pseudorandom number generation apparatus comprising:
the data acquisition module is used for acquiring an initial key, a primitive polynomial and an initialization vector;
a linear module, configured to obtain a first subsequence according to the primitive polynomial and the initialization vector; the linear module includes:
the structure generating unit is used for obtaining the structure of the linear feedback shift register according to the primitive polynomial;
the linear feedback shift register generating unit is used for obtaining a linear feedback shift register according to the structure of the linear feedback shift register;
a first subsequence obtaining unit, configured to substitute the initialization vector into the linear feedback shift register to obtain the first subsequence;
the nonlinear module is used for obtaining a second subsequence according to the initial key; wherein the non-linear module comprises:
the structure generating unit is used for obtaining structures of a plurality of small-size nonlinear feedback shift registers according to the initial key;
the nonlinear feedback shift register generating unit is used for obtaining a nonlinear feedback shift register according to the structure of the nonlinear feedback shift register; wherein, a plurality of small-size nonlinear feedback shift registers are cascaded, and the output of the 1 st small-size nonlinear feedback shift register is fed back to the Nth small-size nonlinear feedback shift register to form a nonlinear feedback shift register with a ring structure;
a second subsequence obtaining unit, configured to substitute the initial key into the nonlinear feedback shift register to obtain the second subsequence;
a filtering module, configured to obtain a third subsequence according to the first subsequence and the second subsequence;
and the pseudo-random sequence generating module is used for obtaining a pseudo-random sequence according to the first subsequence, the second subsequence and the third subsequence.
6. The apparatus of claim 5, wherein the pseudo-random sequence generating module comprises:
a function acquisition unit for acquiring an output function;
and the pseudo-random sequence acquisition unit is used for substituting the first subsequence, the second subsequence and the third subsequence into the output function to obtain a pseudo-random sequence.
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