CN102664731B - Encrypting and rapid processing method for electronic ballot information - Google Patents

Encrypting and rapid processing method for electronic ballot information Download PDF

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CN102664731B
CN102664731B CN201210100596.3A CN201210100596A CN102664731B CN 102664731 B CN102664731 B CN 102664731B CN 201210100596 A CN201210100596 A CN 201210100596A CN 102664731 B CN102664731 B CN 102664731B
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CN102664731A (en
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崔喆
代翔
方佳嘉
王晓京
彭程
官磊
张宇
史志明
李永华
陈渝
董锴
李晓恺
巫浩
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Chengdu Information Technology Co Ltd of CAS
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Abstract

The invention discloses an encrypting and rapid processing method for electronic ballot information. The method comprises the following steps: replacing ballot result information by characters, wherein each character represents different selection significances, constructing a ballot matrix, selecting a polynomial at random to carry out block computing on the ballot matrix, and transmitting the ballot matrix to n independent counting computers, thereby achieving safe transmission of the ballot information. Nobody can obtain any ballot information even if obtaining an election matrix sub-block in advance, and the ballot matrix can be rapidly restored by merging k (k is smaller than or equal to n) counting machines at the counting stage. The encrypting and rapid processing method has the beneficial effects of achieving ballot confidentiality, ballot security and counting rapidity.

Description

Encryption and the immediate processing method of electronics ballot paper information
Technical field
The present invention relates to a kind of encryption and immediate processing method of electronics ballot paper information.
Background technology
The most of papery ballot paper that adopts of existing domestic campaign, as the carrier of expressing wish, uses the mode of hand-counted ballots to carry out, election flow process complexity, and the length consuming time of calling out the names of those voted for while counting ballot-slips, and there is the possibility of erroneous judgement in the mode of manually examining tickets.Along with scientific and technological development and the raising of citizens'quality, the election equipment of electronization and way to elect will be promoted and use in vast basic unit of China.Existing electronic voting system conventionally by expressly transfer mode of electronics ballot paper result, can cause the leakage in advance of ballot paper information for the processing of electronics ballot paper in transport process.
Some cryptologists provide based on cryptographic electronic voting technology, but based on cryptographic election Technology Need too loaded down with trivial details cryptographic calculations and protocol interaction, and for China's security of network and information present situation, the at present domestic network election system that not yet occurs this class input practical, commercial.The appearance of above-mentioned situation is all unfavorable for carrying out smoothly of elections at the basic level activity.
Summary of the invention
In order to overcome the above-mentioned shortcoming of prior art, the invention provides a kind of encryption and immediate processing method of electronics ballot paper information, ballot paper object information is substituted by character, every kind of character represents different selection meanings, construct a ballot paper matrix, and ballot paper matrix is chosen to multinomial at random and carry out piecemeal calculating, and send to nthe count of votes computer of platform independent, realized ballot paper information safety transmit, even and if anyone obtain in advance election the partitioning of matrix also cannot therefrom obtain any vote information; Only need merge wherein in the count of votes stage kplatform ( k≤ n) count of votes machine can this ballot paper matrix of fast quick-recovery.
The technical solution adopted for the present invention to solve the technical problems is: a kind of encryption and immediate processing method of electronics ballot paper information, comprise the following steps:
1) computer is according to candidate's figure place and name structure
Figure 244903DEST_PATH_IMAGE001
× lballot paper matrix, wherein mfor candidate's figure place, lfor every a line candidate's figure place, when last column is less than lwhen row, not enough figure place is with 0 polishing;
2) the digitlization binary system that every voter ballot paper matrix that vote is selected on ballot equipment is carried out 0/1 form by ballot equipment transforms;
3) burst of ballot paper matrix calculates:
According to the number of units of count of votes machine n, arrange one ( k, n) threshold structure, kfor threshold parameter, with the data of every a line in ballot paper matrix s i , wherein i=1,2 ...,
Figure 130950DEST_PATH_IMAGE001
as secret information, it is carried out to the secret sharing based on Lagrange interpolation polynomial:
Get a prime number p, meet p> nand p> 2 l -1, construct finite field gF( p)={ 0,1,2 ..., p-1} mod p, in finite field gF( p) in choose at random nindividual different open numerical value x 1, x 2..., x n , in this finite field, choose at random k-the value of 1 need to be keep secret a 1, a 2..., a k-1 , and construct k-1 order polynomial
(1)
The element in ballot paper matrix s i , wherein i=1,2 ...,
Figure 574799DEST_PATH_IMAGE001
, in substitution multinomial (1) s, simultaneously respectively x 1, x 2..., x n substitution multinomial (1) xin, calculate
Figure 20824DEST_PATH_IMAGE003
　　
4) burst matrix construction:
Utilize the 3rd) step obtains
Figure 213908DEST_PATH_IMAGE004
, build
Figure 165814DEST_PATH_IMAGE001
× 1 burst matrix
Figure 811559DEST_PATH_IMAGE005
, and by burst matrix
Figure 372859DEST_PATH_IMAGE005
be distributed to jthe storage of platform count of votes machine, then destroy original ballot paper information, multinomial and k-the value of 1 need to be keep secret a 1, a 2..., a k-1 ;
5) ballot paper reconstruct:
In the count of votes stage, take out at least successively kthe each row of data of the burst matrix of platform count of votes machine, utilizes following Lagrange interpolation polynomial:
(2)
Determine multinomial (1), multinomial (1) determine after in numerical value 0 substitution multinomial (1) x, obtain secret information s= f(0), schange into string of binary characters, and insert the corresponding row in the blank ballot transforming through matrix;
6) ballot equipment to all voters' ballot paper information according to above-mentioned 3) to 5) step method of operation carries out the corresponding operating of ballot paper matrix, after all recovering, all ballot papers directly carry out the decimal addition on matrix, the gained vote information that calculates each candidate, finally counts election results.
Described ballot equipment is made up of touch-screen type all-in-one and corresponding ballot software, voter obtains after electronics ballot paper, on touch-screen, click its wish candidate and complete submission, the opposition to every candidate or agree with selecting to convert 0/1 form to according to voter of ballot software.
Compared with prior art, good effect of the present invention is:
1) ballot paper confidentiality: the transmission of ballot paper information does not adopt cleartext information, is divided into ballot paper after multi-disc is calculated and is distributed to count of votes machine, and anyone obtains any raw information that cannot obtain ballot paper after ballot paper.Use point sheet mode to send ballot paper, also avoided loaded down with trivial details cryptographic calculations and protocol interaction process.
2) ballot paper fail safe: ballot paper burst usage threshold mechanism, at least k platform count of votes machine just can recover ballot paper raw information, ensure that in election process, anyone cannot obtain election results in advance, realize the fail safe of ballot paper, and the mode that adopts threshold mechanism, also makes ballot paper have disaster tolerance speciality to a certain extent.
3) count of votes rapidity: the burst matrix that all count of votes machines are collected by election mechanism recovers after original ballot paper, by using decimal addition to calculate to the each coordinate of ballot paper matrix, can realize fast to every candidate's and whole ballot paper statistics.
Brief description of the drawings
Examples of the present invention will be described by way of reference to the accompanying drawings, wherein:
Fig. 1 is the pie graph of ballot paper matrix;
Fig. 2 is the pie graph of the ballot paper matrix after digitlization binary system transforms;
Fig. 3 is the pie graph of the ballot paper matrix of neotectonics during the burst of matrix calculates;
Fig. 4 is the ballot paper share matrix that whole count of votes machines are received;
Fig. 5 is that in specific embodiment, certain legal voter fills in complete ballot paper information structure figure.
Embodiment
Might as well suppose to carry out mchoosing telection form, have mposition candidate, need to select tthe final candidate in position.For a ballot paper of being filled in by legal voter, the candidate's gained vote information on ballot paper is considered as to an element (as corresponding in " agreeing with " numerical value " 1 ", " opposition " is " 0 "), extract these elements, with lindividual element is a line, total
Figure 730209DEST_PATH_IMAGE001
oK, last not enough figure place, with 0 polishing, is configured to the form of a matrix.
To the ballot paper information of matrix form implement based on interpolation polynomial ( k, n) threshold secret sharing technology, every ballot paper is split into nindividual share, each share is and the matrix form of ballot paper same structure, is distributed to nplatform count of votes computer, is only more than or equal to kthe share of platform count of votes computer just can recover ballot paper information, can also prevent like this fraud such as non-honest grade in count of votes process in ensureing ballot paper information security.
Encryption and the immediate processing method of describing electronics ballot paper information below in detail, comprise the steps:
1) computer is according to candidate's figure place structure ballot paper matrix
Supposing has mposition candidate, number of people due to be elected is tposition, the count of votes machine that needs acceptance to share secret information has nplatform.Might as well candidate with lposition is a line, total
Figure 613982DEST_PATH_IMAGE001
oK, when last column is less than lwhen row, not enough figure place, with 0 polishing, is so just configured to one × lmatrix form, the pie graph of ballot paper matrix is as shown in Figure 1.
2) the digitlization binary system that every voter ballot paper matrix that vote is selected on ballot equipment is carried out 0/1 form by ballot equipment transforms
Definition election only has the option of opposing/agreeing with (0/1) form, participation in the election voter uses electronic ballot equipment to every selection that candidate agrees with or opposes on this ballot paper, ballot equipment, after popular ballot finishes, changes into every voter ballot paper matrix that vote is selected on ballot equipment the digitlization binary-coded character of 0/1 form.The pie graph of the ballot paper matrix after digitlization binary system transforms as shown in Figure 2.
Described ballot equipment is made up of touch-screen type all-in-one and corresponding ballot software, and voter obtains after electronics ballot paper, clicks its wish candidate and complete submission on touch-screen.Ballot software according to voter the opposition to every candidate or agree with select convert 0/1 form to, successively all candidates of this ballot paper are carried out to aforesaid operations, completed ballot paper matrix digitlization binary system transform.
3) burst of ballot paper matrix calculates
If directly to the each element secret sharing in matrix, every ballot paper will carry out
Figure 881070DEST_PATH_IMAGE001
× linferior sharing, amount of calculation increases considerably.Might as well be with in matrix lclassify one group as, can be this
Figure 424047DEST_PATH_IMAGE001
row data form one
Figure 529537DEST_PATH_IMAGE001
× 1 matrix, × lmatrix conversion become
Figure 454823DEST_PATH_IMAGE001
× 1 matrix, is wherein considered as a binary number (0 and 1) candidate's gained vote information, and the data of every a line will be one l(this numerical value is 0 ~ 2 for the binary number of position l in-1 scope), fill up successively new matrix, the pie graph of the ballot paper matrix of neotectonics is as shown in Figure 3.
Because count of votes machine is total nplatform, might as well arrange one ( k, n) threshold structure, kfor threshold parameter, (based on Shamir Secret Sharing Scheme, the value of k is arbitrarily, is less than or equal to the n) data with every a line in matrix as long as meet s i ( i=1,2 ...,
Figure 168701DEST_PATH_IMAGE001
) as secret information, it is carried out to the secret sharing based on Lagrange interpolation polynomial:
This ballot paper matrix is total
Figure 27067DEST_PATH_IMAGE001
individual element
Figure 484593DEST_PATH_IMAGE007
, 0≤ s i ≤ 2 l -1, wherein i=1,2 ..., .Get a prime number p, meet p> nand p> 2 l -1.Selected pafter construct finite field gF( p)={ 0,1,2 ..., p-1} mod p, in finite field gF( p) choose at random nindividual different open numerical value x 1, x 2..., x n , above parameter can disclose.
In this finite field, choose at random k-the value of 1 need to be keep secret a 1, a 2..., a k-1 , and construct k-1 order polynomial
(1)
The element in ballot paper matrix s i ( i=1,2 ...,
Figure 592990DEST_PATH_IMAGE001
) in substitution multinomial (1) s, simultaneously respectively x 1, x 2..., x n substitution multinomial (1) xin, calculating can obtain
Figure 588627DEST_PATH_IMAGE008
4) burst matrix construction:
Utilize the 3rd) step obtains
Figure 569091DEST_PATH_IMAGE004
, build
Figure 890350DEST_PATH_IMAGE001
× 1 burst matrix
Figure 192150DEST_PATH_IMAGE005
:
Figure 257058DEST_PATH_IMAGE009
，
By burst matrix
Figure 92028DEST_PATH_IMAGE005
be distributed to jthe storage of platform count of votes machine, then destroy original ballot paper information, multinomial and k-the value of 1 need to be keep secret a 1, a 2..., a k-1 .
So just complete the encryption distribute work of every electronics ballot paper information, whole count of votes machines ( nplatform) the ballot paper share matrix received is as shown in Figure 4.
5) ballot paper reconstruct
In the count of votes stage, use nin platform count of votes machine at least kplatform count of votes machine is combined the burst matrix of receiving separately the ballot paper order that can recover line by line every row, and is less than kplatform count of votes machine cannot obtain any ballot paper information.Take out at least successively kthe each row of data of the burst matrix of platform count of votes machine, utilizes Lagrange interpolation polynomial
Figure 256293DEST_PATH_IMAGE006
(2)
Determine multinomial (1).For example: multinomial is q( x)= a 0+ a 1 x+ a 2 x 2, can calculate by the concrete numerical value of substitution, q( x 1)= s 1, q( x 2)= s 2, q( x 3)= s 3, then, even if destroy multinomial q( x), and still can reconstruct multinomial by these three dual points q( x), as follows:
Figure 560235DEST_PATH_IMAGE010
Multinomial (1) is determined rear numerical value 0 substitution, obtains secret information s= f(0), schange into string of binary characters, and insert the corresponding row in the blank ballot transforming through matrix, successively each row of data being carried out to above-mentioned calculating is each ballot paper of restructural.
6) ballot equipment to all voters' ballot paper information according to above-mentioned 3) to 5) step method of operation carries out the corresponding operating of ballot paper matrix, after all recovering, all ballot papers directly carry out the decimal addition on matrix, calculate each candidate's gained vote information, finally count after election results are all recovered all ballot papers and directly carry out the decimal addition on matrix, the gained vote information that calculates each candidate, finally counts election results.
Now said method is illustrated as follows:
Suppose and have an election, have 25 candidates, need to select 10 people, this ballot paper might as well be configured to the matrix of 5 × 5, l=5, m/ l=5, certain legal voter fills in complete ballot paper information structure figure as shown in Figure 5, wherein 1 agrees, and 0 makes difficulties.
Therefore the matrix A of this ballot paper is:
，
Further, the splicing of all elements of every a line, be considered as a binary character string, then be converted to decimal representation mode, we can be the matrix of matrix 5 × 5 abe converted into 5 × 1 matrix b, represent as follows:
Figure 354196DEST_PATH_IMAGE012
Suppose to have 5 count of votes machines, selected threshold parameter is 4, and threshold structure is (4,5).Due to 2 5-1=31,31>5, selected prime number p=37>31, thus be configured with confinement gF(37)=0,1,2 ..., 36}mod 37.In this finite field, choosing at random 5 can disclosed numerical value x 1, x 2..., x 5, simple for narrating, there is no harm in value x 1=1, x 2=2, x 3=3, x 4=4, x 5=5.
In finite field gF(37) on, choose at random again 3 numerical value a 1=15, a 2=26, a 3=9.Construct 3 order polynomials
f( x)=(9 x 3+26 x 2+15 x+ s) mod 37
In order matrix beach row element respectively substitute s, obtain 5 multinomials
f 1( x) = (9 x 3+26 x 2+15 x+8) mod 37
f 2( x) = (9 x 3+26 x 2+15 x+5) mod 37
f 3( x) = (9 x 3+26 x 2+15 x+22) mod 37
f 4( x) = (9 x 3+26 x 2+15 x+9) mod 37
f 5( x) = (9 x 3+26 x 2+15 x+12) mod 37
Will x 1=1, x 2=2, x 3=3, x 4=4, x 5=5 substitutions respectively f 1( x), obtain f 1(1)=21, f 1(2)=29, f 1(3)=12, f 1(4)=24, f 1(5)=8, are placed in respectively the first row of 55 × 1 corresponding burst matrixes.Method calculates according to this f 2(1) ~ f 2(5), f 3(1) ~ f 3(5), f 4(1) ~ f 4(5), f 5(1) ~ f 5(5).Finally obtain:
Figure 266526DEST_PATH_IMAGE013
Figure 792185DEST_PATH_IMAGE014
be distributed to the 1st count of votes machine,
Figure 949628DEST_PATH_IMAGE015
be distributed to the 2nd ...,
Figure 509922DEST_PATH_IMAGE016
be distributed to the 5th count of votes machine.Store completely, original ballot paper information and multinomial are all destroyed.
Need to add up ballot paper time, must there be at least 4 count of votes machines on the scene, be less than 4, cannot obtain any information.Might as well suppose to have obtained the information of front 4 count of votes machines.
By the given value 21,29,12 and 24 of the first row, obtain f 1(1)=21, f 1(2)=29, f 1(3)=12, f 1(4)=24, substitution formula
Figure 549652DEST_PATH_IMAGE018
Thereby obtain secret information s= f(0)=8, the first row data in ballot paper matrix are 8, same method is obtained the secret data of residue 4 row, construct ballot paper matrix, be converted into again binary representation form, this binary-coded character inserted successively in 5 × 5 blank ballot matrix, as shown in the table:
Figure 307523DEST_PATH_IMAGE019
So just, completed the reconstruct (being recovery process) of this ballot paper.

Claims (2)

1. the encryption of electronics ballot paper information and an immediate processing method, is characterized in that: comprise the following steps:
1) computer is according to candidate's figure place and name structure
Figure FDA0000487882550000013
ballot paper matrix, the figure place that wherein m is candidate,
Figure FDA0000487882550000017
for every a line candidate's figure place, when last column is less than
Figure FDA0000487882550000018
when row, not enough figure place is with 0 polishing;
2) the digitlization binary system that every voter ballot paper matrix that vote is selected on ballot equipment is carried out 0/1 form by ballot equipment transforms;
3) burst of ballot paper matrix calculates:
According to the number of units n of count of votes machine, (k, a n) threshold structure is set, k is threshold parameter, with the data S of every a line in ballot paper matrix i, wherein i=1,2 ...,
Figure FDA0000487882550000014
as secret information, it is carried out to the secret sharing based on Lagrange interpolation polynomial:
Get a prime number p, meet p>n and , construct finite field gf (p)=0,1,2 ..., p-1}modp chooses at random n different open numerical value x in finite field gf (p) 1, x 2..., x n, in this finite field, choose at random the value a of k-1 need to be keep secret 1, a 2..., a k-1, and construct k-1 order polynomial
f ( x ) = ( a k - 1 x k - 1 + a k - 2 x k - 2 + · · · + a 1 x + s ) mod p = ( s + Σ i = 1 k - 1 a i x i ) mod p - - - ( 1 )
The element S in ballot paper matrix i, wherein i=1,2 ...,
Figure FDA0000487882550000015
s in substitution multinomial (1), simultaneously respectively x 1, x 2..., x nin the x of substitution multinomial (1), calculate
Figure FDA0000487882550000012
4) burst matrix construction:
Utilize the 3rd) s that obtains of step ij, build
Figure FDA0000487882550000016
burst matrix α j, and by burst matrix α jbe distributed to the storage of j platform count of votes machine, then destroy the value a of original ballot paper information, multinomial and k-1 need to be keep secret 1, a 2..., a k-1;
5) ballot paper reconstruct:
In the count of votes stage, take out successively at least each row of data of the burst matrix of k platform count of votes machine, utilize following Lagrange interpolation polynomial:
f i ( x ) = Σ j = 1 k s ij ( Π i ≠ j , i = 1 k x - x i x j - x i ) mod p - - - ( 2 )
Determine multinomial (1), multinomial (1) is determined rear the x in numerical value 0 substitution multinomial (1), obtain secret information s=f (0), s is changed into string of binary characters, and insert the corresponding row in the blank ballot transforming through matrix;
6) ballot equipment to all voters' ballot paper information according to above-mentioned 3) to 5) step method of operation carries out the corresponding operating of ballot paper matrix, after all recovering, all ballot papers directly carry out the decimal addition on matrix, the gained vote information that calculates each candidate, finally counts election results.
2. encryption and the immediate processing method of electronics ballot paper information according to claim 1, it is characterized in that: described ballot equipment is made up of touch-screen type all-in-one and corresponding ballot software, voter obtains after electronics ballot paper, on touch-screen, click its wish candidate and complete submission, the opposition to every candidate or agree with selecting to convert 0/1 form to according to voter of ballot software.
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CN106373251A (en) * 2016-08-30 2017-02-01 中科院成都信息技术股份有限公司 Electronic vote counting method based on secret sharing
CN109949472A (en) * 2019-02-28 2019-06-28 阿里巴巴集团控股有限公司 System, method and apparatus for ballot
CN110035057A (en) * 2019-02-28 2019-07-19 阿里巴巴集团控股有限公司 System, method and apparatus for ballot
CN110555933B (en) * 2019-07-31 2021-04-30 中钞信用卡产业发展有限公司杭州区块链技术研究院 Electronic voting method, device, equipment and computer storage medium
CN114299656B (en) * 2020-09-23 2023-08-01 成都中科信息技术有限公司 Voting method
CN114299655B (en) * 2020-09-23 2023-09-05 成都中科信息技术有限公司 Electronic voting system and working method thereof

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CN101276524A (en) * 2007-03-23 2008-10-01 株式会社东芝 Secret sharing apparatus and method
CN101650644A (en) * 2009-04-10 2010-02-17 北京邮电大学 Galois field multiplying unit realizing device

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CN101650644A (en) * 2009-04-10 2010-02-17 北京邮电大学 Galois field multiplying unit realizing device

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