CN102857339B - Secret distribution sharing and recovery recombining method based on sequences - Google Patents
Secret distribution sharing and recovery recombining method based on sequences Download PDFInfo
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- CN102857339B CN102857339B CN201210335986.9A CN201210335986A CN102857339B CN 102857339 B CN102857339 B CN 102857339B CN 201210335986 A CN201210335986 A CN 201210335986A CN 102857339 B CN102857339 B CN 102857339B
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- secret
- share
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- order
- described secret
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Abstract
The invention provides a secret distribution sharing and recovery recombining method based on sequences, which needs to adopt a correct sequence to recombine and recover various secret portions obtained after splitting to recover original secrets; any one false sequence combination can cause the failure of recovering the secret, so that even the attacker gets all portions, the original secret still cannot be illegally recovered through calculation; and the security of the secret is effectively ensured.
Description
Technical field
The present invention relates to field of information security technology, the secret distribution be specially based on order is shared and recovers recombination method.
Background technology
At present, each share that original private obtains after often passing fractionation carries out keeping by multiple personnel, when needs original private time, then each custodial staff provides several required shares can carry out recalculating obtaining original private, this is also the basic thought of threshold schemes technology, but in this process, each necessary fractionation share may to be leaked in management process or custodial staff carries out ganging up and causes original private illegally to be recovered.
Summary of the invention
For the problems referred to above, the secret distribution that the invention provides based on order is shared and recovers recombination method, though its can make assailant obtain all shares after also cannot recover original private by calculating privately, effectively ensure that secret fail safe.
Its technical scheme is such: it is characterized in that: it comprises following operating procedure:
(1), define:
Define secret k, described secret k is divided into some shares
, wherein
,
represent that described secret k splits into
data total collection after individual share, by described set
in each share be presented to respectively
individual personnel carry out keeping, wherein
, and the secret number that each personnel obtain is
individual, wherein
if provide the necessary share set of the described secret k of reconstruct
, then described secret k can be reconstructed; If provide
, then described secret k can not be reconstructed; And in the described secret of reconstruct
process in,
be orderliness requirement, run counter to the order of making an appointment and then can not reconstruct described secret k, wherein subscript
for natural number, represent the certain share number at the described secret k needs of reconstruct, that meet this definition is exactly order threshold schemes (k, n, t, m, p);
(2), split:
Described secret k uses Lagrange interpolation polynomial to carry out function
split computing and obtain each share
, and calculate each multinomial
, the described multinomial obtained
be stored in trusted party, file layout is:
wherein subscript
represent respectively
required share number in the described secret k order of layer reconstruct,
for reconstructing the combination number of plies that described secret k must experience, any described share after fractionation
be distributed to the keeping of each validated user;
(3), recover:
Definition counting variable, uses binary operation to calculate described share according to the order of defined
reconstruct after combinatorial operation is secret
, then carry out judging the described counting variable number of definition and the certain share number reconstructing described secret k and need
whether identical, if identical, described reconstruct is secret
be exactly described secret k, if different, then continue to use binary operation to calculate described reconstruct secret
until draw final described secret k;
(4), safety analysis:
Utilize computing formula to carry out derivation to draw:
,
for
the combination form number of individual share reconstruct order,
be
individual share participates in the total number of assembled arrangement that order reconstruct needs, and draws
be worth with
growth and factorial rank increase.
It is further characterized in that: described step 3 also comprises:
(3.1), suppose that counting variable is respectively
,
,
;
(3.2), when
time,
;
When
time,
;
Wherein
，
,
computing is binary operator,
for the set of the share after the described secret k fractionation of each row;
(3.3),
,
, wherein
for described set
the number of middle share;
(3.4), judge
whether set up, if set up,
be exactly described secret k, algorithm terminates; If
be false, then continue to jump to described step (3.2) and continue this algorithm, until calculate described secret k.
The invention has the beneficial effects as follows, the secret number that in these threshold schemes, each personnel obtain is
, and this that any personnel obtain
individual share may reconstruct by full entry, also all reconstruct may do not participated in, perhaps part participates in restructuring procedure, assailant is also unclear in addition has how many shares on earth, even if know the number of members of keeping share, but do not know the number of all shares, thus add the difficulty that assailant obtains enough shares, simultaneously through safety analysis, participate in the total number of assembled arrangement that order reconstruct needs
be with
growth and factorial rank increases, even assailant has grasped all fractionation shares, but to own owing to attempting one by one
individual number of combinations is impossible, and the order that each share participates in reconstruct is stored in trusted party, the permission that effectively prevent without trusted party after each legal personnel taking care of secret shadow gang up illegally recovers original private privately, substantially increase secret fail safe, each security fields can be widely used in.
Accompanying drawing explanation
Fig. 1 is definition procedure flow chart of the present invention;
Fig. 2 is recovery process flow chart of the present invention;
Fig. 3 is that secret shadow analyzes schematic diagram;
Fig. 4 is that secret shadow analyzes schematic diagram;
Fig. 5 is that secret shadow analyzes schematic diagram.
Embodiment
As shown in Figure 1 and Figure 2, the present invention includes following operating procedure:
(1), define:
Define secret k, secret k is divided into some shares
, wherein
,
represent that secret k splits into
data total collection after individual share, will gather
in each share be presented to respectively
individual personnel carry out keeping, wherein
, and the secret number that each personnel obtain is
individual, wherein
if provide the necessary share set of the secret k of reconstruct
, then secret k can be reconstructed; If provide
, then secret k can not be reconstructed; And it is secret in reconstruct
process in,
be orderliness requirement, run counter to the order of making an appointment and then can not reconstruct secret k, wherein subscript
for natural number, represent the certain share number at the secret k needs of reconstruct, that meet this definition is exactly order threshold schemes (k, n, t, m, p);
(2), split:
Secret k uses Lagrange interpolation polynomial to carry out function
split computing and obtain each share
, and calculate each multinomial
, multinomial
be specially:
, the multinomial obtained
be stored in trusted party, file layout is:
wherein subscript
represent respectively
required share number in the secret k order of layer reconstruct,
for reconstructing the combination number of plies that secret k must experience, any share after fractionation
be distributed to the keeping of each validated user;
(3), recover:
Definition counting variable, uses binary operation to calculate share according to the order of defined
reconstruct after combinatorial operation is secret
, then carry out judging the counting variable number of definition and the certain share number reconstructing secret k and need
whether identical, if identical, reconstruct secret
be exactly secret k, if different, then continue to use binary operation to calculate reconstruct secret
until draw final secret k;
Step (3) also comprises:
(3.1), suppose that counting variable is respectively
,
,
;
(3.2), when
time,
;
When
time,
;
Wherein
，
,
computing is binary operator,
for each arranges the set of the share after secret k fractionation;
(3.3),
,
, wherein
for set
the number of middle share;
(3.4), judge
whether set up, if set up,
be exactly secret k, algorithm terminates; If
be false, then continue to jump to step (3.2) and continue this algorithm, until calculate secret k.
(4), safety analysis:
Utilize computing formula to carry out derivation to draw:
,
for
the combination form number of individual share reconstruct order,
be
individual share participates in the total number of assembled arrangement that order reconstruct needs, as shown in table 1:
Draw
be worth with
growth and factorial rank increases, even then assailant has grasped all fractionation shares, but attempt all one by one
individual number of combinations is impossible, and therefore secret k has the fail safe guaranteed.
Below order threshold schemes (k, 4, t, 4, p) in situation in conjunction with the embodiments describe the present invention is based on order secret distribution share and recover recombination method:
Embodiment 1
As shown in Figure 3, share
orderly composition ground floor share, the order that this layer of all share is preserved according to trusted party is first reconstructed process, produces
, namely
; Then
according to the reconstruct order of making an appointment with all shares of lower one deck be successively
orderly group is reconstructed again, produces final
, namely
,
be exactly originally by the secret k split.
Embodiment 2
As shown in Figure 4, share
orderly group of composition ground floor share, the order that this layer of all share is preserved according to trusted party is first reconstructed process, generation
, namely
; Then
according to the reconstruct order of making an appointment with all shares of lower one deck be successively
orderly group is reconstructed again, produces
, namely
,
according to the reconstruct order of making an appointment with all shares of lower one deck be again
orderly group is reconstructed again, produces final
, namely
,
be exactly originally by the secret k split.
Embodiment 3
As shown in Figure 5, share
orderly group of composition ground floor share, the order that this layer of all share is preserved according to trusted party is first reconstructed process, produces final
, namely
,
be exactly originally by the secret k split.
Claims (1)
1. the secret distribution based on order is shared and recovers recombination method, it is characterized in that: it comprises following operating procedure:
(1), define:
Define secret k, described secret k is divided into some shares
, wherein
,
represent described secret k split into n share after data total collection, by described set
in each share be presented to t personnel respectively and carry out keeping, wherein
, and the secret number that each personnel obtain is p, wherein
if provide the necessary share set of the described secret k of reconstruct
, then described secret k can be reconstructed; If provide
, then described secret k can not be reconstructed; And in the process of the described secret k of reconstruct,
be orderliness requirement, run counter to the order of making an appointment and then can not reconstruct described secret k, wherein subscript m is natural number, represents the certain share number at the described secret k needs of reconstruct, and that meet this definition is exactly order threshold schemes (k, n, t, m, p);
(2), split:
Described secret k uses Lagrange interpolation polynomial f to carry out function fractionation computing and obtains each share
, and calculate each multinomial
, the described multinomial obtained
be stored in trusted party, file layout is:
Wherein subscript
represent respectively
required share number in the described secret k order of layer reconstruct, the combination number of plies that q must experience for the described secret k of reconstruct, any described share after fractionation
be distributed to the keeping of each validated user;
(3), recover:
Definition counting variable, uses binary operation to calculate described share according to the order of defined
reconstruct after combinatorial operation is secret
, then carry out judging the described counting variable number m that defines with whether reconstruct the certain share number m that described secret k needs identical, if identical, described reconstruct secret
be exactly described secret k, if different, then continue to use binary operation to calculate described reconstruct secret
until draw final described secret k;
(4), safety analysis:
Utilize computing formula to carry out derivation to draw:
, S is the combination form number of n share reconstruct order, participate in total L is n share the assembled arrangement number that order reconstruct needs, and draws the factorial rank increase with the growth of n of L value;
Described step (3) also comprises:
(3.1), suppose counting variable be respectively i,
;
(3.2), when
time,
;
When
time,
;
Wherein
,
computing is binary operator,
for the set of the share after the described secret k fractionation of each row;
(3.3),
, wherein
for described set
the number of middle share;
(3.4), judge
whether set up, if set up,
be exactly described secret k, algorithm terminates; If
be false, then continue to jump to described step (3.2) and continue this algorithm, until calculate described secret k.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210335986.9A CN102857339B (en) | 2012-09-12 | 2012-09-12 | Secret distribution sharing and recovery recombining method based on sequences |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210335986.9A CN102857339B (en) | 2012-09-12 | 2012-09-12 | Secret distribution sharing and recovery recombining method based on sequences |
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| Publication Number | Publication Date |
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| CN102857339A CN102857339A (en) | 2013-01-02 |
| CN102857339B true CN102857339B (en) | 2015-06-03 |
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Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105897409B (en) * | 2014-05-13 | 2019-05-10 | 无锡科技职业学院 | A method of the management of the key based on crypto chip |
| US9906505B2 (en) * | 2015-05-08 | 2018-02-27 | Nxp B.V. | RSA decryption using multiplicative secret sharing |
| CN107979461B (en) * | 2017-10-27 | 2020-07-17 | 财付通支付科技有限公司 | Key retrieving method, device, terminal, key escrow server and readable medium |
| CN107908932B (en) * | 2017-12-10 | 2020-10-13 | 吕文华 | Digital currency anti-counterfeiting and verification method, system and equipment based on L algorithm |
| CN109191095A (en) * | 2018-10-23 | 2019-01-11 | 湖北工业大学 | It is a kind of can quick localization of internal attacker electronic cash distribution method and system |
| CN110688670B (en) * | 2019-09-04 | 2023-06-23 | 创新先进技术有限公司 | Data processing method and device and electronic equipment |
| CN111049644B (en) * | 2019-10-22 | 2021-03-23 | 贵州财经大学 | Rational and fair secret information sharing method based on confusion incentive mechanism |
| CN111182171B (en) * | 2019-12-16 | 2022-03-15 | 成都信息工程大学 | Image secret sharing information processing method and system for staged decryption |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6182214B1 (en) * | 1999-01-08 | 2001-01-30 | Bay Networks, Inc. | Exchanging a secret over an unreliable network |
| CN101425902A (en) * | 2008-11-12 | 2009-05-06 | 电子科技大学 | Threshold digital signature method and system having forward security |
-
2012
- 2012-09-12 CN CN201210335986.9A patent/CN102857339B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6182214B1 (en) * | 1999-01-08 | 2001-01-30 | Bay Networks, Inc. | Exchanging a secret over an unreliable network |
| CN101425902A (en) * | 2008-11-12 | 2009-05-06 | 电子科技大学 | Threshold digital signature method and system having forward security |
Non-Patent Citations (3)
| Title |
|---|
| 一个新的(t, n)门限多级秘密共享方案;于丹 等;《计算机工程与应用》;20070911;第43卷(第26期);142-143页 * |
| 一种改进的基于拉格朗日插值的(t,n)门限秘密共享;戴元军 等;《北京邮电大学学报》;20040430;第27卷(第2期);全文 * |
| 门限多重秘密共享方案;许春香 等;《电子学报》;20041031;第32卷(第10期);全文 * |
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| CN102857339A (en) | 2013-01-02 |
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Granted publication date: 20150603 Termination date: 20170912 |