CN104735081A - Method and system for outsourcing security mode indexes in cloud environment - Google Patents

Method and system for outsourcing security mode indexes in cloud environment Download PDF

Info

Publication number
CN104735081A
CN104735081A CN201510159658.1A CN201510159658A CN104735081A CN 104735081 A CN104735081 A CN 104735081A CN 201510159658 A CN201510159658 A CN 201510159658A CN 104735081 A CN104735081 A CN 104735081A
Authority
CN
China
Prior art keywords
user
server
rand
servers
result
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201510159658.1A
Other languages
Chinese (zh)
Inventor
叶俊
兰恒友
林旭东
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sichuan University of Science and Engineering
Original Assignee
Sichuan University of Science and Engineering
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sichuan University of Science and Engineering filed Critical Sichuan University of Science and Engineering
Priority to CN201510159658.1A priority Critical patent/CN104735081A/en
Publication of CN104735081A publication Critical patent/CN104735081A/en
Pending legal-status Critical Current

Links

Classifications

    • 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
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • 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
    • H04L63/06—Network architectures or network communication protocols for network security for supporting key management in a packet data network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00—Network arrangements or protocols for supporting network services or applications
    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • H04L67/1097—Protocols in which an application is distributed across nodes in the network for distributed storage of data in networks, e.g. transport arrangements for network file system [NFS], storage area networks [SAN] or network attached storage [NAS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Hardware Design (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer And Data Communications (AREA)

Abstract

The invention relates to the technical field of cloud computing, and discloses a method for outsourcing security mode indexes in a cloud environment. The method specially includes the steps that u<a> is split into a formula shown in the specification by a user T according to pairs returned by Rand, the formula is sent to an idle server U1 and an idle server U2 which are not collaborated to be computed, the two servers return the computing results to the user T, and the user T verifies the returned results. By the adoption of the method, calling of Rand is small, logic splitting of u<a> is simple, the computing amount is small, and the detection rate can reach 100%. The invention further discloses a system for outsourcing the security mode indexes in the cloud environment.

Description

Safe module exponent outsourcing method and system under a kind of cloud environment
Technical field
The present invention relates to field of cloud computer technology, safe module exponent outsourcing method and system under particularly relating to a kind of cloud environment.
Background technology
In recent years, cloud computing is fast-developing in IT field, has good application in industrial technical field, for the problem solving computational resource limited brings very large hope.Under cloud environment, outsourcing calculates the mode allowing resource-constrained user can select to pay and loaded down with trivial details calculation task is contracted out to the abundant server calculating of computational resource.But outsourcing just means that user data control is by self transfer to cloud service provider, and inevitably create new safety problem: the first, some privacy of user may be revealed; The second, server also may correctly not calculate for various reasons, thus causes huge loss to user.
First, in order to protect the privacy of user, before data outsourcing, user blinds calculative data, although this makes server calculate, and does not know that user needs what is, thus carries out secret protection to the input and output of user.Secondly, because the excitation on economic returns is inadequate, server may calculate halfheartedly.It or reduce calculation times, return the result that user one is wrong, or do not calculate and return user's random value.In this case, user needs the correctness of verification computation result.At this moment, user's need the result of some precomputations to be used for value that authentication server returns, and require that the amount of calculation of the precomputation of user and proof procedure will be far smaller than user and be contracted out to server and do the amount of calculation calculated.
Module exponent computing is normally taken advantage of formed by a series of mould.In public key cryptography, in order to safety, we select a very large modulus usually.Like this, make user be difficult to take advantage of with simple mould calculate module exponent, namely use the most efficient algorithm also to need to consume a large amount of computing times.Module exponent computing is one of computing the most basic in cryptography, needs to use a large amount of module exponent computings in polynomial computation and Bilinear map calculate, and is therefore very necessary to the outsourcing research of module exponent computing.
In recent years, outsourcing calculates the focus having become research, and many scholars have done deep research in this respect.Safe module exponent expoeridium has been applied in many cryptographic schemes.At present, most of module exponent outsourcing scheme is all that the fixing end is constant or fixation index is constant.2005, S.Hohenberger etc. are at S.Hohenberger and A.Lysyanskaya.How to securely outsource cryptographic computations.In TCC, 2005, LNCS, volume3378, pages 264 – 282.Springer-Verlag, the classical module exponent outsourcing numerical procedure calculated based on precomputation and server-aided is proposed in 2005. (hereinafter referred to as existing methods 1), to be considered in module exponent outsourcing scheme good one, to obtain the evaluation that academia is very high.But this scheme only has 50% to the verification and measurement ratio of result correctness under the server environment of laziness.After this, the garbled Circuit such as Chung devises a user to carry out verification computation result scheme by precomputation, but the efficiency of Garbled Circuit is too low.Propose at M.Barbosa and P.Farshim in 2012 and solve validation problem by the method for homomorphic cryptography, but same efficiency is lower.The same year, Chen etc. improved the program, X.Chen, J.Li, J.Ma, Q.Tang, and Wenjing Lou.New algorithmsfor secure outsourcing of modular exponentiations.In Proc.of 17 theuropeanSymposium on Research in Computer Security, Pisa, Italy, volume 7459, pages541 – 556.Springer-Verlag, September 2012 (hereinafter referred to as existing method 2), the verification and measurement ratio of the result obtained under cloud environment by lazy server has risen to 2/3 from 1/2, and efficiency increases.But still have many times user to be difficult to the correctness of the result.
Existing disclosed application number is the patent application of 201210191461.2, it discloses the safe module exponent outsourcing computational algorithm in a kind of cloud computing, but the verifiability of the method equally also can only reach 1/2 or 2/3.The method also exists the call number of Rand many simultaneously, causes the problem of calculation of complex.
Summary of the invention
There is verifiability for outsourcing method of the prior art low, the technical problem that the deception of lazy server to user is this kind of cannot be found, safe module exponent outsourcing method and system under the invention discloses a kind of cloud environment.
Technical scheme of the present invention is as follows:
Safe module exponent outsourcing method under a kind of cloud environment, it is specially: user T according to Rand return right, by u abe split as then the lazy server U that two are not colluded with is sent to respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
Further, said method is specially:
Step 1, user T call subroutine Rand twice, obtain two right with order h = g t 2 ;
It is right that step 2, user T use subprogram Rand to return, by u asplit, then user T calculates b, b is met, t 2a=t 1b, such f b=h a; Wherein: v=u/h, s 1=a-l 1, s 2=a-l 2;
Step 3, user T send computation requests to two servers:
U 1(b,f)→f b， U 1 ( l 1 , v ) &RightArrow; v l 1 , U 1 ( s 1 , v ) &RightArrow; v s 1 ;
U 2(b,f)→f b， U 2 ( l 2 , v ) &RightArrow; v l 2 , U 2 ( s 2 , v ) &RightArrow; v s 2 ;
Whether following two formulas of step 4, user T checking are set up,
U 1(b, f)=U 2(b, f), U 1(l 1, v) U 2(l 2, v)=U 1(s 1, v) U 2(s 2, v), two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
Further, when judgement two servers all do not have user cheating T, user T calculates
Further, when judgement two servers all do not have user cheating T, user T calculates
Under the invention also discloses a kind of cloud environment, the outer packet system of safe module exponent, is characterized in that specifically comprising user T, two server U 1and U 2, and Rand subroutine module, described user T be used for according to Rand return right, by u abe split as then the lazy server U that two are not colluded with is sent to respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
Further, above-mentioned user T call subroutine Rand twice, obtain two right with order it is right that user T uses subprogram Rand to return, by u asplit, then user T calculates b, b is met, t 2a=t 1b, such f b=h a; Wherein: v=u/h, s 1=a-l 1, s 2=a-l 2; User T sends computation requests to two servers:
U 1(b,f)→f b， U 1 ( l 1 , v ) &RightArrow; v l 1 , U 1 ( s 1 , v ) &RightArrow; v s 1 ;
U 2(b, f) → f b, user T verifies whether following two formulas are set up,
U 1(b, f)=U 2(b, f), U 1(l 1, v) U 2(l 2, v)=U 1(s 1, v) U 2(s 2, v), two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
By adopting above technical scheme, beneficial effect of the present invention is: in the present invention, two servers all return f bvalue, if the result that two lazy servers of not colluding with return is inconsistent, then can judge that presence server is cheated user immediately.If result is consistent, then user continues checking whether set up.In this computational process, if wherein the server of any one laziness decreases calculating, or do not calculate and return user's random value, so this just can not pass through formula through the correct result calculated checking.If the server of two lazinesses of not colluding with all correctly does not calculate, the formula that the result that such two servers return can be just the probability set up is insignificant.Therefore the server of two lazinesses of not colluding with all can not be cheated user.Once lazy server returns user's error result, user can go out with the Probability Detection of 100%.Therefore the verification and measurement ratio of result correctness is 100%.Method of the present invention is few to calling of Rand, to u alogic split simple, amount of calculation is little, and verification and measurement ratio can reach 100%.
Accompanying drawing explanation
Fig. 1 is the system architecture schematic diagram of outsourcing module exponent method of the present invention.
Embodiment
The specific embodiment of the present invention is described in detail below in conjunction with Figure of description.
Suppose p, q is two Big prime, q|p-1, and u q=1mod p, provides arbitrary index and the truth of a matter calculate u amod p, requires in outsourcing computational process, require that the value of a and u is to U 1, U 2maintain secrecy.This is the requirement of safe module exponent outsourcing method.
The system architecture schematic diagram of outsourcing module exponent method of the present invention as shown in Figure 1.There are four participant: subprogram Rand in the present invention, user T, two lazy server U do not colluded with 1and U 2.Subprogram Rand: that calls energy honesty returns one at random to (t, g at every turn t) mod p, by can computational efficiency be improved to calling of Rand.
Server: computing capability is very powerful, but be not completely believable, the result that user one is correct may be returned, also may return a random value.
User T is right for what return according to Rand, by u abe split as then the lazy server U that two are not colluded with is sent to respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
Further, above-mentioned user T call subroutine Rand twice, obtain two right with order it is right that user T uses subprogram Rand to return, by u asplit, then user T calculates b, b is met, t 2a=t 1b, such f b=h a; Wherein: v=u/h, s 1=a-l 1, s 2=a-l 2; User T sends computation requests to two servers:
U 1(b，f)→f b， U 1 ( l 1 , v ) &RightArrow; v l 1 , U 1 ( s 1 , v ) &RightArrow; v s 1 ;
U 2(b, f) → f b, user T verifies whether following two formulas are set up,
U 1(b, f)=U 2(b, f), U 1(l 1, v) U 2(l 2, v)=U 1(s 1, v) U 2(s 2, v), two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
Safe module exponent outsourcing method under the invention discloses a kind of cloud environment, it is specially: user T according to Rand return right, by u abe split as then the lazy server U that two are not colluded with is sent to respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
It specifically comprises the following steps:
Step 1, user T call subroutine Rand twice, obtain two right with order h = g t 2 ;
It is right that step 2, user T use subprogram Rand to return, by u asplit, then user T calculates b, b is met, t 2a=t 1b, such f b=h a; Wherein: v=u/h, s 1=a-l 1, s 2=a-l 2;
Step 3, user T send computation requests to two servers:
U 1(b,f)→f b， U 1 ( l 1 , v ) &RightArrow; v l 1 , U 1 ( s 1 , v ) &RightArrow; v s 1 ;
U 2(b,f)→f b， U 2 ( l 2 , v ) &RightArrow; v l 2 , U 2 ( s 2 , v ) &RightArrow; v s 2 ;
Whether following two formulas of step 4, user T checking are set up,
U 1(b, f)=U 2(b, f), U 1(l 1, v) U 2(l 2, v)=U 1(s 1, v) U 2(s 2, v), two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
Further, said method also comprises when judgement two servers all do not have user cheating T, and user T calculates U a = v l 1 v s 1 h a .
In like manner, user T also can be allowed to calculate
In the present invention, two servers all return f bvalue, if the result that two lazy servers of not colluding with return is inconsistent, then can judge that presence server is cheated user immediately.If result is consistent, then user continues checking whether set up.In this computational process, if wherein the server of any one laziness decreases calculating, or do not calculate and return user's random value, so this just can not pass through formula through the correct result calculated checking.If the server of two lazinesses of not colluding with all correctly does not calculate, the formula that the result that such two servers return can be just the probability set up is insignificant.Therefore the server of two lazinesses of not colluding with all can not be cheated user.Once lazy server returns user's error result, user can go out with the Probability Detection of 100%.Therefore the verification and measurement ratio of result correctness is 100%.Method of the present invention is few to calling of Rand, to u alogic split simple, amount of calculation is little, and verification and measurement ratio can reach 100%.
Contrast the difference of existing method 1 and existing method 2 and present patent application below, thus describe technology contents of the present invention and effect in detail.
Under lazy server environment, existing method 1 and 2 be calculate and checking method separately, so cause the checking of result of calculation correctness to reach 100%.This method be the method that calculation and demonstration combines, to u alogic split simple, be that first energy can the whether correct method of 100% verification computation result under the server environment of laziness.
In existing method 1, first user calls Rand twice, obtains (α, g α) and (β, g b).Make v=g α, v b=g βwherein b=beta/alpha.
Then by u asplit, u a=(vw) a=v bv cw a=v b(fh) cw dw e=v bf ch cw dw e, wherein w=u/v, b+c=a, d+e=a.Now v b=g β, user need not be contracted out to server and calculate.
User calls Rand tetra-times again, obtains with f c, h c, w d, w ebe the server being contracted out to the laziness that two are not colluded with respectively, two servers calculate f respectively c, h c, w d, w ein two, then result is returned to user.
User is with any order request server U 1calculate
U 1(d,w)→w d，
U 1(c,f)→f c，
U 1 ( t 1 / r 1 , g r 1 ) &RightArrow; g t 1 ,
U 1 ( t 1 / r 2 , g r 2 ) &RightArrow; g t 2 .
User is with any order request server U 2calculate
U 2(e,w)→w e，
U 2(c,h)→h c，
U 2 ( t 1 / r 1 , g r 1 ) &RightArrow; g t 1 ,
U 2 ( t 1 / r 2 , g r 2 ) &RightArrow; g t 2 .
Do not relate to f in the process c, h c, w d, w ethe checking of result of calculation.Like this for f c, h c, w d, w eresult of calculation, user is cannot the correctness of testing result.In this algorithm, user allows the server of two lazinesses of not colluding with calculate four values with random sequence altogether respectively, wherein these two can be detected, and other result of calculation cannot detect, and therefore the verification and measurement ratio of result correctness is
In existing method 2, first user calls Rand twice, obtains (α, g α) and (β, g β).Make μ=g β.
Then by u asplit, u a = ( vw ) a = g aa w a = g &beta; g &gamma; w a = &mu; g &gamma; w k w l , Wherein w=u/v, γ=a alpha-beta, k+l=a.Now μ=g β, user need not be contracted out to server and calculate.
User calls Rand tri-times again, obtains with g g, w k, w lbe contracted out to two servers, then result returned to user.
User is with any order request server U 1calculate
U 1 ( t 2 / t 1 , g t 1 ) &RightArrow; g t 2 ,
U 1 ( &gamma; / r 3 , g r 3 ) &RightArrow; g &gamma; ,
U 1(l,w)→w l。
User is with any order request server U 2calculate
U 2 ( t 2 / t 1 , g t 1 ) &RightArrow; g t 2 ,
U 2 ( &gamma; / r 3 , g r 3 ) &RightArrow; g &gamma; ,
U 2(k,w)→w k。
Do not relate to w in the process k, w lthe checking of result of calculation.Like this for w k, w lresult of calculation, user is cannot the correctness of testing result.In this algorithm, user allows the server of two lazinesses of not colluding with calculate three values with random sequence altogether respectively, and wherein two can be detected, and another one result of calculation cannot detect, and therefore the verification and measurement ratio of result correctness is
The present invention compares with method in prior art
Specific embodiment above-mentioned above; object of the present invention, technical scheme and beneficial effect are further described; be understood that; more than above are only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (6)

1. a safe module exponent outsourcing method under cloud environment, it is specially: user T according to Rand return right, will be split as , then send to the lazy server U that two are not colluded with respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
2. safe module exponent outsourcing method under cloud environment as claimed in claim 1, is characterized in that described method is specially:
Step 1, user T call subroutine Rand twice, obtain two right with , order , ;
It is right that step 2, user T use subprogram Rand to return, will split, , then user T calculates , make meet, , like this ; Wherein: , , ;
Step 3, user T send computation requests to two servers:
， ， ；
， ， ；
Whether following two formulas of step 4, user T checking are set up,
, , two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
3. safe module exponent outsourcing method under cloud environment as claimed in claim 2, it is characterized in that described method also comprises when judgement two servers all do not have user cheating T, user T calculates .
4. safe module exponent outsourcing method under cloud environment as claimed in claim 2, it is characterized in that described method also comprises when judgement two servers all do not have user cheating T, user T calculates .
5. the outer packet system of safe module exponent under cloud environment, is characterized in that specifically comprising user T, two server U 1and U 2, and Rand subroutine module, described user T be used for according to Rand return right, will be split as , then send to the lazy server U that two are not colluded with respectively 1and U 2calculate, result of calculation is returned to user T by two servers, and user T verifies the result returned.
6. the outer packet system of safe module exponent under cloud environment as claimed in claim 5, is characterized in that described user T call subroutine Rand twice, obtain two right with , order , ; It is right that user T uses subprogram Rand to return, will split, , then user T calculates , make meet, , like this ; Wherein: , , ; User T sends computation requests to two servers:
， ， ；
, , ; User T verifies whether following two formulas are set up,
, , two equatioies are set up, then judge that server does not have user cheating T, otherwise, judge that there is lazy server does not correctly calculate.
CN201510159658.1A 2015-04-07 2015-04-07 Method and system for outsourcing security mode indexes in cloud environment Pending CN104735081A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201510159658.1A CN104735081A (en) 2015-04-07 2015-04-07 Method and system for outsourcing security mode indexes in cloud environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201510159658.1A CN104735081A (en) 2015-04-07 2015-04-07 Method and system for outsourcing security mode indexes in cloud environment

Publications (1)

Publication Number Publication Date
CN104735081A true CN104735081A (en) 2015-06-24

Family

ID=53458516

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201510159658.1A Pending CN104735081A (en) 2015-04-07 2015-04-07 Method and system for outsourcing security mode indexes in cloud environment

Country Status (1)

Country Link
CN (1) CN104735081A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105119929A (en) * 2015-09-09 2015-12-02 四川理工学院 Safe mode index outsourcing method and system under single malicious cloud server
CN106453276A (en) * 2016-09-23 2017-02-22 南京理工大学 Safe modular exponentiation outsourcing computing method based on single server
CN108521396A (en) * 2018-02-09 2018-09-11 天津职业技术师范大学 The blind operation method of privacy information
CN110336837A (en) * 2019-08-06 2019-10-15 福州大学 A kind of the cloud secret protection outsourcing computing system and its calculation method of practicability

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102750129A (en) * 2012-06-11 2012-10-24 西安电子科技大学 Security model index outsourcing computing algorithm in cloud computing
CN103001957A (en) * 2012-11-26 2013-03-27 广州大学 Key generation method, device and server

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102750129A (en) * 2012-06-11 2012-10-24 西安电子科技大学 Security model index outsourcing computing algorithm in cloud computing
CN103001957A (en) * 2012-11-26 2013-03-27 广州大学 Key generation method, device and server

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
JUN YE，XIAOFENG CHEN: "An Improved Algorithm for Secure Outsourcing of Modular Exponentiations", 《2015 29TH INTERNATIONAL CONFERENCE ON ADVANCED INFORMATION NETWORKING AND APPLICATIONS WORKSHOPS》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105119929A (en) * 2015-09-09 2015-12-02 四川理工学院 Safe mode index outsourcing method and system under single malicious cloud server
CN105119929B (en) * 2015-09-09 2019-02-01 四川理工学院 Safe module exponent outsourcing method and system under single malice Cloud Server
CN106453276A (en) * 2016-09-23 2017-02-22 南京理工大学 Safe modular exponentiation outsourcing computing method based on single server
CN106453276B (en) * 2016-09-23 2019-11-29 南京理工大学 A kind of compound module exponent outsourcing calculation method of safety based on single server
CN108521396A (en) * 2018-02-09 2018-09-11 天津职业技术师范大学 The blind operation method of privacy information
CN108521396B (en) * 2018-02-09 2021-02-26 天津职业技术师范大学 Blind operation method for private information
CN110336837A (en) * 2019-08-06 2019-10-15 福州大学 A kind of the cloud secret protection outsourcing computing system and its calculation method of practicability
CN110336837B (en) * 2019-08-06 2020-10-09 福州大学 Practical cloud privacy protection outsourcing computing system and computing method thereof

Similar Documents

Publication Publication Date Title
CN110166446B (en) Method for realizing geographical weighted average center based on safe multi-party calculation
CN106452745B (en) A kind of verification method and device that secret data is shared
CN102647433B (en) Efficient cloud storage data possession verification method
US20180083780A1 (en) Method for verifying information
US20130326602A1 (en) Digital Signatures
JP2012512574A (en) Accelerating key agreement protocols
CN104735081A (en) Method and system for outsourcing security mode indexes in cloud environment
CN103095450A (en) Finite Field Crytographic Arithmetic Resistant To Fault Attacks
CN105515778B (en) Cloud storage data integrity services signatures method
US20160234021A1 (en) Multivariate public key signature/ verification system and signature/verification method
US20030059041A1 (en) Methods and apparatus for two-party generation of DSA signatures
Su et al. How to securely outsource the inversion modulo a large composite number
CN105119929B (en) Safe module exponent outsourcing method and system under single malice Cloud Server
Zhang et al. Efficient computation outsourcing for inverting a class of homomorphic functions
US20210026971A1 (en) Privacy-preserving Sum-based Consistency Checks for Blockchains
CN102750129B (en) Safe module exponent outsourcing computing method in cloud computing
US9577828B2 (en) Batch verification method and apparatus thereof
CN102769530A (en) Efficiently-calculated on-line/off-line digital signature method
Zhou et al. CASO: Cost-aware secure outsourcing of general computational problems
Zhao et al. Privacy-preserving outsourcing schemes of modular exponentiations using single untrusted cloud server
Huang et al. A black-box construction of strongly unforgeable signature schemes in the bounded leakage model
US20220345312A1 (en) Zero-knowledge contingent payments protocol for granting access to encrypted assets
Liu et al. Secure and verifiable outsourcing protocol for non-negative matrix factorisation
CN113507367A (en) Online/offline integrity auditing method for outsourced data in cloud environment
JP3328597B2 (en) Distributed multiplication apparatus and program recording medium therefor

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20150624