CN107453879A - 一种基于单服务器的群上幂指数安全外包计算方法 - Google Patents
一种基于单服务器的群上幂指数安全外包计算方法 Download PDFInfo
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Abstract
本发明公开了一种基于单服务器的群上幂指数安全外包计算方法,首先通过逻辑分割算法对原始数据进行隐藏,然后将隐藏后的盲化数据发送给云服务器,云服务器收到盲化数据后,利用这些数据进行计算并将计算后的结果返回给用户,由用户验证云服务器返回的计算结果的正确性。本发明使云服务器在外包计算的过程中不能获得有关输入和输出任何敏感信息,并且提高了外包结果的可验证性。
Description
技术领域
本发明属于云计算安全技术领域,特别涉及一种基于单服务器的群上幂指数安全外包计算方法。
背景技术
群域上的幂指数运算在基于身份签名、盲签名等领域有广泛运用。特别是,现有的云存储可证明的数据持有(Provable Data Possession,PDP)和可恢复证明(Proof OfRetrievability,POR)方案都涉及到群上的幂指数运算操作。幂指数运算是最为耗时的运算之一,而客户端缺乏足够的计算资源,因此需要将复杂的计算任务外包给云服务器,以节省计算时间。
在幂指数外包计算领域,特别是基于两个不可信服务器模型方面,学者提出了大量可验证计算外包方案,但现有方案大多关注的是数域上的幂指数运算外包,而鲜有关注群域上的幂指数运算。基于两个不可信服务器模型实现的幂指数外包方案,可能会遭受共谋攻击的影响,进而影响计算结果的准确性。目前现有的基于单个不可信服务器实现的幂指数外包方包计算的结果的可验证概率通常不高(尤其是群域的幂指数外包方案)。
发明内容
本发明所要解决的技术问题是提供一种基于单服务器的群上幂指数安全安全外包计算方法,避免了共谋攻击,实现了输入信息和输出信息的隐私保护,以及用户对外包计算结果的验证。
实现本发明目的的技术方案为:一种基于单服务器的群上幂指数安全外包计算方法,包括如下步骤:
步骤1、利用随机函数返回五个随机数对(α,gα),(β,gβ),(λ,gλ),(η,gη),(t,gt);
步骤2、利用返回的随机数对幂指数ud进行逻辑分割,得到盲化数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2),具体方法为:
步骤2.1、对幂指数ud进行拆分,得到盲化数对(l1,w1)、(k1,w1)和(r/t,gt):
第一次逻辑拆分:
其中,w1=u/v1,v1=gα;
第二次逻辑拆分:
其中,β=αd-r,d=l1+k1t1,l1、k1、t1是用于随机拆分的参数;
步骤2.2、对幂指数ud进行下一次拆分,得到盲化数对(l2,w2)、(k2,w2)和(r′/t,gt):
第一次逻辑拆分:
其中,w2=u/v2,v2=gλ;
第二次逻辑拆分:
其中,η=λd-r′,d=l2+k2t2,l2、k2、t2是用于随机拆分的参数;
步骤3、将盲化后数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2)按照任意的次序向云服务器PCS发起计算请求;
步骤4、云服务器PCS根据收到盲化数对计算相应的幂指数值,并将计算结果返回给客户端:
步骤5、客户端验证返回结果的准确性,如果验证结果准确,则客户端恢复最终的计算结果;否则放弃云服务器的计算结果。
本发明与现有技术相比,其显著优点是:1)本发明方法能够实现输入、输出信息的隐私保护,通过使用新的数学分割的方式实现了对原始的数据隐藏,使得云服务器在外包计算的过程中不能获得有关输入和输出任何敏感信息;2)本发明提高了外包结果的可验证性,实现了对外包计算结果的100%验证,如果服务器不诚实,用户检测出错误的概率将接近于100%。
附图说明
图1是本发明方法的运行模型示意图;
图2是本发明方法的流程示意图。
具体实施方式
下面结合附图及实施示例对本发明作进一步描述。
如图2所示,基于单服务器的群上幂指数安全外包计算方法,首先通过逻辑分割算法对原始数据进行隐藏,然后将隐藏后的盲化数据发送给云服务器,云服务器收到盲化数据后,利用这些数据进行计算并将计算后的结果返回给用户,由用户验证云服务器返回的计算结果的正确性,具体步骤如下:
步骤1、利用随机函数返回五个随机数对(α,gα),(β,gβ),(λ,gλ),(η,gη),(t,gt);
步骤2、利用返回的随机数对幂指数ud进行逻辑分割,得到盲化数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2),具体方法为:
步骤2.1、对幂指数ud进行拆分,得到盲化数对(l1,w1)、(k1,w1)和(r/t,gt):
第一次逻辑拆分:
其中,w1=u/v1,v1=gα;
第二次逻辑拆分:
其中,β=αd-r,d=l1+k1t1,l1、k1、t1是用于随机拆分的参数;
步骤2.2、对幂指数ud进行下一次拆分,得到盲化数对(l2,w2)、(k2,w2)和(r′/t,gt):
第一次逻辑拆分:
其中,w2=u/v2,v2=gλ;
第二次逻辑拆分:
其中,η=λd-r′,d=l2+k2t2,l2、k2、t2是用于随机拆分的参数;
步骤3、将盲化后数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2)按照任意的次序向云服务器PCS发起计算请求;
步骤4、云服务器PCS根据收到盲化数对计算相应的幂指数值,并将计算结果返回给客户端:
步骤5、客户端验证返回结果的准确性,如果云服务器执行了正确的计算,则有:
由上式可知,当时,验证结果准确,此时客户端恢复最终的计算结果:否则放弃云服务器的计算结果。
下面通过实施例1验证本发明方案的有效性。
实施例1:
步骤101:数据初始化
1)输入原始数据u和d:
u=
[4042505994424453505497870829281608917449254416150048189137246965501392171988848753624419370228122868475520438617006038236267485407188352761037126540472934,7985140452193439137994672140134472557428602726687160087632554249466576459915718778890338361127086433351684556089264562335869999468503866726660801991658306,0]
d=2422224723210030436046267665772787748740584541230687138255938046710365999545253273535054327711642124831026076902601200648298520598665469073291583788999
2)利用随机函数返回五个随机数对:
(α,gα)=(877102552924449423126167044613,[7361717425933978509477719124439362631182950262184125391765276665275014343620006788655055770973783182474700457377268038361167873302010612440376554211012491,6207328033745722175963559420464349130315637157207618435551088554275352563908777469095386357715314659811873927490655642715251817085751106017348190241202645,0])
(β,gβ)=(905699689621280065165242772147,[7388573983669707488433705020753446898006385260719019552793440976924250762457145021278006841422480628281915717431365395949088372165265530369974269670276409,2795890352243058429208139155273142101773734866792346904137184407084909332256366000217763493050511031003159928017902000924748645882600179492932598964607050,0])
(λ,gλ)=(903370086593142382804952977567,[1445958254240653355924265264054523110346865989541034535196430029724502432261086928197951526635698616922038130167081905878447859487832896923576233320160153,2316430439949229727221010752756821881343945018070128924790268071119676139418543996984347293449897025124564421198721616244736161954112294936717084676828661,0])
(η,gη)=(962585691671824620766765218689,[5922633441463408100918470292831826810615348868296105530150369005890321057222012537388769683377035520249433616200846104600761499131191352021968430794052562,5155942194891662789023416551256635139300670600970842388603838006875422370866144636784923516265755507527906418161180557264284215672791148000507110562235806,0])
(t,gt)=(1069702563319666009740289942121,[8312328909352190527905489346820497388781289660239406941213896209171421358454320817121330799301056252638009283347359494405041078935076506752843788830958100,5466829608022686344852316316530668515422410921494250327017855346258089229068874346767381413102216888940272170075441571246114013485627527133635422894393912,0])
步骤102:逻辑拆分
1)对幂指数ud进行拆分,得到盲化数对
(l1,w1)=(8331455383193435944,[2287026490634649110920594083305409415292962135457300456724334087535231093663431354392542665213405655706098537764591120381350565183452813891889912023793524,6767241987548907438272631993646771841979541517407628126045243286818429262723067783069761332692720363742632980934576366785943869059786668693053087780130795,0])
(k1,w1)=(184134213086886758962515708215293815055102581359123685614250694352588249238777137177668752586579485620697083716152343065299410554445,[2287026490634649110920594083305409415292962135457300456724334087535231093663431354392542665213405655706098537764591120381350565183452813891889912023793524,6767241987548907438272631993646771841979541517407628126045243286818429262723067783069761332692720363742632980934576366785943869059786668693053087780130795,0])
(r/t,gt)=(172529059765623754802260283176384793917815669339,[8312328909352190527905489346820497388781289660239406941213896209171421358454320817121330799301056252638009283347359494405041078935076506752843788830958100,5466829608022686344852316316530668515422410921494250327017855346258089229068874346767381413102216888940272170075441571246114013485627527133635422894393912,0])
2)对幂指数ud进行下一次拆分,得到盲化数对
(l2,w2)=(3837127172945991848,[4057139148666976835944512748243092136857102277832868683993756740554266843622242890269350657682806249109512724725074991447708278998032070865585140975150346,3921717216528666960142145530726416627254326513999517713793665655323705321593472738409305056070916502335390755918171941489319647658487190119511194939341578,0])
(k2,w2)=(133520211630141572132723596306093633337894549632998700485145881557916563741160962836153737903998536023883610643518474965496969066019,[4057139148666976835944512748243092136857102277832868683993756740554266843622242890269350657682806249109512724725074991447708278998032070865585140975150346,3921717216528666960142145530726416627254326513999517713793665655323705321593472738409305056070916502335390755918171941489319647658487190119511194939341578,0])
(r′/t,gt)=(656956188616607788927618481182063662182590645403,[8312328909352190527905489346820497388781289660239406941213896209171421358454320817121330799301056252638009283347359494405041078935076506752843788830958100,5466829608022686344852316316530668515422410921494250327017855346258089229068874346767381413102216888940272170075441571246114013485627527133635422894393912,0])
步骤103:请求云服务器
1)将盲化后数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2)按照任意的次序向云服务器PCS发起计算请求。
2)云服务器PCS根据收到盲化数对计算相应的幂指数值,并将计算结果返回给客户端:
步骤104:检测计算结果的正确性
对比两组数据,由于(1)式与(2)式相等,即
ud=3166932553278780684384918954213506242416161279600560134897678504374209379190779923255568779871299253065678523269588081677881867030898295879802449054295605,6645972042672487374119565344248759437921140461492411936660120447233509051124700711822067585869050997509548896851375794690923165588118026974674794557183376,0。
所以可以判断云服务器是否正确执行了计算。
Claims (3)
1.一种基于单服务器的群上幂指数外包计算方法,其特征在于,包括如下步骤:
步骤1、利用随机函数返回五个随机数对(α,gα),(β,gβ),(λ,gλ),(η,gη),(t,gt);
步骤2、利用返回的随机数对幂指数ud进行逻辑分割,得到盲化数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2),具体方法为:
步骤2.1、对幂指数ud进行拆分,得到盲化数对(l1,w1)、(k1,w1)和(r/t,gt):
第一次逻辑拆分:
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其中,β=αd-r,d=l1+k1t1,l1、k1、t1是用于随机拆分的参数;
步骤2.2、对幂指数ud进行下一次拆分,得到盲化数对(l2,w2)、(k2,w2)和(r′/t,gt):
第一次逻辑拆分:
<mrow>
<msup>
<mi>u</mi>
<mi>d</mi>
</msup>
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</mrow>
</msup>
<msubsup>
<mi>w</mi>
<mn>2</mn>
<mi>d</mi>
</msubsup>
</mrow>
其中,w2=u/v2,v2=gλ;
第二次逻辑拆分:
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<mi>d</mi>
</msup>
<mo>=</mo>
<msup>
<mi>g</mi>
<mrow>
<mi>&gamma;</mi>
<mi>d</mi>
</mrow>
</msup>
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<msub>
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</msup>
</mrow>
其中,η=λd-r′,d=l2+k2t2,l2、k2、t2是用于随机拆分的参数;
步骤3、将盲化后数对(r/t,gt),(r′/t,gt),(l1,w1),(l2,w2),(k1,w1),(k2,w2)按照任意的次序向云服务器PCS发起计算请求;
步骤4、云服务器PCS根据收到盲化数对计算相应的幂指数值,并将计算结果返回给客户端:
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步骤5、客户端验证返回结果的准确性,如果验证结果准确,则客户端恢复最终的计算结果;否则放弃云服务器的计算结果。
2.根据权利要求1所述的基于单服务器的群上幂指数外包计算方法,其特征在于,步骤5验证返回结果准确性的公式为:
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</mrow>
3.根据权利要求1所述的基于单服务器的群上幂指数外包计算方法,其特征在于,步骤5客户端恢复最终计算结果的公式为:
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</mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
</msup>
<mo>.</mo>
</mrow>
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