Copyright2017NTTcorp.
AllRightsReserved.
CubeAttacksonNon-BlackboxPolynomialsbasedonDivisionPropertyYosukeTodoNTTSecurePlatformLaboratoriesandKobeUniv.
ThisisjointworkwithTakanoriIsobeKobeUniv.
YonglinHaoTsinghuaUniv.
WilliMeierFHNWESC20172Copyright2017NTTcorp.
AllRightsReserved.
OverviewAkindofhigher-orderdifferentialcryptanalysis.
‐Especially,it'spowerfulforstreamciphers.
Experimentalapproach.
‐Thecubeattackanalyzessymmetric-keycryptosystembyregardingitasblackboxpolynomials.
Newgenerictoolsforcubeattackstoexploittheinternalstructureofstreamciphers.
renewbestattacks.
CubeAttacksonBlackboxPolynomialsCubeAttacksonNon-BlackboxPolynomials3Copyright2017NTTcorp.
AllRightsReserved.
OurapproachDivisionpropertyintheworldofcubeattacksWhatisdivisionproperty‐Tooltofindintegraldistinguishersforblockciphers.
Firstapplicationtostreamciphers.
‐Zero-sumdistinguishersaretrivial.
‐But,It'snontrivialtorecoverthesecretkey.
Newinsight.
‐Whatdivisionpropertycando.
‐Anewhowtousedivisionproperty.
ItisusedtoanalyzeANFcoefficients.
‐Keysthatarenotinvolvedto"superpoly"areevaluated.
4Copyright2017NTTcorp.
AllRightsReserved.
Outline1.
Preliminaries.
1.
Cubeattacks(onblackboxpolynomial).
2.
Divisionproperty.
3.
Mixed-integerlinearprogramming.
2.
Zero-sumintegraldistinguishers.
3.
Ourapproach.
1.
AnalyzetheANFof"superpoly".
2.
Whatdivisionpropertycando.
3.
Howkeysarerecovered.
4.
Applications.
5Copyright2017NTTcorp.
AllRightsReserved.
Modelofstreamciphers.
secretvariables(key)publicvariables(iv)Letberegardedasthefirstbitofkeystream.
Keyinitialization6Copyright2017NTTcorp.
AllRightsReserved.
CubeattacksonblackboxpolynomialsLet=1,…,||{1,2,…,}betheindicesofactivebitsandbeasetof2||valueswhere{1,…,||}aretakingallcombinationsofvalues.
–bethemonomial,=1||.
–(,)iscalledthesuperpolyof.
–(,)missesatleastonevariablefrom.
–Attackersrecoverbyanalyzing(,).
7Copyright2017NTTcorp.
AllRightsReserved.
Howisrecoveredfromsuperpoly(,)ofrealstreamciphersistoocomplicatedtoanalyzeit.
Heuristicevaluation‐Randomlychosen.
‐isregardedasblackbox‐Wecannoticewhetherornotthesuperpolyislinearforwithhighprobability.
Significantdrawbacksofthisapproach.
‐Thesizeofcubeislimitedtoexperimentalrange.
‐Thesizeisatmostabout40.
8Copyright2017NTTcorp.
AllRightsReserved.
DivisionpropertyProposedatEurocrypt2015.
Tooltofindintegraldistinguishers.
DefinitionLetbeamultisetwhoseelementstakeavalueof2.
Letbeasetwhoseelementstakeavalueon2.
Whenthemultisethasthedivisionproperty1,itfulfillsthefollowingconditions:9Copyright2017NTTcorp.
AllRightsReserved.
DivisionpropertySincethreepropagationrules(copy,xor,and)aredefined,wecanevaluatearbitrarycircuit.
HowtomodelthreepropagationsbyMILP.
MILPsolvercanefficientlyevaluatethepropagationofdivisionproperty.
PropagationsearchusingMILP(XiangetalAC16)Bit-baseddivisionproperty(TodoetalFSE16)10Copyright2017NTTcorp.
AllRightsReserved.
Divisiontrail1230121Thereisadivisiontrail0,1,…,∈0*1**satisfyingthepropagationcharacteristic.
IfthereisNOTdivisiontrail,thethbitofciphertextisbalanced.
11Copyright2017NTTcorp.
AllRightsReserved.
ApplicationtostreamciphersTrivialapplicationiszero-sumdistinguisher.
‐CreateMILPmodelthatrepresentsthepropagationofdivisionpropertyfor(,).
‐Let=1,…,||{1,2,…,}betheindicesofactivebitsandevaluate(,).
‐Letbevalues.
t.
=.
‐IfthereisNOTdivisiontrail,thefirstbitofkeystreamisbalanced.
Wecan'trecoversecretvariables.
12Copyright2017NTTcorp.
AllRightsReserved.
OurapproachesforkeyrecoveryIt'spossibleifwecanenoughevaluateANFcoefficientsofsuperpoly.
Anewapplicationofdivisionproperty.
‐Weneverusedivisionpropertytofindzero-sumdistinguisher.
‐DivisionpropertyisusedtoanalyzeANFcoefficientof(,).
‐Secretvariablesinvolvedtothesuperpolyofgivencubeareevaluated.
13Copyright2017NTTcorp.
AllRightsReserved.
BasicknowledgeAlgebraicNormalFromIt'spracticallyinfeasibletoanalyzeall.
Let∈2beANFcoefficients.
14Copyright2017NTTcorp.
AllRightsReserved.
ANFofSuperpolyDecomposeaccordingtos.
t.
=15Copyright2017NTTcorp.
AllRightsReserved.
WhatdivisionpropertycandoAssumingthereisNOTtrail,Inotherwords,‐isalways0forany.
WecanusedivisionpropertyasatooltoevaluatefeatureofANFcoefficients.
isalwayszeroforany.
16Copyright2017NTTcorp.
AllRightsReserved.
Extensiontokeyrecovery.
AssumingthereisNOTtrail,isalways0forany(||).
Then,Thesuperpolyisindependentof.
17Copyright2017NTTcorp.
AllRightsReserved.
Attackstrategy1.
Evaluationphase.
‐Involvedsecretvariablesareevaluatedinthisphase.
‐ThisphaseisfeasiblebyusingMILP.
2.
Off-linephase.
‐Computethesumofgivencube.
‐Thisphaseisnotpractical,butthetimecomplexityisbounded.
3.
On-linephase.
‐Queryencryptionoracle.
‐Recoversecretvariables.
18Copyright2017NTTcorp.
AllRightsReserved.
1stphase--evaluationphase.
1.
Decidethepositionofactivebits=1,…,||{1,2,…,}.
2.
Preparetheset=.
3.
EvaluatewhetherornotthereisdivisiontrailLetbean-bitunitvectorwhosethbitis1.
Letbean-bitvectors.
t.
=.
4.
Ifthereisasuchtrail,=∪{}.
5.
Repeatallpossibleof∈{1,2,…}.
Finally,containsbitsthatmaybeinvolvedtothesuperpoly.
secretvariables(key)publicvariables(iv)19Copyright2017NTTcorp.
AllRightsReserved.
2ndphase--off-linephase.
1.
Decideinitialiv.
2.
Preparethesetofchosenivsbyflippingbitsin.
3.
Guess-bitsecretvariables(1,2,…,).
Foreachguess,computeandstore(,).
Thetimecomplexityofthisphaseis2||+||.
secretvariables(key)publicvariables(iv)20Copyright2017NTTcorp.
AllRightsReserved.
3rdphase--on-linephase.
1.
Accessencryptionoracleunderchosenivsetting.
Querythecubeusedintheoff-linephase.
Computethesum(,).
2.
Comparethesuminon-linephasewiththesumofeach{1,2,…,}inoff-linephase.
Ifthesumisdifferent,guessedsecretvariablesareincorrect.
Thedatacomplexityofthisphaseis2||.
secretvariables(key)publicvariables(iv)21Copyright2017NTTcorp.
AllRightsReserved.
ApplicationtoTriviumzistatesize=288bitsinitialization=1152rounds22Copyright2017NTTcorp.
AllRightsReserved.
ApplicationtoTriviumzi80-bitsecretkey80-bitinitializationvectorstatesize=288bitsinitialization=1152rounds23Copyright2017NTTcorp.
AllRightsReserved.
VerifyourideaexperimentallyActiveIVsInvolvedkeysRoundComplexity#ofactiveIVs=50,2,4,6,8#ofinvolvedkeys=418,19,20,6255729Experimentalresults–initialIV:515B6628BB3160851515–Wetest100randomkeys.
If(18|19|20|62)={0,3,4,7,8,B,D,E},thesumis1.
If(18|19|20|62)={1,2,5,6,9,A,C,F},thesumis0.
24Copyright2017NTTcorp.
AllRightsReserved.
TheoreticalcubeattacksActiveIVsInvolvedkeysRoundComplexity#ofactiveIVs=660,1,2,…,5254,56,58,…,78#ofinvolvedkeys=1022,24,25,26,35,41,55,66,67,68829276#ofactiveIVs=690,1,2,…,5860,62,64,…,78#ofinvolvedkeys=70,36,41,55,66,67,68830276#ofactiveIVs=710,1,2,…,6264,66,68,70,72,74,76,78#ofinvolvedkeys=448,73,74,75831275#ofactiveIVs=720,1,2,…,6466,68,70,72,74,76,78#ofinvolvedkeys=533,57,58,59,60832277Weonlyexecutethe1stphase(evaluationphase)25Copyright2017NTTcorp.
AllRightsReserved.
OtherapplicationsGrain128a‐Previousbestattackis177rounds,andit'sonlydistinguisher.
‐Ourattackis183roundsandit'spossibletorecoverthesecretkey.
ACORN(oneof3rdroundCAESARcandidates)‐Previousattackis477rounds.
‐Ourattackisatleast604rounds.
26Copyright2017NTTcorp.
AllRightsReserved.
ConclusionCubeattacksonnon-blackboxpolynomials.
‐Anewmethodtousedivisionpropertywasproposed.
ItisusedtoanalyzeANFcoefficients.
‐ThetaskofcryptographersisonlycreatingMILPmodelfordivisionproperty.
Thecostisverysmall.
It'sveryeasytoapplytovariousstreamciphers.
‐Wecanevaluatecubeattacksevenifthesizeofcubeistheoreticalrange.
亚洲云Asiayun怎么样?亚洲云Asiayun好不好?亚洲云成立于2021年,隶属于上海玥悠悠云计算有限公司(Yyyisp),是一家新国人IDC商家,且正规持证IDC/ISP/CDN,商家主要提供数据中心基础服务、互联网业务解决方案,及专属服务器租用、云服务器、云虚拟主机、专属服务器托管、带宽租用等产品和服务。Asiayun提供源自大陆、香港、韩国和美国等地骨干级机房优质资源,包括B...
商家介绍:创梦云是来自国内的主机销售商,成立于2018年4月30日,创梦云前期主要从事免备案虚拟主机产品销售,现在将提供5元挂机宝、特惠挂机宝、香港云服务器、美国云服务器、低价挂机宝等产品销售。主打高性价比高稳定性挂机宝、香港云服务器、美国云服务器、香港虚拟主机、美国虚拟主机。官方网站:http://cmy0.vnetdns.com本次促销产品:地区CPU内存硬盘带宽价格购买地址香港特价云服务器1...
数脉科技(shuhost)8月促销:香港独立服务器,自营BGP、CN2+BGP、阿里云线路,新客立减400港币/月,老用户按照优惠码减免!香港服务器带宽可选10Mbps、30Mbps、50Mbps、100Mbps带宽,支持中文本Windows、Linux等系统。官方网站:https://www.shuhost.com* 更大带宽可在选购时选择同样享受优惠。* 目前仅提供HKBGP、阿里云产品,香港...
esc为你推荐
视频截图软件列出5种非常好用的视频截图工具邮箱怎么写正确的邮箱格式怎么写安装程序配置服务器失败SQL安装程序配置服务器失败yy频道中心yy频道怎么进频道中心,求图~!站长故事爱迪生的故事人人时光机五月天的专辑都有哪些?1433端口1433端口怎么打开百度手写百度手写怎么不见了手机区号打电话怎么加区号?网站联盟网络联盟是什么意思
花生壳域名 域名管理 河北服务器租用 荷兰vps 淘宝二级域名 怎么申请域名 冰山互联 bandwagonhost godaddy主机 香港机房 diahosting cdn服务器 2014年感恩节 免费网络电视 域名转向 新天域互联 200g硬盘 vip购优惠 太原网通测速平台 卡巴斯基免费试用 更多