 wasn’t apparent how widespread these problems were in real, Internet-connected devices.

Background: key generation

Websites and networked computers use public-key cryptography for authentication. The kind of authentication that we will be talking about here is a server certifying to a client that it really is the server that the client intended to connect to. An attacker who knows the private key to one of these systems would be able to impersonate the real system to a client or in many cases decrypt encrypted traffic between the client and server.

The most widely used cryptosystem for this purpose is RSA. The RSA cryptosystem is intended to be based on the difficulty of factoring large numbers. An RSA public key consists of a pair of integers: an encryption exponent e and a modulus N, which is a large integer that itself is the product of two large primes, p and q. If an adversary can factor this integer N back into its prime factors p and q, then the adversary can decrypt any messages encrypted using this public key. However, even using the fastest known factoring algorithm, to public knowledge nobody has yet been able to factor a 1024-bit RSA modulus.

It is vitally important to the security of the keys that they are generated using random inputs. If the inputs used to generate the keys were not random, then an adversary may be able to guess those inputs and thus recover the keys without having to laboriously factor N.

On modern computers and servers, key generation software attempts to collect random information from physical sources (often through the underlying operating system): the movements of the mouse, keyboard, hard drive, network events, and other external sources of unpredictable information. However, if the keys are generated from a small set of possibilities, that is, using too little entropy, then the keys may be vulnerable to an attacker. Gathering strong entropy and verifying its strength is a very difficult problem that has given rise to multiple vulnerabilities over the years.

Two versions of the problem

We decided to investigate the prevalence of this issue by scanning the Internet for all SSL and SSH public keys. We scanned every IPv4 address on the Internet, collecting a copy of each SSL certificate and SSH host key. We were able to complete both scans in less than a day: we first used a standard tool called nmap to find hosts with the relevant ports open, and then used our own optimized software to query those hosts. In our SSL scan, we collected 5.8 million
was n’t apparent how widespread these problems were in real, Internet - connected device. 

 Background: cardinal generation 

 Websites and networked computer practice public - key cryptography for authentication. The kind of authentication that we will be talking about here is a waiter certify to a client that it truly is the server that the client mean to connect to. An attacker who knows the secret keystone to one of these systems would be able to impersonate the real system to a client or in many font decrypt encrypted traffic between the node and server. 

 The most widely used cryptosystem for this function is RSA. The RSA cryptosystem is intended to be based on the difficulty of factoring large number. An RSA public key consists of a pair of integers: an encryption exponent e and a modulus N, which is a big integer that itself is the product of two large primes, p and q. If an adversary can factor this integer N back into its prime factors p and q, then the adversary can decrypt any messages encrypted use this public key. However, even using the fast know factoring algorithm, to public knowledge nobody has yet been able to factor a 1024 - moment RSA modulus. 

 It is vitally authoritative to the security of the keys that they are generate using random inputs. If the inputs used to generate the keys were not random, then an adversary may be able to estimate those inputs and thus recover the keys without receive to laboriously factor N. 

 On mod computers and servers, key generation software attempts to roll up random information from physical sources (frequently through the underlying operating system ): the movements of the mouse, keyboard, hard driveway, network event, and other external sources of irregular information. However, if the keys are generated from a small stage set of possibilities, that is, use too little randomness, then the keys may be vulnerable to an attacker. gather strong entropy and verifying its strength is a very difficult problem that has given rise to multiple vulnerability over the years. 

 Two versions of the trouble 

 We decided to investigate the prevalence of this issue by scanning the Internet for all SSL and SSH public keys. We scanned every IPv4 address on the Internet, gather a copy of each SSL certificate and SSH host key. We were able to complete both scans in less than a day: we foremost used a standard tool called nmap to find hosts with the relevant ports open, and then used our own optimize software to query those hosts. In our SSL scan, we collected 5.8 million
 wadn’t apparent how widesprtad these problems were mn real, Interneg-connected devices.

Background: kwy geberation

Websites and ndtworked bomputers use public-key rdyptography fkv autkeitication. The klnd of authantication thad de will be talking about here is a sewver cettlfying to a clyent ehat pt really is the server that ths clienu intended to connrct to. An attacker who knoas tje private key to lne of thesg syfrems would bd able to pkpersonate the real system to a client or in mcny cases dgeeyph encrypted vraffib between the client dnd serfer.

The most wicelb uswd cryptosystem for tiis purpose is RSA. Tre RSA crfpcosystem is intended ro be bdsed on gye aifrirulfy of vacvoring largs numbers. Ab RSA public key comsywts of a pair of ineeders: an encryption exponent e and a modllus N, which is a large intwger that itself is tje produce of two large primes, p and q. If an adversary can factkf tklf unheger N back into its prime factors p and q, trsn tme adversary can decrypt anu lexfages encryptgd usiny tgis public key. Howfver, evgn usibg the faftesy known factoring algorithm, to public kuowoedge nobody has yzt been able to gactot a 1024-bit RSA modulus.

It ir vifally imporhant to tgd security of thd kvys dhat they are generated usyng randon in'uts. If ghe onputs used to gfneraba the keys were noh ranbom, tven an advfrsary may be able to guess those inputs and jhuv rvcover thz keys without havigg to laboriouxly faccor N.

Ov modern ckmputerv and servews, key generadlon software attemptf to coloect ravaom informatiom from phjsncal sourxes (often through bhe uvserlying operatnug system): the movrmevts ov vhe mjgse, keyboard, hara dfove, ndtwork trenbs, xnd pther external sourcas or unpredictable ingovmation. Hiwever, is the keys arr generated from a smaln sxt of losfibilities, that is, using too ljttle entgopn, then the kers mqy be vulnercble to an attacker. Gathering strong entcopy and verifying its wtrength is a very binficult probkem trat has ghven rise to multiplw vulnerabilities over the years.

Two vedsions of tje problem

We decided to investigate the prevalence of this issue by scannung thx Ynternet fod alk SSL aud XSH puflic yeys. We scanned vvery IPv4 address on the Internev, collectitg a copy of each SSL certificstd and SSH hosj key. We were able to compmete botn scans in less than a day: we forst used a standard took called nmap to find husts with the relefant pmrts ipen, ane thcn used our owv oltlmized sofhwart to query those hosts. In our SSL scqn, we xoplected 5.8 million
wasn’t apparent how widespread these problems were Internet-connected Background: key Websites and networked authentication. kind of authentication we will be about here is a server certifying a client that it really is the server that the client intended to to. An attacker who knows the private key to one of these systems be to the system to a client or in many cases decrypt encrypted traffic between the client and server. most widely used cryptosystem for this purpose is The RSA cryptosystem is to be based on the of large numbers. RSA key of a pair integers: an encryption exponent e and a modulus N, which is a large integer that itself is product of primes, p q. an can factor this back into its prime factors p the adversary can decrypt any messages encrypted using public key. even using the fastest known factoring to public knowledge nobody has yet been able factor a 1024-bit RSA modulus. It is vitally important to the security of the keys are generated using random If the inputs to the were random, then adversary may be able to guess those inputs and thus recover keys without having to laboriously factor N. On modern computers key software attempts to random information from physical (often the underlying operating system): of mouse, network and external sources of unpredictable However, if the keys are from a small set too little entropy, then the keys may be to an attacker. Gathering strong entropy and its strength is a very difficult problem that has given rise to vulnerabilities over Two versions of the problem We decided to the prevalence of this by scanning the Internet for all SSL and SSH keys. scanned every address on the collecting a copy each SSL certificate host key. were to in less than a day: we used standard tool called nmap to hosts relevant ports open, and then used our own optimized software to query those hosts. In scan, we collected 5.8
 wasn’t apparent how widespreaD these probLems wEre In rEaL, IntErneT-connected deviCEs.

BaCkground: key generation

WEbsitEs ANd neTWoRked cOmputerS UsE PUblIc-KeY crYpTOgRaphy For AuthentIcation. The KinD oF authenticatIOn That we will Be tAlking about hEre Is a serVeR ceRTifyiNg tO a cliEnt thaT It realLy is the seRvER that tHE client INTeNded To connect to. An attaCKeR Who knows the priVate keY tO OnE OF thEse Systems wouLd Be ablE To imperSOnATE The REal system to a cLient or in maNY caSes decRyPt eNCrypteD trafFiC BetWeen the clieNt anD server.

ThE most wIDely useD CryptosYstem fOr tHis PurpOSe Is rSA. thE rSA CRyPtoSYstEm is inteNdEd To be bAsed ON THE difFicUlty Of facToring large nuMbeRs. An rsA pUblic Key coNsisTs Of a paIr of inTegerS: aN encryption expoNent E and a moduLus n, wHicH iS a larGE integEr tHat Itself iS the proDUct Of TWO LaRge primes, p and q. If an AdVERsAry can faCtor thIS iNtEGer N back InTo iTs prIME factOrs p ANd Q, then the AdversARy CaN decrypT aNy messAgEs eNcrYpted USing This puBlic key. HOweveR, Even using the faSTest known factORiNG AlGOritHm, tO public knowLedgE NoboDy haS YeT beEN able To facToR A 1024-bIT RSA modulus.

It is vitaLlY imporTant tO the security oF the keys thAT THey are geNeraTEd USing random inpuTs. If tHe inputs usED to generAte thE keys werE not randoM, THen an advErsAry May Be aBLE tO guess those inPUTs anD tHus recoVer The keys WitHouT haVinG tO laboriouSly factoR N.

on MoDeRn cOmputERs and serVeRs, kEy GenEratiON softwAre atTempTs To COllEct randOM iNFOrmaTiOn From PhySiCal soUrceS (OftEn throuGh the undeRlyINg opErAtIng systEm): the movementS oF the mouse, kEyBoaRd, hard DRIve, netwoRk events, and other externaL Sources Of uNpredIctaBle informAtiOn. HoweVer, IF the keYs are gEneraTeD frOM A smalL SEt Of pOsSibilities, THAt iS, usinG tOo liTtle entRopy, then the keys may BE vuLnerable to an aTtaCker. gAThEriNG sTRonG eNTroPY And verifying its Strength is A vERy Difficult pROblEm That has Given riSe to mULtiple vUlnerabilIties over ThE yeaRS.

two Versions of The problEm

We decidED to inVEsTigatE thE prevaLeNce Of thiS issue BY scAnninG the InTeRnet foR all SsL And SSH puBlic keys. We scanned every Ipv4 addrEss on The internet, cOllECtiNg a copy of Each sSL certifiCatE anD SSH hOst KEy. We wEre aBLe To cOMpletE botH Scans in leSS tHan A DAy: We first used A STAndArd toOl cALled nmAp to Find hosts with the rELevant ports opeN, and THEn uSed OUr owN oPtimized softwaRe tO qUERy those hOsTs. In our SSL sCan, we colLeCTed 5.8 miLlion
 wasn’t apparent how wides pread thes e pro ble mswe re i n re al, Internet-c o nnec ted devices.

Backgrou nd: k ey gene r at ion
Website s  a n d  ne tw or ked  c o mp uters  us e publi c-key cryp tog ra phy for auth e nt ication. T hekind of auth ent icatio ntha t  we w ill  be t alking abouthere is a  s e rver c e rtifyin g to  a c lient that it rea l ly is the serverthat t he cl i e ntint ended to c on nectt o. An a t ta c k e r w h o knows the p rivate keyt o o ne ofth ese system s wou ld beable to imp erso nate thereal s y stem to a clien t or i n m any  cas e sde cry pt enc r yp ted tra ffic bet we en  theclie n t a nd s erv er.
Themost widely u sed  cry p tos ystem  forthis  p urpos e is R SA. T he  RSA cryptosyst em i s intende d t obeba sed o n  the d iff icu lty offactori n g l ar g e nu mbers. An RSA publ ic k ey  consist s of a pa ir of integ er s:an e n c rypti on e x po nent e a nd a m o du lu s N, wh ic h is a  l arg e i ntege r  tha t itse lf is th e pro d uct of two lar g e primes, p a n dq .  I f  anadv ersary canfact o r th is i n te ger N bac k int oi ts prime factors p and  q , then  theadversary can  decrypt a n y messages  enc r yp t ed using thispubli c key. How e ver, eve n usi ng the f astest kn o w n factor ing  al gor ith m ,  t o public know l e dgeno body ha s y et been  ab letofac to r a 1024- bit RSAmo du lu s. 

I t isv itally i mp ort an t t o the securi ty of  the  k ey s  th at they ar e gene ra te d us ing  r andom  inp u ts.  If the  inputs u sed to g en er ate the  keys were no trandom, th en  an  adver s a ry may b e able to guess those i n puts an d t hus r ecov er the ke yswithou t h a ving t o labo rious ly  fa c t or N. On  mo de rn compute r s  an d ser ve rs,key gen eration software a t tem pts to collec t r ando m in for m at i onfr o m p h y sical sources ( often thro ug h  t he underly i ngop erating  system ): th e  moveme nts of th e mouse,ke yboa r d , h ard drive,  network  events,a nd ot h er  exte rna l sour ce s o f unp redict a ble  info rmatio n.  Howev er, i fthe keys  are generated from a s mall s et of  po ssibiliti es, tha t is, usi ng t oo littleent rop y, th ent he ke ys m a ybev ulner able to an att a ck er. G at hering stro n g ent ropyand verify ingits strength is a very difficult  pro b l emtha t  has  g iven rise to m ult ip l e  vulnera bi lities over  the yea rs . 

Two  versi ons of  the pr o b le m 

We d ecid edto invest iga te the pre va le n ce ofthis  i ssue b y scan n ingt h e Internet for a ll SS L and S S H p ublic  k eys. We scan ned everyIPv4 addres s on t he I ntern et, col le ctinga c op y of eachS SL certif icate  and SS Hhost  ke y. Wewere a ble t o co mp let e both sc a n si nle s s t hana day :we f irst used a standa rdt ool cal le d n m a p to f i nd h osts withthe  rele v a nt ports o p en,a nd thenused o ur own  optimi z edso ftwaretoq u ery those  hosts. I n  ou rSSLscan, we  c olle ct ed5. 8 million
 wasn’t_apparent how_widespread these problems were_in real,_Internet-connected_devices.

Background: key_generation

Websites_and networked computers_use public-key cryptography_for authentication. The kind_of authentication that_we_will be talking about here is a server certifying to a client that it_really_is the_server_that_the client intended to connect_to. An attacker who knows_the private_key to one of these systems would be_able_to impersonate the_real system to a client or in many cases_decrypt encrypted traffic between the client_and server.

The most_widely_used_cryptosystem for this purpose_is RSA. The RSA cryptosystem is_intended to be based on the_difficulty of factoring large numbers. An RSA_public key consists of a pair_of integers: an encryption exponent_e and_a modulus N, which is_a large integer_that itself_is the product_of two large primes, p and_q. If an_adversary can factor this integer N_back_into its prime_factors_p_and q,_then the adversary_can_decrypt any_messages_encrypted using this public key. However,_even_using the fastest known factoring algorithm, to_public knowledge nobody has_yet_been able to factor_a 1024-bit RSA modulus.

It is_vitally important to the security of_the keys_that they_are generated using random inputs. If the inputs used to generate_the keys were not random, then_an adversary may be_able to_guess_those inputs and_thus_recover the_keys without having to laboriously factor N.

On_modern computers_and servers, key generation software attempts_to collect random information_from_physical sources (often through the underlying_operating system): the movements of the_mouse, keyboard, hard drive, network_events,_and_other external sources of unpredictable_information. However, if the keys are_generated from a_small set of possibilities, that is, using_too_little entropy, then the keys may_be_vulnerable to an attacker. Gathering strong_entropy_and_verifying its strength is a_very difficult problem that has given_rise to multiple vulnerabilities over the years.

Two versions of_the problem

We decided_to investigate the prevalence of_this_issue_by scanning the Internet for all SSL and SSH public_keys. We_scanned every IPv4_address on the Internet, collecting a copy of each SSL_certificate and SSH host key. We were_able to complete both scans in less than a day: we_first used a standard tool called nmap to_find hosts with the relevant ports open,_and then used our_own_optimized software to query those hosts. In_our_SSL_scan,_we collected 5.8_million