1. Encryption & Security
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1. Encryption & Security
Overview
¤ Securityissues
¤ Encryptionandcryptanalysis
¤ Encryptioninthedigitalage¤ Symmetricencryption¤ Asymmetricencryption
¤ Applicationsofencryption
¤ Encryptionisnotsecurity!
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Securityissues
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Networkingisasecurityissue
¤ Why?
¤ Ifyouwantareallysecuremachine,lockitinanelectromagneticallyshieldedroomanddon’tconnectittoanynetworksorothersourcesofdatabeyondyourcontrol(totallyisolatedisland)
¤ Notmuchfun,isit?
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TheProblem¤ TheInternetispublic
¤ Messagessentpassthroughmanymachinesandmedia
¤ Anyoneinterceptingamessagemight¤ readitand/or¤ replaceitwithadifferentmessage
¤ TheInternetisanonymous¤ IPaddressesdon’testablishidentity
¤ Anyonemaysendmessagesunderafalseidentity
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TheProblem¤ TheInternetispublic
¤ Messagessentpassthroughmanymachinesandmedia
¤ Anyoneinterceptingamessagemight¤ readitand/or¤ replaceitwithadifferentmessage
¤ TheInternetisanonymous¤ IPaddressesdon’testablishidentity
¤ Anyonemaysendmessagesunderafalseidentity
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Cryptography offers partial
solutions to all of these problems
AShadyExample¤ Iwanttomakeapurchaseonlineandclickalinkthattakesmeto
http://www.sketchystore.com/checkout.jsp
¤ WhatIseeinmybrowser:
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AShadyExample(cont’d)¤ WhenIpressSUBMIT,mybrowsersendsthis:
POST /purchase.jsp HTTP/1.1
Host: www.sketchystore.com
User-Agent: Mozilla/4.0
Content-Length: 48
Content-Type: application/x-www-form-urlencoded
userid=rbd&creditcard=2837283726495601& exp=01/09
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AShadyExample(cont’d)
¤ Ifthisinformationissentunencrypted,whohasaccesstomycreditcardnumber?¤ Otherpeoplewhocanconnecttomywireless
ethernet¤ Otherpeoplephysicallyconnectedtomywired
ethernet¤ …
¤ Packetsarepassedfromroutertorouter.¤ Allthoseroutershaveaccesstomydata.
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Acaveatcryptography is not security
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Encryptionandcryptanalysisbasic concepts
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Encryption
¤ Weencrypt(encode)ourdatasootherscan’tunderstandit(easily)exceptforthepersonwhoissupposedtoreceiveit.
¤ Wecallthedatatoencodeplaintextandtheencodeddatatheciphertext.
¤ Encodinganddecodingareinversefunctionsofeachother
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ATTACKATDAWNEncryptionalgorithm
AGSTRMBNDO
ATTACKATDAWN
plaintext
ciphertext
secretkey
secretkey
Decryptionalgorithm
Encryption/decryption
ATTACKATDAWN AGSTRMBNDO
ATTACKATDAWN
ciphertext
Mathematical,logical,empirical
analysis
secretkey
plaintext
Encryptionalgorithm
Cryptanalysis
Encryptiontechniquessubstitution and transposition
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Twobasicwaysofalteringtexttoencrypt/decrypt
¤ Substituteoneletterforanotherusingsomekindofrule
¤ Scrambletheorderofthelettersusingsomekindofrule
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Substitution Ciphers
SubstitutionCiphers
¤ Simpleencryptionschemeusingasubstitutioncipher:¤ Shifteveryletterforwardby1:A→ B,B→ C,...,Z→A
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SubstitutionCiphers
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SubstitutionCiphers
¤ Simpleencryptionschemeusingasubstitutioncipher:¤ Shifteveryletterforwardby1:A→ B,B→ C,...,Z→A
¤ Example:MESSAGE→NFTTBHF
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SubstitutionCiphers
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MESSAGE→NFTTBHF
SubstitutionCiphers
¤ Simpleencryptionschemeusingasubstitutioncipher:¤ Shifteveryletterforwardby1:A→ B,B→ C,...,Z→A
¤ Example:MESSAGE→NFTTBHF
¤ CanyoudecryptTFDSFU?
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SubstitutionCiphers
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TFDSFU
SubstitutionCiphers
¤ Simpleencryptionschemeusingasubstitutioncipher:¤ Shifteveryletterforwardby1:A→ B,B→ C,...,Z→A
¤ Example:MESSAGE→NFTTBHF
¤ CanyoudecryptTFDSFU?SECRET
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CaesarCipher
¤ Shiftforwardnletters;nisthesecretkey
¤ Forexample,shiftforward3letters:A→D,B→E,...,Z→C¤ ThisisaCaesarcipherusingakeyof3(n=3).
¤ MESSAGE→ PHVVDJH
¤ Howcanwecrackthisencryptedmessageifwedon’tknowthekey?DEEDUSEKBTFEIIYRBOTUSETUJXYI
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CaesarCipher(cont’d)
¤ Howlongwouldittakeacomputertotryall25shifts?
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DEEDUSEKBTFEIIYRBOTUSETUJXYI EFFEVTFLCUGFJJZSCPUVTFUVKYZJ FGGFWUGMDVHGKKATDQVWUGVWLZAK GHHGXVHNEWIHLLBUERWXVHWXMABL HIIHYWIOFXJIMMCVFSXYWIXYNBCM IJJIZXJPGYKJNNDWGTYZXJYZOCDN JKKJAYKQHZLKOOEXHUZAYKZAPDEO KLLKBZLRIAMLPPFYIVABZLABQEFP LMMLCAMSJBNMQQGZJWBCAMBCRFGQ MNNMDBNTKCONRRHAKXCDBNCDSGHR NOONECOULDPOSSIBLYDECODETHIS OPPOFDPVMEQPTTJCMZEFDPEFUIJT PQQPGEQWNFRQUUKDNAFGEQFGVJKU
QRRQHFRXOGSRVVLEOBGHFRGHWKLV RSSRIGSYPHTSWWMFPCHIGSHIXLMW STTSJHTZQIUTXXNGQDIJHTIJYMNX TUUTKIUARJVUYYOHREJKIUJKZNOY UVVULJVBSKWVZZPISFKLJVKLAOPZ VWWVMKWCTLXWAAQJTGLMKWLMBPQA WXXWNLXDUMYXBBRKUHMNLXMNCQRB XYYXOMYEVNZYCCSLVINOMYNODRSC YZZYPNZFWOAZDDTMWJOPNZOPESTD ZAAZQOAGXPBAEEUNXKPQOAPQFTUE ABBARPBHYQCBFFVOYLQRPBQRGUVF BCCBSQCIZRDCGGWPZMRSQCRSHVWG CDDCTRDJASEDHHXQANSTRDSTIWXH
VigenèreCipher
¤ Shiftdifferentamountforeachletter.Useakeyword;eachletterinthekeydetermineshowmanyshiftswedoforthecorrespondingletterinthemessage.
¤ Example:keyword“cmu”:shiftby2,12,20
¤ Message“pittsburgh”
cmucmucmuc
encrypted:runvevwdaj
¤ Tryityourselfathttp://www.simonsingh.net/The_Black_Chamber/v_square.html
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ABCDEFGHIJKLMNOPQRSTUVWXYZ A ABCDEFGHIJKLMNOPQRSTUVWXYZ noshift B BCDEFGHIJKLMNOPQRSTUVWXYZA shiftby1 C CDEFGHIJKLMNOPQRSTUVWXYZAB shiftby2 D DEFGHIJKLMNOPQRSTUVWXYZABC shiftby3 E EFGHIJKLMNOPQRSTUVWXYZABCD etc. F FGHIJKLMNOPQRSTUVWXYZABCDE
...
• Message: ATTACKATDAWN• Pickasecretkey DECAFDECAFDE • Encrypted: D
1st letter in the message is shifted by 3, 2nd letter is shifted by 4, …
ABCDEFGHIJKLMNOPQRSTUVWXYZ A ABCDEFGHIJKLMNOPQRSTUVWXYZ
B BCDEFGHIJKLMNOPQRSTUVWXYZA C CDEFGHIJKLMNOPQRSTUVWXYZAB
D DEFGHIJKLMNOPQRSTUVWXYZABC
E EFGHIJKLMNOPQRSTUVWXYZABCD F FGHIJKLMNOPQRSTUVWXYZABCDE
...
• Message: ATTACKATDAWN• Pickasecretkey DECAFDECAFDE • Encrypted: DX
1st letter in the message is shifted by 3, 2nd letter is shifted by 4, …
ABCDEFGHIJKLMNOPQRSTUVWXYZ A ABCDEFGHIJKLMNOPQRSTUVWXYZ
B BCDEFGHIJKLMNOPQRSTUVWXYZA C CDEFGHIJKLMNOPQRSTUVWXYZAB
D DEFGHIJKLMNOPQRSTUVWXYZABC
E EFGHIJKLMNOPQRSTUVWXYZABCD F FGHIJKLMNOPQRSTUVWXYZABCDE
...
• Message: ATTACKATDAWN• Pickasecretkey DECAFDECAFDE • Encrypted: DXV
1st letter in the message is shifted by 3, 2nd letter is shifted by 4, …
ABCDEFGHIJKLMNOPQRSTUVWXYZ A ABCDEFGHIJKLMNOPQRSTUVWXYZ
B BCDEFGHIJKLMNOPQRSTUVWXYZA C CDEFGHIJKLMNOPQRSTUVWXYZAB
D DEFGHIJKLMNOPQRSTUVWXYZABC
E EFGHIJKLMNOPQRSTUVWXYZABCD F FGHIJKLMNOPQRSTUVWXYZABCDE
...
• Message: ATTACKATDAWN• Pickasecretkey DECAFDECAFDE • Encrypted: DXVAHNEVDFZR
1st letter in the message is shifted by 3, 2nd letter is shifted by 4, …
VernamCipher
¤ VigenèrecipherwasbrokenbyCharlesBabbageinthemid1800sbyexploitingtherepeatedkey¤ Thelengthofthekeydeterminesthecycleinwhichthe
cipherisrepeated.
¤ Vernamcipher:makethekeythesamelengthasthemessage;Babbage’sanalysisdoesn’twork.
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One-timePads
¤ Vernamcipheriscommonlyreferredtoasaone-timepad.
¤ Ifrandomkeysareusedone-timepadsareunbreakableintheory.
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AliceandBobhaveidentical“pads”(sharedkeys)
Transposition Ciphers
Transpositionciphers
STSF…EROL...NOUA...DOTN…MPHK…OSEA…RTRN…EOND…
image:http://crypto.interactive-maths.com/simple-transposition-ciphers.html
an ancient Greek method
Encryptionincomputingfast computation makes encryption usable by all of us
Encryptionincomputing
¤ One-timepadsimpracticalonthenet(why?)
¤ Basicassumption:theencryption/decryptionalgorithmisknown;onlythekeyissecret(why?)
¤ Verycomplicatedencryptionscanbecomputedfast:• typically,elaboratecombinationsofsubstitutionand
transposition
HTTPS
¤ SecurityprotocolfortheWeb,thepeoples’encryption
¤ Purpose:¤ confidentiality(preventeavesdropping)¤ messageintegrityandauthentication(prevent“maninthe
middle”attacksthatcouldalterthemessagesbeingsent)
¤ Techniques:¤ asymmetricencryption(“publickey”encryption)toexchange
secretkey¤ certificateauthoritytoobtainpublickeys¤ symmetricencryptiontoexchangeactualmessages
Keyspace
¤ Keyspaceisjargonforthenumberofpossiblesecretkeys,foraparticularencryption/decryptionalgorithm
¤ Numberofbitsperkeydeterminessizeofkeyspace• importantbecausewewanttomakebruteforceattacksinfeasible
¤ Bruteforceattack:runthe(known)decryptionalgorithmrepeatedlywitheverypossiblekeyuntilasensibleplaintextappears
¤ Typicalkeysizes:severalhundredbits
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Symmetricvs.asymmetricencryption
¤ Symmetric(shared-keybetweensenderandreceiver)encryption:commonlyusedforlongmessages• Oftenacomplicatedmixofsubstitutionandtranspositionencipherment• Reasonablyfasttocompute• Examples(CaesarCipher)• Requiresasharedsecretkeyusuallycommunicatedusing(slower)
asymmetricencryption
Bob Alice
Symmetric(SharedKey)Encryption
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Ciphertext = Enc(plaintext, key)
Bob uses the shared key to decrypt the ciphertext to recover the plaintext
Plaintext Plaintext = Dec(Ciphertext, key)
Encrypt using key Decrypt using key
Alice uses the shared key to encrypt the plaintext to produce the ciphertext
Ciphertext
EstablishingSharedKeys
¤ Problem:howcanAliceandBobsecretlyagreeonakey,usingapubliccommunicationsystem?
¤ Solution:asymmetricencryptionbasedonnumbertheory¤ Alicehasonesecret,Bobhasadifferentsecret;workingtogetherthey
establishasharedsecret¤ Examples:Diffie-Hellmankeyexchange,RSApublickeyencryption
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Symmetricvs.asymmetricencryption
¤ Symmetric(shared-keybetweensenderandreceiver)encryption:commonlyusedforlongmessages• Oftenacomplicatedmixofsubstitutionandtranspositionencipherment• Reasonablyfasttocompute• Examples(CaesarCipher)• Requiresasharedsecretkeyusuallycommunicatedusing(slower)
asymmetricencryption
¤ Asymmetricencryption(twokeys):differentkeysareusedtoencryptandtodecrypt• Publickey:availabletoeveryone,usedtoencrypt• Privatekey:availableonlytoreceiver,usedtodecrypt• Anyonewiththepublickeycanencrypt,onlytheprivatekeycanbe
usedtodecrypt!
Onetypeofasymmetricencryption:RSA
¤ CommonencryptiontechniquefortransmittingsymmetrickeysontheInternet(https,ssl/tls)¤ Namedafteritsinventors:Rivest,Shamirand
Adleman¤ Usedinhttps(youknowwhenyou’reusingitbecause
youseetheURLintheaddressbarbeginswithhttps://)
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Bob Alice
AsymmetricPublicKeyEncryption
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ciphertext = Enc(plaintext, pubA)
Alice’spublickeypubA
plaintext plaintext = Dec(ciphertext, privA
Encrypt using pubA Decrypt using privA
Alice uses herprivate key to decrypt the ciphertext to recover the plaintext
Bob uses Alice’s public key to encrypt the plaintext to produce the ciphertext
ciphertext
Alice’sprivatekeyprivA
HowRSAworks
¤ First,wemustbeabletorepresentanymessageasasinglenumber(itmayalreadybeanumberasisusualforasymmetrickey)
¤ Forexample:
A T T A C K A T D A W N
012020010311012004012314
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PublicandPrivateKeys
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Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
PublicandPrivateKeys
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Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
PublicandPrivateKeys
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Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
PublicandPrivateKeys
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Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
RSAExample
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Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
• Bob wants to send Alice the message M=4 • Bob knows Alice’s Public Key: (3, 33) (e = 3,
n = 33) • Bob encrypts the message using e and n
• (M e modulo n → C): • 43 modulo 33 → 31 • ... Bob sends 31
• Alice’s Public Key: (3, 33) (e = 3, n = 33) • Alice’s Private Key: (7, 33) (d = 7, n = 33)
• Usually these are really huge numbers with many hundreds of digits!
• Alice receives the encoded message 31 • Alice decrypts the message using d and
n • (C d modulo n → M ): • 317 modulo 33 → 4
Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
RSAExample
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Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
• Bob wants to send Alice the message M=4 • Bob knows Alice’s Public Key: (3, 33) (e = 3,
n = 33) • Bob encrypts the message using e and n
• (M e modulo n → C): • 43 modulo 33 → 31 • ... Bob sends 31
• Alice’s Public Key: (3, 33) (e = 3, n = 33) • Alice’s Private Key: (7, 33) (d = 7, n = 33)
• Usually these are really huge numbers with many hundreds of digits!
• Alice receives the encoded message 31 • Alice decrypts the message using d and
n • (C d modulo n → M ): • 317 modulo 33 → 4
Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
RSAExample
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Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
• Bob wants to send Alice the message M=4 • Bob knows Alice’s Public Key: (3, 33) (e = 3,
n = 33) • Bob encrypts the message using e and n
• (M e modulo n → C): • 43 modulo 33 → 31 • ... Bob sends 31
• Alice’s Public Key: (3, 33) (e = 3, n = 33) • Alice’s Private Key: (7, 33) (d = 7, n = 33)
• Usually these are really huge numbers with many hundreds of digits!
• Alice receives the encoded message 31 • Alice decrypts the message using d and
n • (C d modulo n → M ): • 317 modulo 33 → 4
Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
RSAExample
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Receiver decrypts using private key • Alice is the receiver • Every receiver has a:
• public key (e, n) • private key (d, n)
• Decryption: The receiver decodes the encrypted message C to get the original message M using the private key (which no one else knows).
• C d modulo n → M (plaintext)
• Bob wants to send Alice the message M=4 • Bob knows Alice’s Public Key: (3, 33) (e = 3,
n = 33) • Bob encrypts the message using e and n
• (M e modulo n → C): • 43 modulo 33 → 31 • ... Bob sends 31
• Alice’s Public Key: (3, 33) (e = 3, n = 33) • Alice’s Private Key: (7, 33) (d = 7, n = 33)
• Usually these are really huge numbers with many hundreds of digits!
• Alice receives the encoded message 31 • Alice decrypts the message using d and
n • (C d modulo n → M ): • 317 modulo 33 → 4
Sender encrypts using public key • Bob is sender/transmitter • Every sender has the receiver’s public key:
• publickey(e,n) • Encryption: The sender encrypts a (numerical) message M into ciphertext C using the receiver’s public key:
• M e modulo n → C (ciphertext)
Generatingn,eandd
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• pandqare(big)randomprimes.
• n=p×q• φ=(p-1)(q-1)• eissmallandrelativelyprimetoφ
• d,suchthat:e × dmodφ=1
p=3,q=11
n=3×11=33φ=2×10=20e=3
3 × dmod20=1d=7
Usually the primes are huge numbers--hundreds of digits long.
CrackingRSA
¤ Everyoneknows(e,n).OnlyAliceknowsd.
¤ Ifweknoweandn,canwefigureoutd?¤ Ifso,wecanreadsecretmessagestoAlice.
¤ Wecandeterminedfromeandn.¤ Factornintopandq.
n=p×qφ=(p-1)(q-1)e×d=1(modφ)
¤ Weknowe(whichispublic),sowecansolveford.
¤ Butonlyifwecanfactorn
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Every receiver has a: • public key (e, n) • private key (d, n)
Every sender has the receiver’s public key: • publickey(e,n)
RSAissafe(fornow)
¤ Supposesomeonecanfactormy5-digitnin1ms,
¤ Atthisrate,tofactora10-digitnumberwouldtake2minutes.
¤ …tofactora15-digitnumberwouldtake4months.
¤ …20-digitnumber…30,000years.
¤ …25-digitnumber…3billionyears.
¤ We'resafewithRSA!(atleast,fromfactoringwithdigitalcomputers)
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CertificateAuthorities
¤ Howdoweknowwehavetherightpublickeyforsomeone?
¤ CertificateAuthoritiessigndigitalcertificatesindicatingauthenticityofasenderwhotheyhavecheckedoutintherealworld.
¤ Sendersprovidecopiesoftheircertificatesalongwiththeirmessageorsoftware.
¤ Butcanwetrustthecertificateauthorities?(onlysome)
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Encryptionisnotsecurity!It’sjustasetoftechniques
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How(in)secureistheInternet?
¤ TheNSAhasabudgetof$11B;weknowfromEdwardSnowdenhowsomeofitisused
¤ Corporationsandcriminalsalsospyonus
¤ Whatcangowrong?¤ Insecurepseudo-randomnumbergenerators¤ Untrustworthycertificateauthorities¤ Malware¤ “Socialengineering”attackslikephishing¤ Deliberatelybuilt-ininsecurityincryptoproducts¤ PhysicaltappingofInternetrouters
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Securityisanunsolvedproblem
Yourcybersystemscontinuetofunctionandserveyounotduetotheexpertiseofyoursecuritystaffbutsolelyduetothesufferanceofyouropponents.
–formerNSAInformationAssuranceDirectorBrianSnow(quotedbyBruceSchneier,https://www.schneier.com/blog/archives/2013/03/phishing_has_go.html)
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Summary
¤ Cryptographyiscoolmathematicsandprotocoldesign
¤ Butcryptographyisnotsecurity,onlyasetoftechniques
¤ Securityisabroaderissueinvolving¤ Othertechnology¤ Socialandlegalfactors
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“Only amateurs attack machines; professionals target people” –Bruce Schneier
Two closing thoughts
Use Signal…
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