international security system data threats

1. Principle of Least Privilege (POLP) This principle states that every user and program on the system should be granted only the specific rights and permissions needed to perform their tasks, with no more.

1. UNIT-2
PUBLICKEYCRYPTOGRAPHYANDRSA
InformationSecurity
BY
KhushbuGarg
Assistant Professor
Jecrcu

2. Plain Text to Cipher Text Conversion
Techniques

3. Introduction
Encryption is the process of converting
plaintext into ciphertext to secure
information.
Importance:
• Used in communication, data security, and
cryptography.

4. Substitution Ciphers
Caesar Cipher:
• Each letter shifted by a fixed number.
• Example: HELLO → KHOOR (Shift = 3)
Vigenère Cipher:
• Uses a keyword for multiple shifts.
• Example (Keyword = 'KEY'): HELLO →
RIJVS

5. Transposition Ciphers
Rail Fence Cipher:
• Letters written diagonally, read row-wise.
• Example: HELLO WORLD →
HLOWRDELLOOL (Depth = 2)
Columnar Transposition:
• Text written in a grid and rearranged by
key order.
• Example (Key = 4312): HELLO → OHLLE

6. PRIVATE-KEYCRYPTOGRAPHY
??????traditionalprivate/secret/single
key cryptographyusesonekey
??????sharedbybothsenderandreceiver
??????ifthiskeyisdisclosedcommunications
are compromised
??????alsoissymmetric,partiesareequal
??????hencedoesnotprotectsenderfromreceiver
forgingamessage&claimingissentbysender

7. PUBLIC-KEYCRYPTOGRAPHY
??????probablymostsignificantadvanceinthe
3000 yearhistoryofcryptography
??????usestwokeys–apublic&aprivatekey
??????asymmetricsincepartiesarenotequal
??????usescleverapplicationofnumber
theoretic conceptstofunction
??????complementsratherthanreplacesprivate
key crypto

8. WHYPUBLIC-KEYCRYPTOGRAPHY?
??????developedtoaddresstwokeyissues:
??????keydistribution–howtohavesecure
communicationsingeneralwithouthavingto
trustaKDCwithyourkey
??????digitalsignatures–howtoverifya
message comesintactfromtheclaimed
sender
??????publicinventionduetoWhitfieldDiffie
&MartinHellmanatStanfordUniin
1976
??????knownearlierinclassifiedcommunity

9. PUBLIC-KEYCRYPTOGRAPHY
??????public-key/two-key/asymmetriccryptography
involves theuseoftwokeys:
??????apublic-key,whichmaybeknownbyanybody,andcan
be usedtoencryptmessages,andverifysignatures
??????aprivate-key,knownonlytotherecipient,usedto
decrypt messages,andsign(create)signatures
??????isasymmetricbecause
??????thosewhoencryptmessagesorverifysignatures
cannot decryptmessagesorcreatesignatures

10. PUBLIC-KEYCRYPTOGRAPHY

11. PUBLIC-KEYCHARACTERISTICS
??????Public-Keyalgorithmsrelyontwokeyswhere:
??????itiscomputationallyinfeasibletofinddecryption
key knowingonlyalgorithm&encryptionkey
??????itiscomputationallyeasytoen/decryptmessageswhen
the relevant(en/decrypt)keyisknown
??????eitherofthetworelatedkeyscanbeusedfor
encryption, withtheotherusedfordecryption(forsome
algorithms)

12. PUBLIC-KEYCRYPTOSYSTEMS

13. PUBLIC-KEYAPPLICATIONS
??????canclassifyusesinto3categories:
??????encryption/decryption(providesecrecy)
??????digitalsignatures(provideauthentication)
??????keyexchange(ofsessionkeys)
??????somealgorithmsaresuitableforall
uses, othersarespecifictoone

14. RSA
??????byRivest,Shamir&AdlemanofMITin1977
??????bestknown&widelyusedpublic-keyscheme
??????basedonexponentiationinafinite(Galois)field
over integersmoduloaprime
??????nb.exponentiationtakesO((logn)
3)operations(easy)
??????useslargeintegers(eg.1024bits)
??????securityduetocostoffactoringlargenumbers
??????nb.factorizationtakesO(e
lognloglogn)operations(hard)

15. RSAKEYSETUP
??????eachusergeneratesapublic/privatekeypair
by:
??????selectingtwolargeprimesatrandom-p,q
??????computingtheirsystemmodulusn=p.q
??????note ø(n)=(p-1)(q-1)
??????selectingatrandomtheencryptionkeye
??????where1<e<ø(n),gcd(e,ø(n))=1
??????solvefollowingequationtofinddecryptionkey
d
??????e.d=1modø(n)and0≤d≤n
??????publishtheirpublicencryptionkey:PU={e,n}
??????keepsecretprivatedecryptionkey:PR={d,n}

16. RSAUSE
??????toencryptamessageMthesender:
??????obtainspublickeyofrecipientPU={e,n}
??????computes:C=M
e
modn,where0≤M<n
??????todecrypttheciphertextCtheowner:
??????usestheirprivatekeyPR={d,n}
??????computes:M=C
d
modn
??????notethatthemessageMmustbesmaller
than themodulusn(blockifneeded)

17. WHYRSAWORKS
??????becauseofEuler'sTheorem:
??????a
ø(n)modn=1wheregcd(a,n)=1
??????inRSAhave:
??????n=p.q
??????ø(n)=(p-1)(q-1)
??????carefullychosee&dtobeinversesmodø(n)
??????hencee.d=1+k.ø(n)forsomek
??????hence:
C
d=M
e.d=M
1+k.ø(n)=M
1.(M
ø(n))
k
=M
1
.(1)
k
= M
1
= Mmodn

18. RSAEXAMPLE-KEYSETUP
1.Selectprimes:p=17&q=11
2.Computen= pq=17x11=187
3.Computeø(n)=(p–1)(q-1)=16x10=160
4.Selecte:gcd(e,160)=1;choosee=7
5.Determined:de=1mod160and d<160Value
isd=23since23x7=161=10x160+1
6.PublishpublickeyPU={7,187}
7.KeepsecretprivatekeyPR={23,187}

19. RSAEXAMPLE-EN/DECRYPTION
??????sampleRSAencryption/decryption
is:
??????givenmessageM=88(nb.
88<187)
??????encryption:
C=88
7
mod187=11
??????decryption:
M=11
23
mod187=88

20. EXPONENTIATION
??????canusetheSquareandMultiplyAlgorithm
??????afast,efficientalgorithmforexponentiation
??????conceptisbasedonrepeatedly squaring
base
??????andmultiplyingintheonesthatareneeded
to computetheresult
??????lookatbinaryrepresentationofexponent
??????onlytakesO(log
2n)multiplesfornumbern
??????eg.7
5 =7
4.7
1 =3.7=10
mod11
=3
128.3
1
??????eg.3
129 =5.3=4mod11

21. EXPONENTIATION
c=0;f=1
fori=kdownto0
doc=2xc
f=(fxf)modn
ifb
i==1then
c=c+1
f=(fxa)modn
returnf

22. EFFICIENTENCRYPTION
??????encryptionusesexponentiationtopowere
??????henceifesmall,thiswillbefaster
??????oftenchoosee=65537(2
16
-1)
??????alsoseechoicesofe=3ore=17
??????butifetoosmall(ege=3)canattack
??????usingChineseremaindertheorem&3
messages withdifferentmodulii
??????ifefixedmustensuregcd(e,ø(n))=1
??????ierejectanyporqnotrelativelyprimetoe

23. EFFICIENTDECRYPTION
??????decryptionusesexponentiationtopowerd
??????thisislikelylarge,insecureifnot
??????canusetheChineseRemainderTheorem
(CRT) tocomputemodp&qseparately.then
combinetogetdesiredanswer
??????approx4timesfasterthandoingdirectly
??????onlyownerofprivatekeywhoknowsvalues
of p&qcanusethistechnique

24. RSAKEYGENERATION
??????usersofRSAmust:
??????determinetwoprimesatrandom-p,q
??????selecteithereordandcomputetheother
??????primesp,qmustnotbeeasilyderived
from modulusn=p.q
??????meansmustbesufficientlylarge
??????typicallyguessanduseprobabilistictest
??????exponentse,dareinverses,souse
Inverse algorithmtocomputetheother

25. RSASECURITY
??????possibleapproachestoattackingRSAare:
??????bruteforcekeysearch(infeasiblegivensize
of numbers)
??????mathematicalattacks(basedondifficulty
of computingø(n),byfactoringmodulusn)
??????timingattacks(onrunningofdecryption)
??????chosenciphertextattacks(givenpropertiesof
RSA)

26. InformationSecurity
Diffie–HellmanKeyExchange&
EllipticCurveCryptography

27. Diffie-HellmanKeyExchange
•firstpublic-keytypeschemeproposed
•byDiffie&Hellmanin1976alongwiththe
expositionofpublickeyconcepts
•note:nowknowthatWilliamson(UKCESG)
secretlyproposedtheconceptin1970
•isapracticalmethodforpublicexchangeofa
secretkey
•usedinanumberofcommercialproducts
[Continue…]

28. Diffie-HellmanKeyExchange
•apublic-keydistributionscheme
•cannotbeusedtoexchangeanarbitrarymessage
•ratheritcanestablishacommonkey
•knownonlytothetwoparticipants
•valueofkeydependsontheparticipants(and
theirprivateandpublickeyinformation)
•basedonexponentiation inafinite(Galois)field
(moduloaprimeorapolynomial)-easy
•securityreliesonthedifficultyofcomputing
discretelogarithms(similartofactoring)–hard
[Continue…]

29. Diffie-HellmanSetup
•allusersagreeonglobalparameters:
•largeprimeintegerorpolynomialq
•abeingaprimitiverootmodq
•eachuser(eg.A)generatestheirkey
•choosesasecretkey(number):x
A<q
A
•computetheirpublickey:y=a
x
A
modq
•eachusermakespublicthatkeyy
A
[Continue…]

30. Diffie-HellmanKeyExchange
•sharedsessionkeyforusersA&BisK
AB:
K
AB
=a
x
A.
x
B
mod q
xB
B
= y
x
A
= y
Amodq
modq
(whichBcancompute)
(whichAcancompute)
•K
ABisusedassessionkeyinprivate-key
encryptionschemebetweenAliceandBob
•ifAliceandBobsubsequentlycommunicate,
theywillhavethesamekeyasbefore,unless
theychoosenewpublic-keys
•attackerneedsanx,mustsolvediscretelog
[Continue…]

31. Diffie-HellmanExample
•usersAlice&Bobwhowishtoswapkeys:
•agreeonprimeq=353anda=3
•selectrandomsecretkeys:
•Achoosesx
A=97,Bchoosesx
B=233
•computerespectivepublickeys:
A
•y=3
97
B
•y=3
233
mod353=40
mod353=248
(Alice)
(Bob)
•computesharedsessionkeyas:
AB B
•K=y
x
A
97
AB A
•K=y
x
B
mod353=248
mod353=40
233
=160
=160
(Alice)
(Bob)
[Continue…]

32. KeyExchangeProtocols
•userscouldcreaterandomprivate/publicD-H
keyseachtimetheycommunicate
•userscouldcreateaknownprivate/publicD-H
keyandpublishinadirectory,thenconsulted
andusedtosecurelycommunicatewiththem
•bothofthesearevulnerabletoameet-in-the-
MiddleAttack
•authenticationofthekeysisneeded

33. DES vs AES Encryption

34. Introduction to Encryption
• Encryption is used to secure information by
converting plaintext into ciphertext.
• Symmetric encryption uses the same key
for both encryption and decryption.
• DES and AES are two widely known
symmetric encryption algorithms.

35. DES (Data Encryption Standard)
• Developed by IBM in the 1970s, adopted
by NIST.
• Uses a 56-bit key and encrypts data in 64-
bit blocks.
• 16 rounds of Feistel structure encryption.
• Vulnerable to brute-force attacks due to
small key size.
• Considered obsolete and replaced by AES.

36. AES (Advanced Encryption Standard)
• Developed by Vincent Rijmen and Joan
Daemen, adopted in 2001.
• Supports 128, 192, or 256-bit key sizes.
• Encrypts data in 128-bit blocks.
• Uses 10, 12, or 14 rounds of substitution-
permutation encryption.
• Highly secure and widely used in modern
encryption.

37. DES vs AES: Key Differences
• Key Size: DES (56-bit) vs AES (128, 192,
256-bit).
• Block Size: DES (64-bit) vs AES (128-bit).
• Rounds: DES (16 rounds) vs AES (10, 12,
or 14 rounds).
• Security: DES is weak against brute-force
attacks; AES is highly secure.
• Usage: DES is obsolete, AES is widely used
in modern encryption applications.

38. Conclusion
• DES was a pioneer in symmetric
encryption but is now outdated.
• AES is the modern standard due to its
enhanced security and flexibility.
• AES is used in secure communication, data
protection, and cybersecurity.
• Understanding these algorithms helps in
choosing the right encryption method.

39. Thank You!
Questions?