Computer Science Public Key Management Lecture 5.

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Public Key Management

Lecture 5

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Outline

• Key management with asymmetric encryption

• Diffie-Hellman key exchange

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Key Management (public)

• public-key encryption helps address key distribution problems

• have two aspects of this:– distribution of public keys– use of public-key encryption to distribute

secret keys

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Distribution of Public Keys

• can be considered as using one of:– Public announcement– Publicly available directory– Public-key authority– Public-key certificates

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Public Announcement

• users distribute public keys to recipients or broadcast to community at large– (e.g. post to a newsgroup)

• major weakness is forgery• Weakness: anyone can create a key claiming to be

someone else and broadcast it (impersonation attack)

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Publicly available directory

• Publicly available directory: Achieve greater security by registering keys with a public directory

• Weakness: directory must be trusted and still vulnerable to forgery

– Public-key certificates (next slide)– Public-key authority (a few slides later)

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Digital Certificate

• To encrypt using a receiver’s public key, the sender needs to be assured that the public key used corresponds to the private key of the receiver.

• To verify a signature, a verifier needs to be assured that the public key used corresponds to the private key of the signer.

• The electronic document that attests to the ownership of a public key is called a certificate.

• How it works:– There is an entity called Certification Authority (CA)– Everyone trusts the certificates issued by the CA– CA has a public key which is publicly known

• e.g. built in all the web browsers– CA issues a certificate by generating a signature on the public key and the

identity of its owner.• Only the CA can create a certificate• Anyone can determine the user ID of a certificate owner• Anyone can verify the authenticity of the certificate (using CA’s public key)• Anyone can verify the validity (e.g. expiry date) of a certificate

CertA = < IDA, PKA, Validity Period, SignCA(IDA, PKA, Validity Period) >

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Public-Key Certificates• Certificates allow key exchange without real-time access to public-key

authority

• a certificate binds the identity (of the public key pair owner) to a public key – usually with other info such as period of validity, rights of use etc

• with all contents signed by a trusted Public-Key or Certificate Authority (CA)

• can be verified by anyone who knows CA’s public key

• E.g.

CertAlice = < IDAlice, SN, Expiry, PKAlice, SigCA(IDAlice, SN, Expiry, PKAlice) >

• So each user only needs to maintain a valid CA’s public key

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Certification Authorities

• Certification authority (CA): binds public key to particular entity, E.

• E (person, router) registers its public key with CA.– E provides “proof of identity” to CA.

– CA creates certificate binding E to its public key.

– certificate containing E’s public key digitally signed by CA – CA says “this is E’s public key”

Bob’s public

key PK B

Bob’s identifying informatio

n

digitalsignature(encrypt)

CA private

key RK CA

PK B

certificate for Bob’s public

key, signed by CA

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Certification Authorities

• When Alice wants Bob’s public key:– gets Bob’s certificate (Bob or elsewhere).– apply CA’s public key to Bob’s certificate,

get Bob’s public key

Bob’s public

key PK B

digitalsignature(decrypt)

CA public

key PK CA

PK B

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Verify the Public Key of a Web Server

• The web browser has CA’s public key built in.• In practice, there could have several trusted CAs for each web browser• New CAs can also be installed by users• The legitimacy of the web browser software becomes crucial for

ensuring the security of digital certificates• A certificate is NO more secure than the security of the web browser

download site

• Exercise: find out the information of three pre-installed CAs in Internet Explorer

Web Browser Internet

Web Server

(PK, SK)

Cert = < IDserver, PK, Expiry, SignCA(…) >

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Pre-installed CAs

Public Key: (RSA 1024-bit) 30 81 89 02 81 81 00 cc 5e d1 11 5d 5c 69 d0 ab d3 b9 6a 4c 99 1f 59 98 308e 16 85 20 46 6d 47 3f d4 85 20 84 e1 6d b3 f8 a4 ed 0c f1 17 0f 3b f9 a7 f9 25 d7 c1 cf 84 63 f2 7c 63 cf a2 47 f2 c65b 33 8e 64 40 04 68 c1 80 b9 64 1c 45 77 c7 d8 6e f5 95 29 3c 50 e8 34 d7 78 1f a8 ba 6d 43 91 95 8f 45 57 5e 7e c5fb ca a4 04 eb ea 97 37 54 30 6f bb 01 47 32 33 cd dc 57 9b 64 69 61 f8 9b 1d 1c 89 4f 5c 67 02 03 01 00 01

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A Certificate

User Name

Certificate Version

Validity Period

Serial No

User's Public Key

Other user attributes

CA's name

CA's signature (of all the above)

e.g.User Name: login.yahoo.comCertificate Version: V3Validity Period: Jan 28, 05 – Jan 29, 06Serial No: 4b5c94d17508e86594593d777e4d7dc4

User’s Public Key: RSA (1024 bits)30 81 89 02 81 81 00 be 33 b1 6b a6 f4 15 e9 54 d3 06 a4 c4 55 f2 ae db 4d 38 b2ce 83 f9 06 cd ad a7 f6 d9 54 76 aa 0c f4 85 e1 b9 3a b1 30 b4 56 c3 e4 ae 5a 3a98 8e 47 52 f5 be 72 5d 38 c1 a8 51 91 85 3b 28 7c f1 f4 a5 5b 19 74 8d 36 38 89ae 26 3e 41 7a c1 b8 54 a9 4c 4e 69 6c 96 51 a5 12 f7 bc e5 78 45 c2 8f 83 f2 ac39 b3 04 7a 44 20 d7 c8 ac 78 eb c7 ce 9c a5 25 48 33 ed 76 b9 6f 68 ef fc 80 6f02 03 01 00 01

Other attributes:e.g. signing algorithm: sha1RSA

CA’s name: Secure Server Certification Authority, RSA Data Security, Inc.

CA’s signature: 1024-bit data

CertA = < IDA, PKA, Validity Period,… SignCA(IDA, PKA, Validity Period, …) >

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Public-Key Certificates

Certificate Authority

Alice Bob

IDAlice, PKAliceIDBob, PKBob

CertAlice

CertAlice = < IDAlice, SN, Expiry, PKAlice, SigCA(IDAlice, SN, Expiry, PKAlice) >

CertBob

CertAlice

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Distribution of Secret Keys usingPublic Key

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Distribution of Secret Keys usingPublic Key

• public-key cryptography can be used for secrecy or authentication– but public-key algorithms are slow

• We want to use symmetric key encryption algorithm encrypt bulk message– Because symmetric key encryption algorithms are hundreds of

times faster than public key encryption algorithms

• So two communicating parties usually1. negotiate a symmetric key (called session key) with the help of

public key algorithms2. Then use the session key to encrypt messages3. For each new session (e.g. login your online banking service

again after closing the web browser), a new session key will be established

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Public-Key Distribution of Secret Keys

Alice Bob

CertAlice

CertBob

…

session key negotiation

Public key encrypted

…

Message flows

Session key encrypted

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Diffie-Hellman Key Exchange

• A Key Exchange Protocol:– provide a secure way for two communicating parties to share a

symmetric key (so called a session key)– This session key is then used to provide privacy and

authentication for subsequent message flow.– History: problem first posed by Merkle at UC Berkeley, Diffie and

Hellman came up with the protocol:

Alice Boba R Zp-1 ga mod p

gb mod pb R Zp-1

Shared Session Key = gab mod p

• More details next…

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Diffie-Hellman Key Exchange Setup

• Alice and Bob agree on global parameters:– Large prime integer p (e.g. 1024 bits long)

– g a primitive root / generator of Zp* (i.e. the multiplicative group modulo p)

• Alice– chooses a random positive integer: a < p

– computes yA = ga mod p

• Bob does the same and generates yB = gb mod p

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Diffie-Hellman Key Exchange

• Shared session key for Alice and Bob is KAB:KAB = ga b mod p

= yAb mod p (which Bob can compute)

= yBa mod p (which Alice can compute)

• KAB will then be used as a session key in symmetric key algorithms between Alice and Bob

• Attacker needs to find KAB from yA and yB

– A difficult problem

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Diffie-Hellman Key Exchange Example

Alice and Bob want to carry out DH Key Exchange:

1. Agree on prime p=353 and g=3

2. Select random secret keys:– A chooses a = 97– B chooses b = 233

3. Compute session key contributions– yA = 397 mod 353 = 40 (Alice)

– yB = 3233 mod 353 = 248 (Bob)

4. Compute shared session key as:

KAB = yBa mod 353 = 24897 mod 353 = 160 (Alice)

KAB = yAb mod 353 = 40233 mod 353 = 160 (Bob)