Key Management CS461/ECE422.

Key Management CS461/ECE422

Reading Chapter 10 in Computer Security: Art and Science
Handbook of Applied Cryptography Section attack on RSA signature Section Key Escrow

Key Management Motivation
Cryptographic security depends on keys Size Generation Retrieval and Storage Example House security system no good if key or code is under the mat

Overview Key Generation Key Exchange and management Digital Signatures
Classical (symmetric) Public/private Digital Signatures Key Storage

Key Management Processes associated with Distribution of keys
Binding identities to keys Generation, maintenance, and revoking keys

Notation X  Y : { Z || W } kX,Y A  T : { Z } kA || { W } kA,T
X sends Y the message produced by concatenating Z and W encrypted by key kX,Y, which is shared by users X and Y A  T : { Z } kA || { W } kA,T A sends T a message consisting of the concatenation of Z encrypted using kA, A’s key, and W encrypted using kA,T, the key shared by A and T r1, r2 nonces (nonrepeating random numbers)

Session and Interchange Keys
Long lived Interchange Keys only exist to boot strap Associated with a principal to the communication, e.g. public keys below Short lived session keys used for bulk encryption, e.g. Kb,Ka Ka,b Ka,b Ka,b Ka,Kb Kb,Ka {Ka,b}Ka {m1}Ka,b

Session and Interchange Keys
Another view---key and message in one shot Alice wants to send a message m to Bob Assume public key encryption Alice generates a random cryptographic key ks and uses it to encrypt m To be used for this message only, not used for authentication Called a session key She encrypts ks with key kB kB encrypts all session keys Alice uses to communicate with Bob : known by Bob, shared with Alice Called an interchange key. Used for authentication Alice sends { m } ks ||{ ks } kB Message m coded with ks Message ks coded with kB

Benefits Limits amount of traffic encrypted with single key
Standard practice, to decrease the amount of traffic an attacker can obtain Prevents some attacks. e.g., Suppose long lived key (public, or broken) kB Suppose set of possible messages is small, e.g. “BUY” or “SELL” Attack can pre-compute possible ciphertexts, observe, compare Example: Alice will send Bob message that is either “BUY” or “SELL”. Eve computes possible ciphertexts { “BUY” } kB and { “SELL” } kB. Eve intercepts encrypted message, compares, and gets plaintext at once

Key Generation Goal: generate keys that are difficult to guess
Problem statement: given a set of K potential keys, choose one randomly Equivalent to selecting a random number between 0 and K–1 inclusive Why is this hard: generating random numbers Actually, numbers are usually pseudo-random, that is, generated by an algorithm

What is “Random”? Sequence of cryptographically random numbers: a sequence of numbers n1, n2, … such that for any integer k > 0, an observer cannot predict nk even if all of n1, …, nk–1 are known Best: physical source of randomness Random pulses Electromagnetic phenomena Characteristics of computing environment such as disk latency Ambient background noise

What is “Pseudorandom”?
Sequence of cryptographically pseudorandom numbers: sequence of numbers intended to simulate a sequence of cryptographically random numbers but generated by an algorithm Very difficult to do this well Linear congruential generators [nk = (ank–1 + b) mod n] broken Polynomial congruential generators [nk = (ajnk–1j + … + a1nk–1 a0) mod n] broken too Here, “broken” means next number in sequence can be determined

Best Pseudorandom Numbers
Strong mixing function: function of 2 or more inputs with each bit of output depending on some nonlinear function of all input bits Examples: DES (mixes key and data), MD5, SHA-1, (multi-stage functions in hashing) avalanche effect Inputs need to be unpredictable

Key Exchange Principals to communication need to agree on key to be used. Criteria Key should not be transmitted in the clear Solutions : encrypt when sent, derive from public keys (e.g. Diffie-Hellman) Assume attacker can view EVERYTHING that is transmitted Permissible to use a trusted third party All protocols, mechanisms, algorithms should be assumed known. The only secrets are the keys involved

Separate Channel Ideally you have separate secure channel for exchanging keys Direct secret sharing grows at N2 Telephone, separate data network, ESP, sneaker net Regular data network

Shared Channel Generally separate channel is not practical
No trustworthy separate channel Want to scale linearly with additional users KA,KB, … KZ KB Key Exchange Regular data network KA

Classical Key Exchange
“Classical” means “no public key infrastructure” Bootstrap problem: how do Alice, Bob begin? Alice can’t send it to Bob in the clear! Assume trusted third party, Cathy Alice and Cathy share secret key kA Bob and Cathy share secret key kB Use this to exchange shared key ks

Simple Protocol { request for session key with Bob } kA Alice Cathy
{ ks } kA || { ks } kB Alice Cathy { ks } kB Alice Bob Notice : Cathy gives Alice the job of sending key to Bob { ks } kB Eve Bob Notice : Eve might break key, and entice Bob to use it with her or might simply replay the communication Alice had with Bob using that key

Problems How does Bob know he is talking to Alice?
Replay attack: Eve records message from Alice to Bob, later replays it; Bob may think he’s talking to Alice, but he isn’t e.g. message is “buy 100 shares of GE stock” Session key reuse: Eve replays message from Alice to Bob, so Bob re-uses session key If Eve has cracked session key off-line, she can say anything she likes in the communication Protocols must provide authentication and defense against replay

Public Key Key Exchange
Here interchange keys known eA, eB Alice and Bob’s public keys known to all dA, dB Alice and Bob’s private keys known only to owners Simple protocol ks is desired session key { ks } eB Alice Bob

Problem and Solution Vulnerable to forgery or replay
Because eB known to anyone, Bob has no assurance that Alice sent message Simple fix uses Alice’s private key ks is desired session key { { ks } dA } eB Alice Bob

Notes Can include message enciphered with ks
Assumes Bob has Alice’s public key, and vice versa If not, each must get it from public server If keys not bound to identity of owner, attacker Eve can launch a man-in-the-middle attack (next slide; Cathy is public server providing public keys) Solution to this (binding identity to keys) discussed later as public key infrastructure (PKI)

Man-in-the-Middle Attack
Pls send Bob’s public key Eve intercepts request Alice Cathy send Bob’s public key Eve Cathy eB Eve Cathy eE Alice Eve Alice believes that is Bob’s public key. It isn’t…. eE { ks } eE Eve intercepts message Alice Bob { ks } eB Eve Bob

Cryptographic Key Infrastructure
Goal: bind identity to key Classical: not possible as all keys are shared Use protocols to agree on a shared key (see earlier) Public key: bind identity to public key Crucial as people will use key to communicate with principal whose identity is bound to key Erroneous binding means no secrecy between principals Assume principal identified by an acceptable name

CA = eA || Alice || T || {h(eA || Alice || T )} dC
Certificates Create token (message) containing Identity of principal (here, Alice) Corresponding public key Timestamp (when issued) Other information (perhaps identity of signer) Compute hash (message digest) of token Hash encrypted by trusted authority (here, Cathy) using private key: called a “signature” CA = eA || Alice || T || {h(eA || Alice || T )} dC OBSERVE : public key, Alice and T are in the clear; hash is signed. Why?

Use Bob gets Alice’s certificate
If he knows Cathy’s public key, he can validate the certificate Decrypt encrypted hash using Cathy’s public key Re-compute hash from certificate and compare Check validity Is the principal Alice? Now Bob has Alice’s public key Problem: Bob needs Cathy’s public key to validate certificate That is, secure distribution of public keys Solution: Public Key Infrastructure (PKI) using trust anchors called Certificate Authorities (CAs) that issue certificates

X.509 Certificates Some certificate components in X.509v3: Version
Serial number Signature algorithm identifier: hash algorithm Issuer’s name; uniquely identifies issuer Interval of validity Subject’s name; uniquely identifies subject Subject’s public key Signature: encrypted hash

Transitive Trust If user U1 has a public-key certificate C issued by certificate authority CA1, then CA1 trusts that the identity on C is user U1’s Some validation used before C is issued U1 also trusts validity of other certs issued by CA1 If CA1 has a certificate D issued by CA2, then CA2 trusts that the identity on D is CA1’s, and that CA1 does due diligence in checking identities on certs that CA1 issues… CA1 trusts other certs that CA2 issues to certificate authorities and (possibly) users 50 50

Transitive Trust Illustrated
cert issued Trusts CA3’s identity and trustworthiness of certs issued CA2 CA3 Trusts certs signed by CA2 Trusts CA4’s identity and trustworthiness of certs issued Trusts CA1’s identity and trustworthiness of certs issued Trusts certs signed by CA2 Trusts certs signed by CA3 CA4 CA1 Trusts Bob’s identity Trusts Alice’s identity Trusts certs signed by CA4 Trusts certs signed by CA1 Bob Alice Suppose Alice has every cert implied in this diagram she trusts the key on Bob’s cert--- Why? She trusts CA2, and CA2 trusts Bob

PKI Trust Models … A Single Global CA Unmanageable, inflexible
There is no universally trusted organization Hierarchical CAs (Tree) Offloads burden on multiple CAs Need to verify a chain of certificates Still depends on a single trusted root CA Root CA Level I CA Level n CA User …

PKI Trust Models Hierarchical CAs with cross-certification Web Model
Multiple root CAs that are cross-certified Cross-certification at lower levels for efficiency Web Model Browsers come pre-configured with multiple trust anchor certificates New certificates can be added Distributed (e.g., PGP) No CA; instead, users certify each other to build a “web of trust”

Validation and Cross-Certifying
Alice’s CA is Cathy; Bob’s CA is Dan; how can Alice validate Bob’s certificate? Have Cathy and Dan cross-certify Each issues certificate for the other Certificates: Cathy<<Alice>> (Cathy issues cert for Alice) Dan<<Bob> (Dan issues cert for Bob) Cathy<<Dan>> (Cathy issues cert for Dan) Dan<<Cathy>> (Dan issues cert for Cathy) Cross-certification

Cross-Certification Alice gets cert from Bob :
Cert binds dest ID to dest PK, signed by src CA Alice gets cert from Bob : is there a common CA ancestor in the directed CA graph? Cathy CA CA Alice CA CA Dan Cross-certification Bob Alice gets Bob’s cert, signed by Dan Sees Dan’s cert is signed by Cathy Trusts Cathy as her own CA Alice uses (known) public key of Cathy to validate Dan’s cert Alice uses Dan’s public key (from cert) to validate Bob’s cert

PGP Chains OpenPGP certificates structured into packets
One public key packet Zero or more signature packets See Public key packet: Version (3 or 4; 3 compatible with all versions of PGP, 4 not compatible with older versions of PGP) Creation time Validity period (not present in version 3) Public key algorithm, associated parameters Public key

OpenPGP Signature Packet
Version 3 signature packet Version (3) Signature type (level of trust) Creation time Signer’s key identifier (identifies key to encrypt hash) Public key algorithm (used to encrypt hash) Hash algorithm Part of signed hash (used for quick check) Signature (encrypted hash) Version 4 packet more complex

Signing Single certificate may have multiple signatures
Notion of “trust” embedded in each signature Range from “untrusted” to “ultimate trust” Signer defines meaning of trust level (no standards!) All version 4 keys signed by subject Called “self-signing”

Validating Certificates
Arrows show signatures Self signatures not shown Alice needs to validate Bob’s OpenPGP cert Does not know Fred, Giselle, or Ellen Alice gets Giselle’s cert Knows Henry slightly, but his signature is at “casual” level of trust Alice gets Ellen’s cert Knows Jack, so uses his cert to validate Ellen’s, then hers to validate Bob’s Jack Henry Ellen Irene Giselle Fred Bob

Key Revocation Certificates invalidated before expiration Problems
Usually due to compromised key May be due to change in circumstance (e.g., someone leaving company) Problems Verify that entity revoking certificate authorized to do so Revocation information circulates to everyone fast enough Network delays, infrastructure problems may delay information

CRLs Certificate revocation list lists certificates that are revoked
X.509: only certificate issuer can revoke certificate Added to CRL PGP: signers can revoke signatures; owners can revoke certificates, or allow others to do so Revocation message placed in PGP packet and signed Flag marks it as revocation message

Digital Signature Construct that authenticated origin, contents of message in a manner provable to a disinterested third party (“judge”) Sender cannot deny having sent message (service is “non-repudiation”) Limited to technical proofs Inability to deny one’s cryptographic key was used to sign One could claim the cryptographic key was stolen or compromised Legal proofs, etc., probably required; not dealt with here

This is not a digital signature
Simple Approach Classical: Alice, Bob share key k Alice sends m || { m } k to Bob This is a digital signature WRONG This is not a digital signature Why? Third party cannot determine whether Alice or Bob generated message

Public Key Digital Signatures
Alice’s keys are (private) dAlice, (public) eAlice Alice sends Bob m || { m } dAlice In case of dispute, judge computes { { m } dAlice } eAlice and if it is m, Alice’s private key signed message She’s the only one who knows dAlice, so we infer Alice did the signing action

RSA Digital Signatures
Use private key to encrypt message Protocol for use is critical Key points: Never sign random documents, and when signing, always sign hash and never document Mathematical properties can be turned against signer Sign message first, then encrypt Changing public keys causes forgery

Attack #1 (m1 x m2 ) mod nb = m Get Bob to sign m1 and m2
Given Bob’s signatures on messages and Alice can compute his signature on message so the attack is to create evil message m, find factors (with appropriate modulus) and get Bob to sign them (m1 x m2 ) mod nb = m Get Bob to sign m1 and m2 m1d mod nb x m2d mod nb = (m1d x m2d ) mod nb = (m1 x m2 )d mod nb = md mod nb

Attack #1 example Example: Alice, Bob communicating
nA = 95, eA = 59, dA = 11 nB = 77, eB = 53, dB = 17 note that ops using Alice’s key are mod nA,, using Bob’s are nB 26 contracts, numbered 00 to 25 Alice has Bob sign 05 and 17: c = mdB mod nB = 0517 mod 77 = 3 c = mdB mod nB = 1717 mod 77 = 19 Alice computes 0517 mod 77 = 08; corresponding signature is (08)17 mod 77 = (0319) mod 77 = 57; claims Bob signed 08 Judge computes ceB mod nB = 5753 mod 77 = 08 Signature validated; Bob is toast

Attack #2: Bob’s Revenge
Bob, Alice agree to sign contract m but Bob wants it to appear that she signed contract M Alice encrypts with Bob’s public key (e.g. for confidentiality), then signs with her private key: c = (meB mod nB)dA mod nA Bob now changes his public key Computes r such that Mr mod nB = m Replace public key with product reB and computes a new matching private key d'B What exactly is the math problem to be solved? Bob claims contract was M. Judge computes: (ceA mod nA)d'B mod nB = M

Attack #2: Bob’s Revenge (cont’d)
Document is c = (meB mod nB)dA mod nA Bob’s new key pair is (r eB, d’B) M and r satisfy Mr mod nB = m What happens if M is encoded using new public key? (M r eB mod nB) = (M r )eB mod nB = m mod nB Bob claims contract was M. Judge computes: (ceA mod nA)d'B mod nB = M Verify Alice signed Decode using new public key Busted Illustrates dangers of encrypt-then-sign Recipient can pull a fast one on you 69 69

Attack #2 Example Bob, Alice agree to sign contract 06
Alice encrypts, then signs: (meB mod 77)dA mod nA = (0653 mod 77)11 mod 95 = 63 Bob now changes his public key Computes r such that 13r mod 77 = 6; say, r = 59 Computes r eB mod (nB) = 5953 mod 60 = 7 Replace public key eB with 7, private key dB = 43 Bob claims contract was 13. Judge computes: (6359 mod 95)43 mod 77 = 13 Verified; now Alice is toast

Digital Signature Algorithm (DSA)
Is a FIPS standard (186-3) proposed by NIST, 1991 See this link Is a bit more technical than it is interesting That has never stopped us before…. Three phases Key generation Signing Verification

DSA Key Generation Algorithmic parameters Hash function h
Key lengths (L, N) specifies options (1024,160), (2048,224), (2048,256), and (3072,256). Choose an N-bit prime q. Choose an L-bit prime modulus p such that p–1 is a multiple of q. Choose g, with multiplicative order modulo p equal to q. (p, q, g) may be shared Key generation---public and private keys Choose random x, with 0 < x < q. Calculate y = (g x ) mod p. Public key is (p, q, g, y). Private key is x.

DSA Signature Generate a random per-message value k where 0 < k < q Calculate r = ((g k) mod p) mod q Calculate s = (k’(H(m) + x*r)) mod q where k’ is the multiplicative inverse mod q of k Remember that x is private key Recalculate the signature in the unlikely case that r = 0 or s = 0 The signature is (r, s)

DSA Verification Given legal signature (r, s) Calculate w = (s’) mod q
s’ multiplicative inverse mod q Calculate u1 = (h(m)*w) mod q m is message whose signature we’re checking Calculate u2 = (r*w) mod q Calculate v = ((gu1 * yu2) mod p) mod q The signature is valid if v = r

Storing Keys Multi-user or networked systems: attackers may defeat access control mechanisms Encrypt file containing key Attacker can monitor keystrokes to decrypt files Key will be resident in memory that attacker may be able to read Use physical devices like “smart card” Key never enters system Card can be stolen, so have 2 devices combine bits to make single key

Key Escrow Key escrow system allows authorized third party to recover key Useful when keys belong to roles, such as system operator, rather than individuals Business: recovery of backup keys Law enforcement: recovery of keys that authorized parties require access to Goal: provide this without weakening cryptosystem Very controversial

Desirable Properties Escrow system should not depend on encryption algorithm Privacy protection mechanisms must work from end to end and be part of user interface Requirements must map to key exchange protocol System supporting key escrow must require all parties to authenticate themselves If message to be observable for limited time, key escrow system must ensure keys valid for that period of time only Beth, Knobloch, Otten, Simmons, Wichmann 94

Components User security component Key escrow component
Does the encryption, decryption Supports the key escrow component Key escrow component Manages storage, use of data recovery keys Data recovery component Does key recovery

Example: ESS, Clipper Chip
Escrow Encryption Standard FIPS 185 ( Set of interlocking components Designed to balance need for law enforcement access to enciphered traffic with citizens’ right to privacy Clipper chip given to user with prepared per- message escrow information Each chip numbered uniquely by UID Special facility programs each chip Key Escrow Decrypt Processor (KEDP) Available to agencies authorized to read messages

User Security Component
Unique device key kunique Non-unique family key kfamily Cipher is Skipjack Classical cipher: 80 bit key (ksession ), 64 bit input, output blocks Attaches Law Enforcement Access Field (LEAF) of 128 bits: { UID || { ksession } kunique || hash } kfamily hash: 16 bit authenticator from session key and initialization vector

User Security Component
message Programmed at initialization UID 64 bits skipjack 80 bit session key Based on session key and Initialization vector 64 bits Law Enforcement Access Field (32) (80) (16) Field sizes (in bits) ciphertext

Initialization of User Security Component
Seed1, Key1, Fam1 Escrow Agent I Secure Facility {ku1}kcomp Creates Combine Fam1, Fam2 to obtain kfamily Combine Key1,Key2 to obtain kcomp Combine Seed1, Seed2 to generate sequence kunique = ku1  ku2 UID, kunique, kfamily User “Clipper” Chip Escrow Agent II Seed2, Key2, Fam2 {ku2}kcomp Essential points Key that encrypts session key requires both and depends on input from both Escrow agents Returned encoding of uses key derived from both Escrow agents

Obtaining Access Alice obtains legal authorization to read message
She runs message LEAF through KEDP LEAF is { UID || { ksession } kunique || hash } kfamily KEDP uses (known) kfamily to validate LEAF (think hash(UID)), obtain sending device’s UID Authorization, LEAF taken to escrow agencies To get session key she needs to get kunique

Agencies’ Role Each validates authorization offered by Alice
Each supplies { kui } kcomp and key number Keyi KEDP takes these and LEAF: { UID || { ksession } kunique || hash } kfamily Key numbers produce kcomp kcomp produces ku1 and ku2 ku1 and ku2 produce kunique kunique and LEAF produce ksession

Problems Clipper would not decode messages with an invalid hash
So naturally the attack is to replace the real LEAF with one that has a valid hash! hash too short LEAF 128 bits, 16-bit “checksum” (hash) 2112 LEAFs have a valid hash, e.g., would validate 1 has actual session key, UID Takes about 42 minutes to find a randomly generated LEAF with a valid hash but meaningless session key and UID Turns out deployed devices would prevent this attack Scheme does not meet temporal requirement As kunique fixed for each unit, once message is read, any future messages can be read

Yaksha Key Escrow Main ideas:
Session keys obtained from a Yaksha server Server escrows generated keys Only messages encoded with the session key are recoverable

Key Points Key management critical to effective use of cryptosystems
Different levels of keys (session vs. interchange) Exchange algorithms can be vulnerable to attacks Replay Identity integrity Digital signatures provide integrity of origin and content Much easier with public key cryptosystems than with classical cryptosystems Keys need infrastructure to identify holders, allow revoking and possible escrow

Key Management CS461/ECE422.

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