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Part 1 Cryptography 1

Protocollen en Handshake Pitfalls

Public Key Cryptography

Public Key Cryptography Two keys

o Sender uses recipient’s public key to encrypto Receiver uses his private key to decrypt

Based on trap door, one way functiono Easy to compute in one directiono Hard to compute in other directiono “Trap door” used to create keyso Example: Given p and q, product N=pq is easy to

compute, but given N, it is hard to find p and q

Public Key Cryptography Encryption

o Suppose we encrypt M with Bob’s public keyo Only Bob’s private key can decrypt to find M

Digital Signatureo Sign by “encrypting” with private keyo Anyone can verify signature by “decrypting”

with public keyo But only private key holder could have signedo Like a handwritten signature (and then some)

RSA Invented by Cocks (GCHQ), independently,

by Rivest, Shamir and Adleman (MIT) Let p and q be two large prime numbers Let N = pq be the modulus Choose e relatively prime to (p−1)(q−1) Find d s.t. ed = 1 mod (p−1)(q−1) Public key is (N,e) Private key is d

RSA To encrypt message M compute

o C = Me mod N To decrypt C compute

o M = Cd mod N Recall that e and N are public If attacker can factor N, he can use e to

easily find d since ed = 1 mod (p−1)(q−1) Factoring the modulus breaks RSA It is not known whether factoring is the

only way to break RSA

Diffie-Hellman

Diffie-Hellman Invented by Williamson (GCHQ) and,

independently, by D and H (Stanford) A “key exchange” algorithm

o Used to establish a shared symmetric key Not for encrypting or signing Security rests on difficulty of discrete log

problem: given g, p, and gk mod p find k

Diffie-Hellman Let p be prime, let g be a generator

o For any x ∈ {1,2,…,p-1} there is n s.t. x = gn mod p Alice selects secret value a Bob selects secret value b Alice sends ga mod p to Bob Bob sends gb mod p to Alice Both compute shared secret gab mod p Shared secret can be used as symmetric key

Diffie-Hellman Suppose that Bob and Alice use gab mod p as

a symmetric key Trudy can see ga mod p and gb mod p Note ga gb mod p = ga+b mod p ≠ gab mod p If Trudy can find a or b, system is broken If Trudy can solve discrete log problem,

then she can find a or b

Diffie-Hellman Public: g and p Secret: Alice’s exponent a, Bob’s exponent b

Alice, a Bob, b

ga mod p

gb mod p

Alice computes (gb)a = gba = gab mod p Bob computes (ga)b = gab mod p Could use K = gab mod p as symmetric key

Diffie-Hellman Subject to man-in-the-middle (MiM) attack

Alice, a Bob, b

ga mod p

gb mod p

Trudy, t

gt mod p

Trudy shares secret gat mod p with Alice Trudy shares secret gbt mod p with Bob Alice and Bob don’t know Trudy exists!

Diffie-Hellman How to prevent MiM attack?

o Encrypt DH exchange with symmetric keyo Encrypt DH exchange with public keyo Sign DH values with private keyo Other?

You MUST be aware of MiM attack on Diffie-Hellman

Elliptic Curve Cryptography

Elliptic Curve Crypto (ECC) “Elliptic curve” is not a cryptosystem Elliptic curves are a different way to do the

math in public key system Elliptic curve versions of DH, RSA, etc. Elliptic curves may be more efficient

o Fewer bits needed for same securityo But the operations are more complex

What is an Elliptic Curve? An elliptic curve E is the graph of

an equation of the formy2 = x3 + ax + b

Also includes a “point at infinity” What do elliptic curves look like? See the next slide!

Elliptic Curve Picture

Consider elliptic curveE: y2 = x3 - x + 1

If P1 and P2 are on E, we can define

P3 = P1 + P2 as shown in picture

Addition is all we need

ECC Diffie-Hellman Public: Elliptic curve and point (x,y) on curve Secret: Alice’s A and Bob’s B

Alice, A Bob, B

A(x,y)

B(x,y)

Alice computes A(B(x,y)) Bob computes B(A(x,y)) These are the same since AB = BA

ECC Diffie-Hellman Public: Curve y2 = x3 + 7x + b (mod 37)

and point (2,5) ⇒ b = 3 Alice’s secret: A = 4 Bob’s secret: B = 7 Alice sends Bob: 4(2,5) = (7,32) Bob sends Alice: 7(2,5) = (18,35) Alice computes: 4(18,35) = (22,1) Bob computes: 7(7,32) = (22,1)

Uses for Public Key Crypto

Uses for Public Key Crypto Confidentiality

o Transmitting data over insecure channelo Secure storage on insecure media

Authentication (later) Digital signature provides integrity

and non-repudiationo No non-repudiation with symmetric keys

Non-non-repudiation Alice orders 100 shares of stock from Bob Alice computes MAC using symmetric key Stock drops, Alice claims she did not order Can Bob prove that Alice placed the order? No! Since Bob also knows symmetric key, he

could have forged message Problem: Bob knows Alice placed the order,

but he can’t prove it

Non-repudiation Alice orders 100 shares of stock from Bob Alice signs order with her private key Stock drops, Alice claims she did not order Can Bob prove that Alice placed the order? Yes! Only someone with Alice’s private key

could have signed the order This assumes Alice’s private key is not

stolen (revocation problem)

Sign and Encrypt vs

Encrypt and Sign

Public Key NotationSign message M with Alice’s private key: [M]Alice

Encrypt message M with Alice’s public key: {M}Alice

Then{[M]Alice}Alice = M[{M}Alice]Alice = M

Confidentiality and Non-repudiation

Suppose that we want confidentiality and non-repudiation

Can public key crypto achieve both? Alice sends message to Bob

o Sign and encrypt {[M]Alice}Bob

o Encrypt and sign [{M}Bob]Alice

Can the order possibly matter?

Sign and Encrypt

Alice Bob

{[M]Alice}Bob

Q: What is the problem? A: Charlie misunderstands crypto!

Charlie

{[M]Alice}Charlie

M = “I love you”

Encrypt and Sign

Alice Bob

[{M}Bob]Alice

Note that Charlie cannot decrypt M Q: What is the problem? A: Bob misunderstands crypto!

Charlie

[{M}Bob]Charlie

M = “My theory, which is mine….”

Public Key Infrastructure

Public Key Certificate Contains name of user and user’s

public key (and possibly other info) Certificate is signed by the issuer

(such as VeriSign) who vouches for it Signature on certificate is verified

using signer’s public key

Certificate Authority Certificate authority (CA) is a trusted 3rd

party (TTP) that issues and signs cert’so Verifying signature verifies the identity of the

owner of corresponding private keyo Verifying signature does not verify the identity

of the source of certificate!o Certificates are public!o Big problem if CA makes a mistake (a CA once

issued Microsoft certificate to someone else!)o Common format for certificates is X.509

PKI Public Key Infrastructure (PKI) consists of

all pieces needed to securely use public key cryptographyo Key generation and managemento Certificate authoritieso Certificate revocation (CRLs), etc.

No general standard for PKI We consider a few “trust models”

PKI Trust Models Monopoly model

o One universally trusted organization is the CA for the known universe

o Favored by VeriSign (for obvious reasons)o Big problems if CA is ever compromisedo Big problem if you don’t trust the CA!

PKI Trust Models Oligarchy

o Multiple trusted CAso This approach used in browsers todayo Browser may have 80 or more certificates,

just to verify signatures!o User can decide which CAs to trust

PKI Trust Models Anarchy model

o Everyone is a CA!o Users must decide which “CAs” to trusto This approach used in PGP (Web of trust)o Why do they call it “anarchy”? Suppose cert. is

signed by Frank and I don’t know Frank, but I do trust Bob and Bob says Alice is trustworthy and Alice vouches for Frank. Should I trust Frank?

Many other PKI trust models

Confidentiality in the Real World

Symmetric Key vs Public Key Symmetric key +’s

o Speedo No public key infrastructure (PKI) needed

Public Key +’so Signatures (non-repudiation)o No shared secret

Notation Reminder Public key notation

o Sign message M with Alice’s private key [M]Alice

o Encrypt message M with Alice’s public key {M}Alice

Symmetric key notationo Encrypt plaintext P with symmetric key K

C = E(P,K) o Decrypt ciphertext C with symmetric key K

P = D(C,K)

Real World Confidentiality Hybrid cryptosystem

o Public key crypto to establish a keyo Symmetric key crypto to encrypt datao Consider the following

Alice Bob

{K}Bob

E(Bob’s data, K)

E(Alice’s data, K)

Can Bob be sure he’s talking to Alice?

Hash Functions

Hash Function Motivation Suppose Alice signs M

o Alice sends M and S = [M]Alice to Bobo Bob verifies that M = {S}Alice

o Is it OK to just send S? If M is big, [M]Alice is costly to compute Suppose instead, Alice signs h(M), where

h(M) is much smaller than Mo Alice sends M and S = [h(M)]Alice to Bobo Bob verifies that h(M) = {S}Alice

Crypto Hash Function Crypto hash function h(x) must provide

o Compression output length is smallo Efficiency h(x) easy to computer for any xo One-way given a value y it is infeasible to

find an x such that h(x) = yo Weak collision resistance given x and h(x),

infeasible to find y ≠ x such that h(y) = h(x)o Strong collision resistance infeasible to

find any x and y, with x ≠ y such that h(x) = h(y)o Lots of collisions exist, but hard to find one

Pre-Birthday Problem Suppose N people in a room How large must N be before the

probability someone has same birthday as me is ≥ 1/2o Solve: 1/2 = 1 − (364/365)N for No Find N = 253

Birthday Problem How many people must be in a room before

probability is ≥ 1/2 that two or more have same birthday?o 1 − 365/365 ⋅ 364/365 ⋅ ⋅ ⋅(365−N+1)/365o Set equal to 1/2 and solve: N = 23

Surprising? A paradox? Maybe not: “Should be” about sqrt(365)

since we compare all pairs x and y

Of Hashes and Birthdays If h(x) is N bits, then 2N different hash

values are possible sqrt(2N) = 2N/2

Therefore, hash about 2N/2 random values and you expect to find a collision

Implication: secure N bit symmetric key requires 2N−1 work to “break” while secure N bit hash requires 2N/2 work to “break”

Non-crypto Hash (1) Data X = (X0,X1,X2,…,Xn-1), each Xi is a byte Spse hash(X) = X0+X1+X2+…+Xn-1

Is this secure? Example: X = (10101010,00001111) Hash is 10111001 But so is hash of Y = (00001111,10101010) Easy to find collisions, so not secure…

Non-crypto Hash (2) Data X = (X0,X1,X2,…,Xn-1) Suppose hash is

o h(X) = nX0+(n-1)X1+(n-2)X2+…+1⋅Xn-1

Is this hash secure? At least

o h(10101010,00001111)≠h(00001111,10101010) But hash of (00000001,00001111) is same as

hash of (00000000,00010001) Not one-way, but this hash is used in the

(non-crypto) application rsync

Non-crypto Hash (3) Cyclic Redundancy Check (CRC) Essentially, CRC is the remainder in a

long division problem Good for detecting burst errors But easy to construct collisions CRC sometimes mistakenly used in

crypto applications (WEP)

Popular Crypto Hashes MD5 invented by Rivest

o 128 bit outputo Note: MD5 collision recently found

SHA-1 A US government standard (similar to MD5)o 160 bit output

Many others hashes, but MD5 and SHA-1 most widely used

Hashes work by hashing message in blocks

Crypto Hash Design Desired property: avalanche effect

o Change to 1 bit of input should affect about half of output bits

Crypto hash functions consist of some number of rounds

Want security and speedo Avalanche effect after few roundso But simple rounds

Analogous to design of block ciphers

Hash Uses Authentication (HMAC) Message integrity (HMAC) Message fingerprint Data corruption detection Digital signature efficiency Anything you can do with symmetric crypto

Online Auction Suppose Alice, Bob and Charlie are bidders Alice plans to bid A, Bob B and Charlie C They don’t trust that bids will stay secret Solution?

o Alice, Bob, Charlie submit hashes h(A), h(B), h(C)o All hashes received and posted onlineo Then bids A, B and C revealed

Hashes don’t reveal bids (one way) Can’t change bid after hash sent (collision)

Spam Reduction Spam reduction Before I accept an email from you, I

want proof that you spent “effort” (e.g., CPU cycles) to create the email

Limit amount of email that can be sent Make spam much more costly to send

Spam Reduction Let M = email message Let R = value to be determined Let T = current time Sender must find R such that

o hash(M,R,T) = (00…0,X), whereo N initial bits of hash are all zero

Sender then sends (M,R,T) Recipient accepts email, provided

o hash(M,R,T) begins with N zeros

Spam Reduction Sender: hash(M,R,T) begins with N zeros Recipient: verify that hash(M,R,T) begins

with N zeros Work for sender: about 2N hashes Work for recipient: 1 hash Sender’s work increases exponentially in N Same work for recipient regardless of N Choose N so that

o Work acceptable for normal email userso Work unacceptably high for spammers!

Secret Sharing

Shamir’s Secret Sharing

(X0,Y0)(X1,Y1)

Two points determine a line Give (X0,Y0) to Alice Give (X1,Y1) to Bob Then Alice and Bob must cooperate to find secret S Also works in discrete case Easy to make “m out of n” scheme for any m ≤ nX

2 out of 2

(X0,Y0)

(X1,Y1)

Give (X0,Y0) to Alice Give (X1,Y1) to Bob Give (X2,Y2) to Charlie Then any two of Alice, Bob and Charlie can cooperate to find secret S But no one can find secret S A “2 out of 3” schemeX

(X2,Y2)

2 out of 3

(X0,Y0)

(X1,Y1)

Give (X0,Y0) to Alice Give (X1,Y1) to Bob Give (X2,Y2) to Charlie 3 points determine a parabola Alice, Bob and Charlie must cooperate to find secret S A “3 out of 3” scheme Can you make a “3 out of 4”?

(X2,Y2)

3 out of 3

Secret Sharing Example Key escrow required that your key be

stored somewhere Key can be used with court order But you don’t trust FBI to store keys We can use secret sharing

o Say, three different government agencieso Two must cooperate to recover the key

Secret Sharing Example

(X0,Y0)

(X1,Y1)

Your symmetric key is K Point (X0,Y0) to FBI Point (X1,Y1) to DoJ Point (X2,Y2) to DoC To recover your key K, two of the three agencies must cooperate No one agency can get K

(X2,Y2)

Random Numbers in Cryptography

Random Numbers Random numbers used to generate keys

o Symmetric keyso RSA: Prime numberso Diffie Hellman: secret values

Random numbers used for nonceso Sometimes a sequence is OKo But sometimes nonces must be random

Random numbers also used in simulations, statistics, etc., where numbers only need to be “statistically” random

Random Numbers Cryptographic random numbers must be

statistically random and unpredictable Suppose server generates symmetric keys

o Alice: KA

o Bob: KB

o Charlie: KC

o Dave: KD

Spse Alice, Bob and Charlie don’t like Dave Alice, Bob and Charlie working together must

not be able to determine KD

Bad Random Number Example

Random numbers used to shuffle the deck Program did not produce a random shuffle Could determine the shuffle in real time!

Online version of Texas Hold ‘em Pokero ASF Software, Inc.

Randomness True randomness is hard to defineEntropy is a measure of randomness Good sources of “true” randomness

o Radioactive decay though radioactive computers are not too popular

o Hardware devices many good ones on the market

o Lava lamp relies on chaotic behavior

Randomness Sources of randomness via software

o Software is (hopefully) deterministico So must rely on external “random” eventso Mouse movements, keyboard dynamics, network

activity, etc., etc. Can get quality random bits via software But quantity of such bits is very limited Bottom line: “The use of pseudo-random

processes to generate secret quantities can result in pseudo-security”

Protocols

Protocol Human protocols the rules followed in

human interactionso Example: Asking a question in class

Networking protocols rules followed in networked communication systemso Examples: HTTP, FTP, etc.

Security protocol the (communication) rules followed in a security applicationo Examples: SSL, IPSec, Kerberos, etc.

Protocols Protocol flaws can be very subtle Several well-known security protocols

have serious flawso Including IPSec, GSM and WEP

Common to find implementation errorso Such as IE implementation of SSL

Difficult to get protocols right…

Ideal Security Protocol Satisfies security requirements

o Requirements must be precise Efficient

o Minimize computational requirement in particular, costly public key operations

o Minimize delays/bandwidth Not fragile

o Must work when attacker tries to break ito Works even if environment changes

Easy to use and implement, flexible, etc. Very difficult to satisfy all of these!

Simple Security Protocols

Secure Entry to NSA1. Insert badge into reader2. Enter PIN3. Correct PIN?

Yes? EnterNo? Get shot by security guard

ATM Machine Protocol1. Insert ATM card2. Enter PIN3. Correct PIN?

Yes? Conduct your transaction(s)No? Machine eats card

Identify Friend or Foe (IFF)

Namibia

Angola

2. E(N,K)SAAFImpala

RussianMIG

MIG in the Middle

Namibia

Angola

4. E(N,K)

5. E(N,K)

6. E(N,K)

SAAFImpala

RussianMiG

Authentication Protocols

Authentication Alice must prove her identity to Bob

o Alice and Bob can be humans or computers May also require Bob to prove he’s Bob

(mutual authentication) May also need to establish a session key May have other requirements, such as

o Use only public keyso Use only symmetric keyso Use only a hash functiono Anonymity, plausible deniability, etc., etc.

Authentication Authentication on a stand-alone computer is

relatively simpleo “Secure path” is the primary issueo Main concern is an attack on authentication

software (we discuss software attacks later) Authentication over a network is much more

complexo Attacker can passively observe messageso Attacker can replay messageso Active attacks may be possible (insert, delete,

change messages)

Simple Authentication

Alice Bob

“I’m Alice”

Prove it

My password is “frank”

Simple and may be OK for standalone system But insecure for networked system

o Subject to a replay attack (next 2 slides)o Bob must know Alice’s password

Authentication Attack

Alice Bob

“I’m Alice”

Prove it

My password is “frank”

Authentication Attack

“I’m Alice”

Prove it

My password is “frank”Trudy

This is a replay attack How can we prevent a replay?

Simple Authentication

Alice Bob

I’m Alice, My password is “frank”

More efficient… But same problem as previous version

Better Authentication

Alice Bob

“I’m Alice”

Prove it

h(Alice’s password)

Better since it hides Alice’s passwordo From both Bob and attackers

But still subject to replay

Challenge-Response To prevent replay, challenge-response used Suppose Bob wants to authenticate Alice

o Challenge sent from Bob to Aliceo Only Alice can provide the correct responseo Challenge chosen so that replay is not possible

How to accomplish this?o Password is something only Alice should know…o For freshness, a “number used once” or nonce

Challenge-Response

“I’m Alice”

h(Alice’s password, Nonce)

Nonce is the challenge The hash is the response Nonce prevents replay, insures freshness Password is something Alice knows Note that Bob must know Alice’s password

Challenge-Response

“I’m Alice”

Something that could only beAlice from Alice (and Bob can verify)

What can we use to achieve this? Hashed pwd works, crypto might be better

Symmetric Key Notation Encrypt plaintext P with key K

C = E(P,K) Decrypt ciphertext C with key K

P = D(C,K) Here, we are concerned with attacks on

protocols, not directly on the crypto We assume that crypto algorithm is secure

Symmetric Key Authentication Alice and Bob share symmetric key KAB

Key KAB known only to Alice and Bob Authenticate by proving knowledge of

shared symmetric key How to accomplish this?

o Must not reveal keyo Must not allow replay attack

Authentication with Symmetric Key

Alice, KABBob, KAB

“I’m Alice”

E(R,KAB)

Secure method for Bob to authenticate Alice Alice does not authenticate Bob Can we achieve mutual authentication?

Mutual Authentication?

Alice Bob

“I’m Alice”, R

E(R,KAB)

What’s wrong with this picture? “Alice” could be Trudy (or anybody else)!

Mutual Authentication Since we have a secure one-way

authentication protocol… The obvious thing to do is to use the

protocol twiceo Once for Bob to authenticate Aliceo Once for Alice to authenticate Bob

This has to work…

Mutual Authentication

Alice Bob

“I’m Alice”, RA

RB, E(RA,KAB)

E(RB,KAB)

This provides mutual authentication Is it secure? See the next slide…

Mutual Authentication Attack

1. “I’m Alice”, RA

2. RB, E(RA,KAB)

3. “I’m Alice”, RB

4. RC, E(RB,KAB)

5. E(RB,KAB)

Mutual Authentication Our one-way authentication protocol not

secure for mutual authentication Protocols are subtle! The “obvious” thing may not be secure Also, if assumptions or environment changes,

protocol may not worko This is a common source of security failureo For example, Internet protocols

Symmetric Key Mutual Authentication

Alice Bob

RB, E(“Bob”,RA,KAB)

E(“Alice”,RB,KAB)

Do these “insignificant” changes help? Yes!

Public Key Notation Encrypt M with Alice’s public key: {M}Alice

Sign M with Alice’s private key: [M]Alice

Theno [{M}Alice ]Alice = Mo {[M]Alice }Alice = M

Anybody can do public key operations Only Alice can use her private key (sign)

Public Key Authentication

Alice Bob

“I’m Alice”

{R}Alice

Is this secure? Trudy can get Alice to decrypt anything!

o Must have two key pairs

Public Key Authentication

Alice Bob

“I’m Alice”

[R]Alice

Is this secure? Trudy can get Alice to sign anything!

o Must have two key pairs

Public Keys Never use the same key pair for

encryption and signing One key pair for

encryption/decryption A different key pair for

signing/verifying signatures

Session Key Usually, a session key is required

o Symmetric key for a particular session Can we authenticate and establish a shared

symmetric key?o Key can be used for confidentialityo Key can be used for integrity

In some cases, we may also require perfect forward secrecy (PFS)o Discussed later…

Authentication & Session Key

Alice Bob

{R,K}Alice

{R +1,K}Bob

Is this secure? OK for key, but no mutual authentication Note that K is acting as Bob’s nonce

Public Key Authentication and Session Key

Alice Bob

[R,K]Bob

[R +1,K]Alice

Is this secure? Mutual authentication but key is not secret!

Alice Bob

{[R,K]Bob}Alice

{[R +1,K]Alice}Bob

Is this secure? Seems to be OK Mutual authentication and session key!

Alice Bob

[{R,K}Alice]Bob

[{R +1,K}Bob]Alice

Is this secure? Seems to be OK

o Though anyone can see {R,K}Alice and {R +1,K}Bob

Perfect Forward Secrecy The concern…

o Alice encrypts message with shared key KAB and sends ciphertext to Bob

o Trudy records ciphertext and later attacks Alice’s (or Bob’s) computer to find KAB

o Then Trudy decrypts recorded messages Perfect forward secrecy (PFS): Trudy

cannot later decrypt recorded ciphertexto Even if Trudy gets key KAB or other secret(s)

Is PFS possible?

Perfect Forward Secrecy Suppose Alice and Bob share key KAB For perfect forward secrecy, Alice

and Bob cannot use KAB to encrypt Instead they must use a session key

KS and forget it after it’s used Problem: How can Alice and Bob agree

on session key KS and insure PFS?

Naïve Session Key Protocol

Trudy could also record E(KS,KAB) If Trudy gets KAB, she gets KS

Alice, KAB Bob, KAB

E(KS, KAB)

E(messages, KS)

Perfect Forward Secrecy Can use Diffie-Hellman for PFS Recall Diffie-Hellman: public g and p

But Diffie-Hellman is subject to MiM How to get PFS and prevent MiM?

Alice, a Bob, b

ga mod p

gb mod p

Perfect Forward Secrecy

Session key KS = gab mod p Alice forgets a, Bob forgets b Ephemeral Diffie-Hellman Not even Alice and Bob can later recover KS

Other ways to do PFS?

Alice, a Bob, b

E(ga mod p, KAB)

E(gb mod p, KAB)

Mutual Authentication, Session Key and PFS

Alice Bob

RB, [{RA, gb mod p}Alice]Bob

[{RB, ga mod p}Bob]Alice

Session key is K = gab mod p Alice forgets a and Bob forgets b If Trudy later gets Bob’s and Alice’s secrets,

she cannot recover session key K

Timestamps A timestamp T is the current time Timestamps used in many security protocols

(Kerberos, for example) Timestamps reduce number of messages

o Like a nonce that both sides know in advance But, use of timestamps implies that time is a

security-critical parameter Clocks never exactly the same, so must allow

for clock skew risk of replay How much clock skew is enough?

Public Key Authentication with Timestamp T

“I’m Alice”, {[T,K]Alice}Bob

{[T +1,K]Bob}Alice

Is this secure? Seems to be OK

“I’m Alice”, [{T,K}Bob]Alice

[{T +1,K}Alice]Bob

Is this secure? Trudy can use Alice’s public key to find {T,K}Bob and then…

“I’m Trudy”, [{T,K}Bob]Trudy

[{T +1,K}Trudy]Bob

Trudy obtains Alice-Bob session key K Note: Trudy must act within clock skew

Public Key Authentication Sign and encrypt with nonce…

o Secure Encrypt and sign with nonce…

o Secure Sign and encrypt with timestamp…

o Secure Encrypt and sign with timestamp…

o Insecure Protocols can be subtle!

“I’m Alice”, [{T,K}Bob]Alice

[{T +1}Alice]Bob

Alice Is this “encrypt and sign” secure? Yes, seems to be Does “sign and encrypt” also work here?

Authentication and TCP

TCP-based Authentication TCP not intended for use as an

authentication protocol But IP address in TCP connection

often used for authentication One mode of IPSec uses IP address

for authentication This can cause problems

TCP 3-way Handshake

Alice Bob

SYN, SEQ a

SYN, ACK a+1, SEQ b

ACK b+1, data

Recall the TCP three way handshake Initial SEQ number must be random Why? See the next slide…

TCP Authentication Attack

BobTrudy

1. SYN, SEQ = t (as Trudy)

2. SYN, ACK = t+1, SEQ = b1

3. SYN, SEQ = t (as Alice)

4. SYN, ACK = t+1, SEQ = b 2

5. ACK = b2+1, data

TCP Authentication Attack

Random SEQ numbersInitial SEQ numbers

Mac OS X

If initial SEQ numbers not very random… …possible to guess initial SEQ number… …and previous attack will succeed

TCP Authentication Attack Trudy cannot see what Bob sends, but she can

send packets to server Bob, while posing as Alice Trudy must prevent Alice from receiving Bob’s

packets (or else connection will terminate) If password (or other authentication) required,

this attack fails If TCP connection is relied on for authentication,

then attack succeeds Bad idea to rely on TCP for authentication

Best Authentication Protocol? What is best depends on many factors… The sensitivity of the application The delay that is tolerable The cost that is tolerable What crypto is supported

o Public key, symmetric key, hash functions Is mutual authentication required? Is a session key required? Is PFS a concern? Is anonymity a concern?, etc.

Real-World Protocols Next, we’ll look at specific protocols

o SSL security on the Webo IPSec security at the IP layero Kerberos symmetric key systemo GSM mobile phone (in)security

Secure Socket Layer

Socket layer “Socket layer”

lives between application and transport layers

SSL usually lies between HTTP and TCP

application

transport

network

physical

Socket“layer”

What is SSL? SSL is the protocol used for most secure

transactions over the Internet For example, if you want to buy a book at

amazon.com…o You want to be sure you are dealing with

Amazon (authentication)o Your credit card information must be protected

in transit (confidentiality and/or integrity)o As long as you have money, Amazon doesn’t care

who you are (authentication need not be mutual)

Simple SSL-like Protocol

Alice Bob

I’d like to talk to you securely

Here’s my certificate

{KAB}Bob

protected HTTP

Is Alice sure she’s talking to Bob? Is Bob sure he’s talking to Alice?

Simplified SSL Protocol

Alice Bob

Can we talk?, cipher list, RA

Certificate, cipher, RB

{S}Bob, E(h(msgs,CLNT,K),K)

Data protected with key Kh(msgs,SRVR,K)

S is pre-master secret K = h(S,RA,RB) msgs = all previous messages CLNT and SRVR are constants

SSL Keys 6 “keys” derived from K = hash(S,RA,RB)

o 2 encryption keys: send and receiveo 2 integrity keys: send and receiveo 2 IVs: send and receiveo Why different keys in each direction?

Q: Why is h(msgs,CLNT,K) encrypted (and integrity protected)?

A: It adds no security…

SSL Authentication Alice authenticates Bob, not vice-versa

o How does client authenticate server?o Why does server not authenticate client?

Mutual authentication is possible: Bob sends certificate request in message 2o This requires client to have certificateo If server wants to authenticate client, server

could instead require (encrypted) password

SSL MiM Attack

Alice Bob

certificateT, RB

{S1}Trudy,E(X1,K1)

E(data,K1)h(Y1,K1)

Q: What prevents this MiM attack? A: Bob’s certificate must be signed by a

certificate authority (such as Verisign) What does Web browser do if sig. not

valid? What does user do if signature is not valid?

certificateB, RB

{S2}Bob,E(X2,K2)

E(data,K2)h(Y2,K2)

SSL Sessions vs Connections SSL session is established as shown on

previous slides SSL designed for use with HTTP 1.0 HTTP 1.0 usually opens multiple simultaneous

(parallel) connections SSL session establishment is costly

o Due to public key operations SSL has an efficient protocol for opening

new connections given an existing session

SSL Connection

Alice Bob

session-ID, cipher list, RA

session-ID, cipher, RB,

h(msgs,SRVR,K)

h(msgs,CLNT,K)

Protected data

Assuming SSL session exists So S is already known to Alice and Bob Both sides must remember session-ID Again, K = h(S,RA,RB)

No public key operations! (relies on known S)

SSL vs IPSec IPSec discussed in next section

o Lives at the network layer (part of the OS)o Has encryption, integrity, authentication, etc.o Is overly complex (including serious flaws)

SSL (and IEEE standard TLS)o Lives at socket layer (part of user space)o Has encryption, integrity, authentication, etc.o Has a simpler specification

SSL vs IPSec IPSec implementation

o Requires changes to OS, but no changes to applications SSL implementation

o Requires changes to applications, but no changes to OS SSL built into Web application early on (Netscape) IPSec used in VPN applications (secure tunnel) Reluctance to retrofit applications for SSL Reluctance to use IPSec due to complexity and

interoperability issues Result? Internet less secure than it should be!

IPSec and SSL IPSec lives at

the network layer

IPSec is transparent to applications

application

transport

network

physical

IPSec and Complexity IPSec is a complex protocol Over-engineered

o Lots of generally useless extra features Flawed

o Some serious security flaws Interoperability is serious challenge

o Defeats the purpose of having a standard! Complex Did I mention, it’s complex?

IKE and ESP/AH Two parts to IPSec IKE: Internet Key Exchange

o Mutual authenticationo Establish shared symmetric keyo Two “phases” like SSL session/connection

ESP/AHo ESP: Encapsulating Security Payload for

encryption and/or integrity of IP packetso AH: Authentication Header integrity only

IKE IKE has 2 phases

o Phase 1 IKE security association (SA)o Phase 2 AH/ESP security association

Phase 1 is comparable to SSL session Phase 2 is comparable to SSL connection Not an obvious need for two phases in IKE If multiple Phase 2’s do not occur, then it is

more expensive to have two phases!

IKE Phase 1 Four different “key” options

o Public key encryption (original version)o Public key encryption (improved version)o Public key signatureo Symmetric key

For each of these, two different “modes”o Main modeo Aggressive mode

There are 8 versions of IKE Phase 1! Evidence that IPSec is over-engineered?

IKE Phase 1 We’ll discuss 6 of 8 phase 1 variants

o Public key signatures (main and aggressive modes)

o Symmetric key (main and aggressive modes)o Public key encryption (main and aggressive)

Why public key encryption and public key signatures?o Always know your own private keyo May not (initially) know other side’s public key

IKE Phase 1 Uses ephemeral Diffie-Hellman to establish

session keyo Achieves perfect forward secrecy (PFS)

Let a be Alice’s Diffie-Hellman exponent Let b be Bob’s Diffie-Hellman exponent Let g be generator and p prime Recall p and g are public

IKE Phase 1: Digital Signature (Main Mode)

CP = crypto proposed, CS = crypto selected IC = initiator “cookie”, RC = responder “cookie” K = h(IC,RC,gab mod p,RA,RB) SKEYID = h(RA, RB, gab mod p) proofA = [h(SKEYID,ga,gb,IC,RC,CP,“Alice”)]Alice

Alice Bob

IC, CPIC,RC, CS

IC,RC, ga mod p, RA

IC,RC, E(“Alice”, proofA, K)IC,RC, gb mod p, RB

IC,RC, E(“Bob”, proofB, K)

IKE Phase 1: Public Key Signature (Aggressive Mode)

Main difference from main modeo Not trying to protect identitieso Cannot negotiate g or p

Alice Bob

IC, “Alice”, ga mod p, RA, CP

IC,RC, “Bob”, RB,

gb mod p, CS, proofB

IC,RC, proofA

Main vs Aggressive Modes Main mode MUST be implemented Aggressive mode SHOULD be implemented

o In other words, if aggressive mode is not implemented, “you should feel guilty about it”

Might create interoperability issues For public key signature authentication

o Passive attacker knows identities of Alice and Bob in aggressive mode

o Active attacker can determine Alice’s and Bob’s identity in main mode

IKE Phase 1: Symmetric Key (Main Mode)

Same as signature mode excepto KAB = symmetric key shared in advance o K = h(IC,RC,gab mod p,RA,RB,KAB)o SKEYID = h(K, gab mod p)o proofA = h(SKEYID,ga,gb,IC,RC,CP,“Alice”)

Alice Bob

IC, CPIC,RC, CS

IC,RC, ga mod p, RA

IC,RC, E(“Alice”, proofA, K)IC,RC, gb mod p, RB

IC,RC, E(“Bob”, proofB, K)

Problems with Symmetric Key (Main Mode)

Catch-22o Alice sends her ID in message 5o Alice’s ID encrypted with Ko To find K Bob must know KAB

o To get KAB Bob must know he’s talking to Alice! Result: Alice’s ID must be IP address! Useless mode for the “road warrior” Why go to all of the trouble of trying to

hide identities in 6 message protocol?

IKE Phase 1: SymmetricKey (Aggressive Mode)

Same format as digital signature aggressive mode Not trying to hide identities… As a result, does not have problems of main mode But does not (pretend to) hide identities

Alice Bob

IC, “Alice”, ga mod p, RA, CP

IC,RC, “Bob”, RB,

gb mod p, CS, proofB

IC,RC, proofA

IKE Phase 1: Public Key Encryption (Main Mode)

CP = crypto proposed, CS = crypto selected IC = initiator “cookie”, RC = responder “cookie” K = h(IC,RC,gab mod p,RA,RB) SKEYID = h(RA, RB, gab mod p) proofA = h(SKEYID,ga,gb,IC,RC,CP,“Alice”)

Alice Bob

IC, CPIC,RC, CS

IC,RC, ga mod p, {RA}Bob, {“Alice”}Bob

IC,RC, E(proofA, K)IC,RC, gb mod p, {RB}Alice, {“Bob”}Alice

IC,RC, E(proofB, K)

IKE Phase 1: Public Key Encryption (Aggressive Mode)

K, proofA, proofB computed as in main mode Note that identities are hidden

o The only aggressive mode to hide identitieso Then why have main mode?

Alice Bob

IC, CP, ga mod p,{“Alice”}Bob, {RA}Bob

IC,RC, CS, gb mod p, {“Bob”}Alice, {RB}Alice, proofB

IC,RC, proofA

Public Key Encryption Issue? Public key encryption, aggressive mode Suppose Trudy generates

o Exponents a and bo Nonces RA and RB

Trudy can compute “valid” keys and proofs: gab mod p, K, SKEYID, proofA and proofB

Also true of main mode

Public Key Encryption Issue?

Trudyas Alice

Trudyas Bob

Trudy can create exchange that appears to be between Alice and Bob

Appears valid to any observer, including Alice and Bob!

IC,RC, CS, gb mod p, {“Bob”}Alice, {RB}Alice, proofB

IC,RC, proofA

IC, CP, ga mod p,{“Alice”}Bob, {RA}Bob

Plausible Deniability Trudy can create “conversation” that

appears to be between Alice and Bob Appears valid, even to Alice and Bob! A security failure? In this mode of IPSec, it is a feature

o Plausible deniability: Alice and Bob can deny that any conversation took place!

In some cases it might be a security failureo If Alice makes a purchase from Bob, she could

later repudiate it (unless she had signed)

IKE Phase 1 Cookies Cookies (or “anti-clogging tokens”) supposed

to make denial of service more difficult No relation to Web cookies To reduce DoS, Bob wants to remain stateless

as long as possible But Bob must remember CP from message 1

(required for proof of identity in message 6) Bob must keep state from 1st message on! These cookies offer little DoS protection!

IKE Phase 1 Summary Result of IKE phase 1 is

o Mutual authenticationo Shared symmetric keyo IKE Security Association (SA)

But phase 1 is expensive (in public key and/or main mode cases)

Developers of IKE thought it would be used for lots of things not just IPSec

Partly explains over-engineering…

IKE Phase 2 Phase 1 establishes IKE SA Phase 2 establishes IPSec SA Comparison to SSL

o SSL session is comparable to IKE Phase 1o SSL connections are like IKE Phase 2

IKE could be used for lots of things But in practice, it’s not!

IKE Phase 2

Key K, IC, RC and SA known from Phase 1 Proposal CP includes ESP and/or AH Hashes 1,2,3 depend on SKEYID, SA, RA and RB

Keys derived from KEYMAT = h(SKEYID,RA,RB,junk) Recall SKEYID depends on phase 1 key method Optional PFS (ephemeral Diffie-Hellman exchange)

Alice Bob

IC,RC,CP,E(hash1,SA,RA,K)

IC,RC,CS,E(hash2,SA,RB,K)

IC,RC,E(hash3,K)

IPSec After IKE Phase 1, we have an IKE SA After IKE Phase 2, we have an IPSec SA Both sides have a shared symmetric key Now what?

o We want to protect IP datagrams But what is an IP datagram?

o From the perspective of IPSec…

IP Review

Where IP header is

IP header data

IP datagram is of the form

IP and TCP Consider HTTP traffic (over TCP) IP encapsulates TCP TCP encapsulates HTTP

IP header TCP hdr HTTP hdr app data

IP header data

IP data includes TCP header, etc.

IPSec Transport Mode IPSec Transport Mode

IP header data

IP header ESP/AH data

Transport mode designed for host-to-host Transport mode is efficient

o Adds minimal amount of extra header The original header remains

o Passive attacker can see who is talking

IPSec Tunnel Mode IPSec Tunnel Mode

IP header data

new IP hdr ESP/AH IP header data

Tunnel mode for firewall to firewall traffic Original IP packet encapsulated in IPSec Original IP header not visible to attacker

o New header from firewall to firewallo Attacker does not know which hosts are talking

Comparison of IPSec Modes Transport Mode

Tunnel Mode

IP header data

IP header ESP/AH data

IP header data

new IP hdr ESP/AH IP header data

Transport Modeo Host-to-host

Tunnel Modeo Firewall-to-

firewall Transport mode

not necessary Transport mode

is more efficient

IPSec Security What kind of protection?

o Confidentiality?o Integrity?o Both?

What to protect?o Data?o Header?o Both?

ESP/AH do some combinations of these

AH vs ESP AH

o Authentication Headero Integrity only (no confidentiality)o Integrity-protect everything beyond IP header

and some fields of header (why not all fields?) ESP

o Encapsulating Security Payloado Integrity and confidentialityo Protects everything beyond IP headero Integrity only by using NULL encryption

ESP’s NULL Encryption According to RFC 2410

o NULL encryption “is a block cipher the origins of which appear to be lost in antiquity”

o “Despite rumors”, there is no evidence that NSA “suppressed publication of this algorithm”

o Evidence suggests it was developed in Roman times as exportable version of Caesar’s cipher

o Can make use of keys of varying lengtho No IV is requiredo Null(P,K) = P for any P and any key K

Security people have a strange sense of humor!

Why Does AH Exist? (1) Cannot encrypt IP header

o Routers must look at the IP headero IP addresses, TTL, etc.o IP header exists to route packets!

AH protects immutable fields in IP headero Cannot integrity protect all header fieldso TTL, for example, must change

ESP does not protect IP header at all

Why Does AH Exist? (2) ESP encrypts everything beyond the IP

header (if non-null encryption) If ESP encrypted, firewall cannot look at

TCP header (e.g., port numbers) Why not use ESP with null encryption?

o Firewall sees ESP header, but does not know whether null encryption is used

o End systems know, but not firewalls Aside 1: Do firewalls reduce security? Aside 2: Is IPSec compatible with NAT?

Why Does AH Exist? (3) The real reason why AH exists

o At one IETF meeting “someone from Microsoft gave an impassioned speech about how AH was useless…”

o “…everyone in the room looked around and said `Hmm. He’s right, and we hate AH also, but if it annoys Microsoft let’s leave it in since we hate Microsoft more than we hate AH.”

Kerberos

Kerberos In Greek mythology, Kerberos is 3-headed

dog that guards entrance to Hadeso “Wouldn’t it make more sense to guard the

exit?” In security, Kerberos is an authentication

system based on symmetric key cryptoo Originated at MITo Based on work by Needham and Schroedero Relies on a trusted third party (TTP)

Motivation for Kerberos Authentication using public keys

o N users ⇒ N key pairs Authentication using symmetric keys

o N users requires about N2 keys Symmetric key case does not scale! Kerberos based on symmetric keys but only

requires N keys for N userso But must rely on TTPo Advantage is that no PKI is required

Kerberos KDC Kerberos Key Distribution Center or KDC

o Acts as a TTPo TTP must not be compromised!o KDC shares symmetric key KA with Alice, key KB

with Bob, key KC with Carol, etc.o Master key KKDC known only to KDCo KDC enables authentication and session keyso Keys for confidentiality and integrityo In practice, the crypto algorithm used is DES

Kerberos Tickets KDC issues a ticket containing info needed

to access a network resource KDC also issues ticket-granting tickets or

TGTs that are used to obtain tickets Each TGT contains

o Session keyo User’s IDo Expiration time

Every TGT is encrypted with KKDC

o TGT can only be read by the KDC

Kerberized Login Alice enters her password Alice’s workstation

o Derives KA from Alice’s passwordo Uses KA to get TGT for Alice from the KDC

Alice can then use her TGT (credentials) to securely access network resources

Plus: Security is transparent to Alice Minus: KDC must be secure it’s trusted!

Kerberized Login

Alice’sAlice wants

password a TGT

E(SA,TGT,KA)

Key KA derived from Alice’s password KDC creates session key SA

Workstation decrypts SA, TGT, forgets KA

TGT = E(“Alice”,SA, KKDC)

Computer

Alice Requests Ticket to Bob

Talk to Bob

I want totalk to Bob

REQUEST

KDC REQUEST = (TGT, authenticator) where

authenticator = E(timestamp,SA) REPLY = E(“Bob”,KAB,ticket to Bob, SA) ticket to Bob = E(“Alice”,KAB,KB) KDC gets SA from TGT to verify timestamp

Computer

Alice Uses Ticket to Bob

ticket to Bob, authenticator

E(timestamp + 1,KAB)

ticket to Bob = E(“Alice”,KAB, KB) authenticator = E(timestamp, KAB) Bob decrypts “ticket to Bob” to get KAB which he

then uses to verify timestamp

Alice’s Computer

Kerberos Session key SA used for authentication Can also be used for confidentiality/integrity Timestamps used for mutual authentication Recall that timestamps reduce number of

messageso Acts like a nonce that is known to both sideso Note: time is a security-critical parameter!

Kerberos Questions When Alice logs in, KDC sends E(SA,TGT,KA)

where TGT = E(“Alice”,SA,KKDC)Q: Why is TGT encrypted with KA?A: Extra work and no added security!

In Alice’s Kerberized login to Bob, why can Alice remain anonymous?

Why is “ticket to Bob” sent to Alice? Where is replay prevention in Kerberos?

Kerberos Alternatives Could have Alice’s workstation remember

password and use that for authenticationo Then no KDC requiredo But hard to protect password on workstationo Scaling problem

Could have KDC remember session key instead of putting it in a TGTo Then no need for TGTso But stateless KDC is big feature of Kerberos

Kerberos Keys In Kerberos, KA = h(Alice’s password) Could instead generate random KA and

o Compute Kh = h(Alice’s password)o And workstation stores E(KA, Kh)

Then KA need not change (on workstation or KDC) when Alice changes her password

But E(KA, Kh) subject to password guessing This alternative approach is often used in

applications (but not in Kerberos)

GSM Security

Cell Phones First generation cell phones

o Analog, few standardso Little or no securityo Susceptible to cloning

Second generation cell phones: GSMo Began in 1982 as Groupe Speciale Mobileo Now, Global System for Mobile Communications

Third generation?o 3rd Generation Partnership Project (3GPP)

GSM System Overview

Mobile

HomeNetwork

“land line”

air interface

BaseStation

Controller

PSTNInternet

Etc.Visited Network

GSM System Components Mobile phone

o Contains SIM (Subscriber Identity Module)

SIM is the security moduleo IMSI (International Mobile

Subscriber ID)o User key Ki (128 bits)o Tamper resistant (smart card)o PIN activated (usually not used)

GSM System Components Visited network network where mobile is

currently locatedo Base station one “cell”o Base station controller manages many cellso VLR (Visitor Location Register) info on all

visiting mobiles currently in the network Home network “home” of the mobile

o HLR (Home Location Register) keeps track of most recent location of mobile

o AuC (Authentication Center) contains IMSI/Ki

GSM Security Goals Primary design goals

o Make GSM as secure as ordinary telephoneo Prevent phone cloning

Not designed to resist an active attack!o At the time this seemed infeasibleo Today such an attack is very feasible…

Designers considered biggest threatso Insecure billingo Corruptiono Other low-tech attacks

GSM Security Features Anonymity

o Intercepted traffic does not identify usero Not so important to phone company

Authenticationo Necessary for proper billingo Very important to phone company!

Confidentialityo Confidentiality of calls over the air interfaceo Not important to phone companyo May be very important for marketing!

GSM: Anonymity IMSI used to initially identify caller Then TMSI (Temporary Mobile Subscriber

ID) used TMSI changed frequently TMSI’s encrypted when sent Not a strong form of anonymity But probably sufficient for most uses

GSM: Authentication Caller is authenticated to base station Authentication is not mutual Authentication via challenge-response

o Home network generates RAND and computes XRES = A3(RAND, Ki) where A3 is a hash

o Then (RAND,XRES) sent to base stationo Base station sends challenge RAND to mobileo Mobile’s response is SRES = A3(RAND, Ki)o Base station verifies SRES = XRES

Note: Ki never leaves home network!

GSM: Confidentiality Data encrypted with stream cipher Error rate estimated at about 1/1000

o Error rate too high for a block cipher Encryption key Kc

o Home network computes Kc = A8(RAND, Ki), where A8 is a hash

o Then Kc sent to base station with (RAND,XRES)o Mobile computes Kc = A8(RAND, Ki)o Keystream generated from A5(Kc)

Note: Ki never leaves home network!

GSM Security

SRES and Kc must be uncorrelatedo Even though both are derived from RAND and Ki

Must not be possible to deduce Ki from known RAND/SRES pairs (known plaintext attack)

Must not be possible to deduce Ki from chosen RAND/SRES pairs (chosen plaintext attack)o With possession of SIM, attacker can choose RAND’s

Mobile Base Station

4. RAND

5. SRES

6. Encrypt with Kc

1. IMSI

HomeNetwork

3. (RAND,XRES,Kc)

2. IMSI

GSM Insecurity (1) Hash used for A3/A8 is COMP128

o Broken by 160,000 chosen plaintextso With SIM, can get Ki in 2 to 10 hours

Encryption between mobile and base station but no encryption from base station to base station controllero Often transmitted over microwave link

Encryption algorithm A5/1o Broken with 2 seconds of known plaintext

BaseStation

Controller

GSM Insecurity (2) Attacks on SIM card

o Optical Fault Induction can attack SIM with a flashbulb to recover Ki

o Partitioning Attacks using timing and power consumption, can recover Ki with only 8 adaptively chosen “plaintexts”

With possession of SIM, attacker can recover Ki in seconds

GSM Insecurity (3) Fake base station exploits two flaws

o Encryption not automatico Base station not authenticated

Mobile Base Station

Fake Base Station

Noencryption

Call todestination

Note: The bill goes to fake base station!

GSM Insecurity (4) Denial of service is possible

o Jamming (always an issue in wireless) Base station can replay triple

(RAND,XRES,Kc)o One compromised triple gives attacker a

key Kc that is valid forevero No replay protection!

GSM Conclusion Did GSM achieve its goals?

o Eliminate cloning? Yeso Make air interface as secure as PSTN? Perhaps…o But design goals were clearly too limited

GSM insecurities weak crypto, SIM issues, fake base station, replay, etc.

PSTN insecurities tapping, active attack, passive attack (e.g., cordless phones), etc.

GSM a (modest) security success?

3GPP: 3rd Generation Partnership Project

3G security built on GSM (in)security 3G fixes known GSM security problems

o Mutual authenticationo Integrity protect signaling (such as “start

encryption” command)o Keys (encryption/integrity) cannot be reusedo Triples cannot be replayedo Strong encryption algorithm (KASUMI)o Encryption extended to base station controller

Protocols Summary Generic authentication protocols

o Protocols can be very subtle! SSL IPSec Kerberos GSM

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