network security. cryptography cryptography functions secret key (e.g., des) public key (e.g., rsa)...

Network Security

CryptographyCryptography functions Secret key (e.g., DES) Public key (e.g., RSA) Message digest (e.g., MD5)

Security services Privacy: preventing unauthorized release of information Authentication: verifying identity of the remote

participant Integrity: making sure message has not been altered

DES

Data Encryption Standard (DES)56 bit key, insecureTriple DES is secure, but supplanted by

AES

Advanced Encryption Standard (AES)Specified for US Government contracts

Neither are provably secure

Encryption Algorithms

Private Key (DES)

64-bit key (56-bits + 8-bit parity)

16 rounds

Round 1

Round 2

Round 16

. . .

plain text

Initial Permutation

Final Permutation

56bitKey

Encrypt w/Secret Key

Decrypt w/Secret Key

plaintext plaintext

ciphertext

Each round

Function F and generation of Ki for each round not shown

Repeat for larger messages

L i -1 R i 1

L i R i

F

+

iK

cipher1

block1

DES

+IV

cipher

block

DES

+

2

2 cipher

block

DES

+

3

3 cipher

block

DES

+

4

4

AES

AES operates on a 4×4 array of bytes, termed the state

For encryption, each round of AES consists of four stages: AddRoundKey - each byte of the state is combined with the

derived cipher key SubBytes - a non-linear substitution step where each byte is

replaced with another according to a lookup table. ShiftRows - a transposition step where each row of the state

is shifted cyclically a certain number of steps. MixColumns - a mixing operation which operates on the

columns of the state, combining the four bytes in each column using a linear transformation.

RSA

Public key/Private Key

Provably secure (NP-Complete type proof)

Slow

Multiplicative inverse for public key

With n=7

4*2 mod 7 = 1

4 and 2 are multiplicative inverses mod 7

4*3 mod 7 = 12 mod 7 = 5

2*5 mod 7 = 10 mod 7 = 3

If you multiply any number by 4, take the result and multiply it by 2, you will get the original number back

Encryption & Decryption

c = me mod n

m = cd mod n

Encrypt w/Public Key

Decrypt w/Private Key

plaintext plaintext

ciphertext

Public Key (RSA)Based on multiplicative group operationsGenerate a public and private key choose two large prime numbers p and q (each 256 bits) multiply p and q together to get n (at most 512 bits) choose the encryption key e, such that e and (p-1) x (q-1)

are relatively prime two numbers are relatively prime if they have no common factor

greater than one. compute decryption key d such that

d = e-1 mod((p-1)*(q-1)) construct public key as <e, n> construct private key as <d, n> discard (do not disclose) original primes p and q

Examplep=5, q=11, n=p*q=55, m=message=9, (p-1)(q-1)=40, e=23 and (p-1)*(q-1) are relatively primeWe want d*e=1mod 40, d*23=1mod40 You can try all values less than 40 23*2=46=6mod40, 23*3=69=29mod40, 23*4=92=12mod40,

23*5=115=35mod40, 23*6=138=18mod40 23*7=161=1mod40, d=7

For a message m=9 c=memodn=923mod55 How big is this? = 910mod55*913mod55= 1*14 mod 55 m=cdmodn=147mod55=105413504mod55=9

Breaking RSA

1977 challenge to break 430-bit message

Estimated 40 Quadrillion years to factor large composites

April 1994 broken with 5000 MIP-years of CPU

Breakage can be easier if something is known about the key generation (time of day)

Message Digest

Cryptographic checksum: just as a regular checksum protects the

receiver from accidental changes to the message, a cryptographic checksum protects the receiver from malicious changes to the message.

One-way function:

given a cryptographic checksum for a message, it is virtually impossible to figure out what message produced that checksum; it is not computationally feasible to find two messages that hash to the same cryptographic checksum.

Relevance:

if you are given a checksum for a message and you are able to compute exactly the same checksum for that message, then it is highly likely this message produced the checksum you were given.

Speed

175MHz DEC AlphaCustom HardwareSonicwall claims 54Mbps DES3 in hardwaressl.com advertises 75Mbps DES todayMd5 1.27GbpsSHA 1.02GbpsRSA 400 keys/second

Message Integrity Protocols

Digital signature using RSAspecial case of a message integrity where

the code can only have been generated by one participant

compute signature with private key and verify with public key

Making Signatures

Compute checksum of signed document

Encrypt checksum, time and date, and other information using private key

Attach digital signature to end of document

Optionally, encrypt signed document with receiver’s public key

Checking Signatures

Decrypt signed document, if necessary, using private key

Decrypt digital signature using public key

Verify checksum for document

Display the time and date of the document

CertificatesCertified EntityCA

Verifier

Decrypt senders public key using CA-publickey

Albert Levi

Albert Levi

Albert Levi

Register with CA, send client Public Key

CA-Publickey and Certificate with RSA(client Public Key,CA-privatekey)

Certificate

Application (e.g., HTTP)

Secure transport layer

TCP

IP

Subnet

TLS,SSL,HTTPSTransport Layer Security, Secure Socket Layer

SSL

Each browser is configured with a root CAWhen a session is initiated, server and client agree on security capabilities. (most clients are 40 bit encryption, but 128 bit encryption is available on many strong serversThe server is authenticated by the certificate authorityUsing the server public key from the CA, the client sends a DES key to the serverThe DES key is used to encrypt the session

IPSEC

Optional in IPv4, mandatory in IPv6Data Confidentiality---The IPSec sender can encrypt packets before transmitting them across a network. Data Integrity---The IPSec receiver can authenticate packets sent by the IPSec sender to ensure that the data has not been altered during transmission. Data Origin Authentication---The IPSec receiver can authenticate the source of the IPSec packets sent. This service is dependent upon the data integrity service. Anti-Replay---The IPSec receiver can detect and reject replayed packets.