UNIT3_class (1).ppt CRYPTOGRAPHY NOTES AND NETWORK

Authentication requirement – Authentication
function – MAC – Hash function – Security of
hash function and MAC –MD5 - SHA - HMAC –
CMAC - Digital signature and authentication
protocols – DSS – EI Gamal – Schnorr.

Message Authentication
• message authentication is concerned with:
– protecting the integrity of a message
– validating identity of originator
– non-repudiation of origin (dispute resolution)
• will consider the security requirements
• then three alternative functions used:
– message encryption
– message authentication code (MAC)
– hash function

Security Requirements
• disclosure
• traffic analysis
• masquerade
• content modification
• sequence modification
• timing modification
• source repudiation
• destination repudiation

1.Authentication Requirements
1. Disclosure:
Release of message contents to any person or process not possessing
the appropriate cryptographic key.
2. Traffic analysis:
Discovery of the pattern of traffic between parties. In a connection-
oriented application, the frequency and duration of connections could
be determined. In either a connection-oriented or connectionless
environment, the number and length of messages between
parties could be determined.
3. Masquerade:
Insertion of messages into the network from a fraudulent source. This
includes the creation of messages by an opponent that are purported
to come from an authorized entity. Also included are fraudulent
acknowledgments of message receipt or non receipt by someone
other than the message recipient.

4. Content modification:
Changes to the contents of a message, including insertion, deletion,
transposition, and modification.
5. Sequence modification:
Any modification to a sequence of messages between parties, including
insertion, deletion, and reordering.
6. Timing modification:
Delay or replay of messages. In a connection-oriented application, an entire
session or sequence of messages could be a replay of some previous valid
session, or individual messages in the sequence could be delayed or replayed.
In a connectionless application, an individual message (e.g., datagram) could
be delayed or replayed.
7. Source repudiation:
Denial of transmission of message by source.
8. Destination repudiation:
Denial of receipt of message by destination.

Message Encryption
• message encryption by itself also provides a
measure of authentication
• if symmetric encryption is used then:
– receiver know sender must have created it
– since only sender and receiver now key used
– know content cannot of been altered
– if message has suitable structure, redundancy or a
checksum to detect any changes

Message Encryption
• if public-key encryption is used:
– encryption provides no confidence of sender
– since anyone potentially knows public-key
– however if
• sender signs message using their private-key
• then encrypts with recipients public key
• have both secrecy and authentication
– again need to recognize corrupted messages
– but at cost of two public-key uses on message

a)Message Encryption(Symmetric and
Public key)
• Message encryption by itself can provide a measure of
authentication. The analysis differs for symmetric and
public-key encryption schemes.
1. Symmetric Encryption
Fig a:
A message M transmitted from source A to destination B
is encrypted using a secret key K shared by A and B. If no
other party knows the key, then confidentiality is
provided.
No other party can recover the plaintext of the message.

UNIT3_class (1).ppt CRYPTOGRAPHY NOTES AND NETWORK

Message Authentication Code (MAC)
• generated by an algorithm that creates a small
fixed-sized block
– depending on both message and some key
– like encryption though need not be reversible
• appended to message as a signature
• receiver performs same computation on
message and checks it matches the MAC
• provides assurance that message is unaltered
and comes from sender

Message Authentication Codes
• as shown the MAC provides authentication
• can also use encryption for secrecy
– generally use separate keys for each
– can compute MAC either before or after encryption
– is generally regarded as better done before
• why use a MAC?
– sometimes only authentication is needed
– sometimes need authentication to persist longer than the
encryption (eg. archival use)
• note that a MAC is not a digital signature

MAC Properties
• a MAC is a cryptographic checksum
MAC = CK(M)
– condenses a variable-length message M
– using a secret key K
– to a fixed-sized authenticator
• is a many-to-one function
– potentially many messages have same MAC
– but finding these needs to be very difficult

Requirements for MACs
• taking into account the types of attacks
• need the MAC to satisfy the following:
1. knowing a message and MAC, is infeasible to
find another message with same MAC
2. MACs should be uniformly distributed
3. MAC should depend equally on all bits of the
message

Using Symmetric Ciphers for MACs
• can use any block cipher chaining mode and
use final block as a MAC
• Data Authentication Algorithm (DAA) is a
widely used MAC based on DES-CBC
– using IV=0 and zero-pad of final block
– encrypt message using DES in CBC mode
– and send just the final block as the MAC
• or the leftmost M bits (16≤M≤64) of final block
• but final MAC is now too small for security

Hash Functions
• condenses arbitrary message to fixed size
h = H(M)
• usually assume that the hash function is
public and not keyed
– cf. MAC which is keyed
• hash used to detect changes to message
• can use in various ways with message
• most often to create a digital signature

Hash Functions & Digital Signatures

Requirements for Hash Functions
1. can be applied to any sized message M
2. produces fixed-length output h
3. is easy to compute h=H(M) for any message M
4. given h is infeasible to find x s.t. H(x)=h
• one-way property
5. given x is infeasible to find y s.t. H(y)=H(x)
• weak collision resistance
6. is infeasible to find any x,y s.t. H(y)=H(x)
• strong collision resistance

Simple Hash Functions
• are several proposals for simple functions
• based on XOR of message blocks
• not secure since can manipulate any message
and either not change hash or change hash
also
• need a stronger cryptographic function (next
chapter)

Birthday Attacks
• might think a 64-bit hash is secure
• but by Birthday Paradox is not
• birthday attack works thus:
– opponent generates 2
m/2 variations of a valid message all
with essentially the same meaning
– opponent also generates 2
m/2 variations of a desired
fraudulent message
– two sets of messages are compared to find pair with same
hash (probability > 0.5 by birthday paradox)
– have user sign the valid message, then substitute the
forgery which will have a valid signature
• conclusion is that need to use larger MAC/hash

Block Ciphers as Hash Functions
• can use block ciphers as hash functions
– using H0=0 and zero-pad of final block
– compute: Hi = EMi
[Hi-1]
– and use final block as the hash value
– similar to CBC but without a key
• resulting hash is too small (64-bit)
– both due to direct birthday attack
– and to “meet-in-the-middle” attack
• other variants also susceptible to attack

Hash Functions & MAC Security
• like block ciphers have:
• brute-force attacks exploiting
– strong collision resistance hash have cost 2
m/2
• have proposal for h/w MD5 cracker
• 128-bit hash looks vulnerable, 160-bits better
– MACs with known message-MAC pairs
• can either attack keyspace (cf key search) or MAC
• at least 128-bit MAC is needed for security

Hash Functions & MAC Security
• cryptanalytic attacks exploit structure
– like block ciphers want brute-force attacks to be the best
alternative
• have a number of analytic attacks on iterated hash
functions
– CVi = f[CVi-1, Mi]; H(M)=CVN
– typically focus on collisions in function f
– like block ciphers is often composed of rounds
– attacks exploit properties of round functions

Hash and MAC Algorithms
• Hash Functions
– condense arbitrary size message to fixed size
– by processing message in blocks
– through some compression function
– either custom or block cipher based
• Message Authentication Code (MAC)
– fixed sized authenticator for some message
– to provide authentication for message
– by using block cipher mode or hash function

28
MD5 Overview
1. pad message so its length is 448 mod 512
2. append a 64-bit length value to message
3. initialise 4-word (128-bit) MD buffer (A,B,C,D)
4. process message in 16-word (512-bit) blocks:
– using 4 rounds of 16 bit operations on message block &
buffer
– add output to buffer input to form new buffer value
5. output hash value is the final buffer value

30
MD5 Compression Function
• each round has 16 steps of the form:
a = b+((a+g(b,c,d)+X[k]+T[i])<<<s)
• a,b,c,d refer to the 4 words of the buffer, but used in
varying permutations
– note this updates 1 word only of the buffer
– after 16 steps each word is updated 4 times
• where g(b,c,d) is a different nonlinear function in
each round (F,G,H,I)
• T[i] is a constant value derived from sin

32
MD4
• precursor to MD5
• also produces a 128-bit hash of message
• has 3 rounds of 16 steps versus 4 in MD5
• design goals:
– collision resistant (hard to find collisions)
– direct security (no dependence on "hard" problems)
– fast, simple, compact
– favors little-endian systems (eg PCs)

33
Strength of MD5
• MD5 hash is dependent on all message bits
• Rivest claims security is good as can be
• known attacks are:
– Berson 92 attacked any 1 round using differential
cryptanalysis (but can’t extend)
– Boer & Bosselaers 93 found a pseudo collision (again
unable to extend)
– Dobbertin 96 created collisions on MD compression
function (but initial constants prevent exploit)
• conclusion is that MD5 looks vulnerable soon

Secure Hash Algorithm
• SHA originally designed by NIST & NSA in 1993
• was revised in 1995 as SHA-1
• US standard for use with DSA signature scheme
– standard is FIPS 180-1 1995, also Internet RFC3174
– nb. the algorithm is SHA, the standard is SHS
• based on design of MD4 with key differences
• produces 160-bit hash values
• recent 2005 results on security of SHA-1 have raised
concerns on its use in future applications

Revised Secure Hash Standard
• NIST issued revision FIPS 180-2 in 2002
• adds 3 additional versions of SHA
– SHA-256, SHA-384, SHA-512
• designed for compatibility with increased
security provided by the AES cipher
• structure & detail is similar to SHA-1
• hence analysis should be similar
• but security levels are rather higher

SHA-512 Compression Function
• heart of the algorithm
• processing message in 1024-bit blocks
• consists of 80 rounds
– updating a 512-bit buffer
– using a 64-bit value Wt derived from the current
message block
– and a round constant based on cube root of first
80 prime numbers

Whirlpool
• now examine the Whirlpool hash function
• endorsed by European NESSIE project
• uses modified AES internals as compression
function
• addressing concerns on use of block ciphers
seen previously
• with performance comparable to dedicated
algorithms like SHA

Whirlpool Block Cipher W
• designed specifically for hash function use
• with security and efficiency of AES
• but with 512-bit block size and hence hash
• similar structure & functions as AES but
– input is mapped row wise
– has 10 rounds
– a different primitive polynomial for GF(2^8)
– uses different S-box design & values

Whirlpool Performance & Security
• Whirlpool is a very new proposal
• hence little experience with use
• but many AES findings should apply
• does seem to need more h/w than SHA, but
with better resulting performance

Keyed Hash Functions as MACs
• want a MAC based on a hash function
– because hash functions are generally faster
– code for crypto hash functions widely available
• hash includes a key along with message
• original proposal:
KeyedHash = Hash(Key|Message)
– some weaknesses were found with this
• eventually led to development of HMAC

HMAC
• specified as Internet standard RFC2104
• uses hash function on the message:
HMACK = Hash[(K+ XOR opad) ||
Hash[(K+ XOR ipad)||M)]]
• where K+ is the key padded out to size
• and opad, ipad are specified padding constants
• overhead is just 3 more hash calculations than the
message needs alone
• any hash function can be used
– eg. MD5, SHA-1, RIPEMD-160, Whirlpool

HMAC Security
• proved security of HMAC relates to that of the
underlying hash algorithm
• attacking HMAC requires either:
– brute force attack on key used
– birthday attack (but since keyed would need to
observe a very large number of messages)
• choose hash function used based on speed
verses security constraints

CMAC
• previously saw the DAA (CBC-MAC)
• widely used in govt & industry
• but has message size limitation
• can overcome using 2 keys & padding
• thus forming the Cipher-based Message
Authentication Code (CMAC)
• adopted by NIST SP800-38B

Digital Signatures & Authentication
Protocols

Digital Signatures
• have looked at message authentication
– but does not address issues of lack of trust
• digital signatures provide the ability to:
– verify author, date & time of signature
– authenticate message contents
– be verified by third parties to resolve disputes
• hence include authentication function with
additional capabilities

Digital Signature Properties
• must depend on the message signed
• must use information unique to sender
– to prevent both forgery and denial
• must be relatively easy to produce
• must be relatively easy to recognize & verify
• be computationally infeasible to forge
– with new message for existing digital signature
– with fraudulent digital signature for given message
• be practical save digital signature in storage

Direct Digital Signatures
• involve only sender & receiver
• assumed receiver has sender’s public-key
• digital signature made by sender signing
entire message or hash with private-key
• can encrypt using receivers public-key
• important that sign first then encrypt message
& signature
• security depends on sender’s private-key

Arbitrated Digital Signatures
• involves use of arbiter A
– validates any signed message
– then dated and sent to recipient
• requires suitable level of trust in arbiter
• can be implemented with either private or
public-key algorithms
• arbiter may or may not see message

Authentication Protocols
• used to convince parties of each others
identity and to exchange session keys
• may be one-way or mutual
• key issues are
– confidentiality – to protect session keys
– timeliness – to prevent replay attacks
• published protocols are often found to have
flaws and need to be modified

Replay Attacks
• where a valid signed message is copied and later
resent
– simple replay
– repetition that can be logged
– repetition that cannot be detected
– backward replay without modification
• countermeasures include
– use of sequence numbers (generally impractical)
– timestamps (needs synchronized clocks)
– challenge/response (using unique nonce)

Using Symmetric Encryption
• as discussed previously can use a two-level
hierarchy of keys
• usually with a trusted Key Distribution Center
(KDC)
– each party shares own master key with KDC
– KDC generates session keys used for connections
between parties
– master keys used to distribute these to them

Needham-Schroeder Protocol
• original third-party key distribution protocol
• for session between A B mediated by KDC
• protocol overview is:
1. A->KDC: IDA || IDB || N1
2. KDC -> A: EKa[Ks || IDB || N1 || EKb[Ks||IDA] ]
3. A -> B: EKb[Ks||IDA]
4. B -> A: EKs[N2]
5. A -> B: EKs[f(N2)]

Needham-Schroeder Protocol
• used to securely distribute a new session key
for communications between A & B
• but is vulnerable to a replay attack if an old
session key has been compromised
– then message 3 can be resent convincing B that is
communicating with A
• modifications to address this require:
– timestamps (Denning 81)
– using an extra nonce (Neuman 93)

Using Public-Key Encryption
• have a range of approaches based on the use
of public-key encryption
• need to ensure have correct public keys for
other parties
• using a central Authentication Server (AS)
• various protocols exist using timestamps or
nonces

Denning AS Protocol
• Denning 81 presented the following:
1. A -> AS: IDA || IDB
2. AS -> A: EPRas[IDA||PUa||T] || EPRas[IDB||PUb||T]
3. A -> B: EPRas[IDA||PUa||T] || EPRas[IDB||PUb||T] ||
EPUb[EPRas[Ks||T]]
• note session key is chosen by A, hence AS need not
be trusted to protect it
• timestamps prevent replay but require synchronized
clocks

One-Way Authentication
• required when sender & receiver are not in
communications at same time (eg. email)
• have header in clear so can be delivered by
email system
• may want contents of body protected &
sender authenticated

Using Symmetric Encryption
• can refine use of KDC but can’t have final
exchange of nonces, vis:
1. A->KDC: IDA || IDB || N1
2. KDC -> A: EKa[Ks || IDB || N1 || EKb[Ks||IDA] ]
3. A -> B: EKb[Ks||IDA] || EKs[M]
• does not protect against replays
– could rely on timestamp in message, though email
delays make this problematic

Public-Key Approaches
• have seen some public-key approaches
• if confidentiality is major concern, can use:
A->B: EPUb[Ks] || EKs[M]
– has encrypted session key, encrypted message
• if authentication needed use a digital signature
with a digital certificate:
A->B: M || EPRa[H(M)] || EPRas[T||IDA||PUa]
– with message, signature, certificate

Digital Signature Standard (DSS)
• US Govt approved signature scheme
• designed by NIST & NSA in early 90's
• published as FIPS-186 in 1991
• revised in 1993, 1996 & then 2000
• uses the SHA hash algorithm
• DSS is the standard, DSA is the algorithm
• FIPS 186-2 (2000) includes alternative RSA & elliptic
curve signature variants

Digital Signature Algorithm (DSA)
• creates a 320 bit signature
• with 512-1024 bit security
• smaller and faster than RSA
• a digital signature scheme only
• security depends on difficulty of computing
discrete logarithms
• variant of ElGamal & Schnorr schemes

Digital Signature Algorithm (DSA)

DSA Key Generation
• have shared global public key values (p,q,g):
– choose q, a 160 bit
– choose a large prime p = 2L
• where L= 512 to 1024 bits and is a multiple of 64
• and q is a prime factor of (p-1)
– choose g = h(p-1)/q
• where h<p-1, h(p-1)/q (mod p) > 1
• users choose private & compute public key:
– choose x<q
– compute y = gx (mod p)

DSA Signature Creation
• to sign a message M the sender:
– generates a random signature key k, k<q
– nb. k must be random, be destroyed after use,
and never be reused
• then computes signature pair:
r = (gk(mod p))(mod q)
s = (k-1.H(M)+ x.r)(mod q)
• sends signature (r,s) with message M

DSA Signature Verification
• having received M & signature (r,s)
• to verify a signature, recipient computes:
w = s-1(mod q)
u1= (H(M).w)(mod q)
u2= (r.w)(mod q)
v = (gu1.yu2(mod p)) (mod q)
• if v=r then signature is verified
• see book web site for details of proof why

UNIT3_class (1).ppt CRYPTOGRAPHY NOTES AND NETWORK

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UNIT3_class (1).ppt CRYPTOGRAPHY NOTES AND NETWORK