Cryptography and Network Security
Spring 2012
http://users.abo.fi/ipetre/crypto/
Lecture 10: Message authentication: MAC, hashes
Ion Petre
Department of IT, Åbo Akademi University
February 9, 2012
http://users.abo.fi/ipetre/crypto/
1
Message authentication

Goal here: having received a message one would like to make sure that the
message has not been altered on the way



This does not necessarily includes encrypting or signing the message





Produce a short sequence of bits that depends on the message and on a secret key
To authenticate the message, the partner will compute the same bit pattern, assuming
he shares the same secret key
The message can be sent in plain, with the authenticator appended
This is not a digital signature: the receiver can produce the same MAC
One may encrypt the authenticator with his private key to produce a digital signature
One may encrypt both the message and the authenticator
Possible attacks on message authentication:



Content modification
Sequence modification – modifications to a sequence of messages, including
insertion, deletion, reordering
Timing modification – delay or replay messages
February 9, 2012
http://users.abo.fi/ipetre/crypto/
2
Authentication functions

Three types of authentication exist


Message encryption – the ciphertext serves as authenticator
Message authentication code (MAC) – a public function of the message
and a secret key producing a fixed-length value to serve as
authenticator


This does not provide a digital signature because A and B share the same
key
Hash function – a public function mapping an arbitrary length message
into a fixed-length hash value to serve as authenticator

February 9, 2012
This does not provide a digital signature because there is no key
http://users.abo.fi/ipetre/crypto/
3
I. Message encryption as authentication



Main idea here: the message must have come from A because the ciphertext can be
decrypted using his (secret or public) key
Also, none of the bits in the message have been altered because an opponent does not
know how to manipulate the bits of the ciphertext to induce meaningful changes to the
plaintext
Conclusion: encryption (either symmetric or public-key) provides authentication as well
as confidentiality
February 9, 2012
http://users.abo.fi/ipetre/crypto/
4
Encryption as authenticator

Some careful considerations are needed here:

How does B recognize a meaningful message from an arbitrary
sequence of bits?




He can apply the decryption key to any sequence of bits he receives
This is not necessarily easy task if the message is some sort of binary
file
Immediate idea of attack: send arbitrary bit sequences to disrupt the
receiver – he will try to figure out the meaning of that bit sequence
Defense against this type of attack: add to the message a certain
structure such as an error-correcting code (e.g., check-sum bits) and
then encrypt the whole file

B will detect illegitimate messages because they will not have the
required structure
February 9, 2012
http://users.abo.fi/ipetre/crypto/
5
Encryption as authenticator
From Stallings: Cryptography
and Network Security
February 9, 2012
http://users.abo.fi/ipetre/crypto/
6
More to authentication than simple encryption?

Often one needs alternative authentication schemes than just encrypting
the message





Sometimes one needs to avoid encryption of full messages due to legal
requirements
Encryption and authentication may be separated in the system architecture
If a message is broadcast to several destinations in a network (such as a
military control center), then it is cheaper and more reliable to have just one
node responsible to evaluate the authenticity – message will be sent in plain
with an attached authenticator
If one side has a heavy load, it cannot afford to decrypt all messages – it will
just check the authenticity of some randomly selected messages
If the message is sent encrypted, it is of course protected over the network.
However, once the receiver decrypts the message, it is no longer secure.
Using a different type of authentication protects the message also on the local
computer
February 9, 2012
http://users.abo.fi/ipetre/crypto/
7
II. Message authentication code (MAC)

To generate the MAC of a message M, Alice gives M and the secret key K to a MAC
function C: MAC=CK(M)



Typical attacks on MACs



Alice will send M plus the MAC to Bob
Bob has the same secret key K and generates the MAC himself to check the match
Produce an illegitimate message with the same signature as a given (or chosen) legitimate one
Produce a valid MAC for an illegitimate message
Requirements for MACs





The MAC function is in general many-to-one – messages are arbitrarily long and the MAC has
fixed length, thus there will be more than one message with the same MAC
Computationally easy to compute the MAC
Knowing M and CK(M) it is computationally infeasible to construct another message M’ with
CK(M’)= CK(M)
CK(M) is uniformly distributed – if the attacker chooses a random bit pattern of length n, the
chances of it being the correct signature is 2-n
If M’ is obtained from M by certain transformations (even switching one bit), then the probability
that the two have the same MAC is 2-n
February 9, 2012
http://users.abo.fi/ipetre/crypto/
8
Basic uses of MAC
February 9, 2012
http://users.abo.fi/ipetre/crypto/
9
Basic uses of MAC
February 9, 2012
http://users.abo.fi/ipetre/crypto/
10
MAC based on DES:
Data Authentication Algorithm (DAA)


One of the most widely used MACs – ANSI standard X9.17, also FIPS
PUB 113
Cipher block chaining mode of DES with an initialization vector of zero



Message to be authenticated is grouped into 64-bit blocks, last block padded
with 0: D1,D2, …, DN
O1=EK(D1), O2=EK(D2⊕O1), O3=EK(D3⊕O2), …, ON=EK(DN⊕ON-1)
MAC is ON or a part of it, e.g., its 32 leftmost bits
February 9, 2012
http://users.abo.fi/ipetre/crypto/
11
III. Authentication based on hash functions

A fixed-length hash value h is generated by a function H that takes as input a
message of arbitrary length: h=H(M)



Requirements for a hash function








A sends M and H(M)
B authenticates the message by computing H(M) and checking the match
H can be applied to a message of any size
H produces fixed-length output
Computationally easy to compute H(M)
Computationally infeasible to find M such that H(M)=h, for a given h
Computationally infeasible to find M’ such that H(M’)=H(M), for a given M
Computationally infeasible to find M,M’ with H(M)=H(M’) (to resist to birthday
attacks)
Note 1: the hash function is not considered secret – some other means
are required to protect it
Note 2: Hash function plus secrecy (key) gives a MAC – these are called
HMACs
February 9, 2012
http://users.abo.fi/ipetre/crypto/
12
Basic uses of hash functions
a.
Classical encryption
of message+hash
b.
Only the hash value
is encrypted
c.
As in (b) but with
private key (provides
digital signature)
February 9, 2012
http://users.abo.fi/ipetre/crypto/
13
Basic uses of hash functions
d.
Hash is encrypted
with an asymmetric
system, then a second
encryption is applied
e.
No encryption here
but the hash is
applied to a message
where a secret text S
has been appended
f.
As in (e), but with
encryption
February 9, 2012
http://users.abo.fi/ipetre/crypto/
14
Basic uses of hash functions
February 9, 2012
http://users.abo.fi/ipetre/crypto/
15
A few simple hash functions

Bit-by-bit XOR of plaintext blocks: h= D1⊕ D2⊕… ⊕ DN





Another example: rotated XOR – before each addition the hash value is
rotated to the left with 1 bit



Provides a parity check for each bit position
Not very effective with text files: most significant bit always 0
Attack: to send blocks X1, X2, …, XN-1, choose XN=X1⊕ X2⊕… ⊕ XN-1 ⊕h
It does not help if (only) the hash is sent encrypted!
Better than the previous hash on text files
Similar attack
Another technique: cipher block chaining technique without a secret key




Divide message into blocks D1, D2,…,DN and use them as keys in the
encryption method (e.g., DES)
H0=some initial value, Hi=EDi(Hi-1)
H=HN
This can be attacked with the birthday attack if the key is short (as in DES)
February 9, 2012
http://users.abo.fi/ipetre/crypto/
16
Birthday paradox

Given at least 23 people, the probability of having two people with
the same birthday is more then 0.5




it is in fact 0.5005
for 30 people it is more than 0.7
for 50 people it is more than 0.97
Related problem: Given two sets X,Y each having k elements from
the set {1,2,…,N}, how large should k be so that the probability that
X and Y have a common element is more than 0.5?


Answer: k should be larger than the square root of N
If N=2m, take k=2m/2
February 9, 2012
http://users.abo.fi/ipetre/crypto/
17
Birthday attack

Suppose a hash value on 64 bits is used (as the one based on DES)


In principle this is secure: given M, to find a message M’ with H(M)=H(M’), one has to
generate in average 263 messages M’
A different much more effective attack is possible








A is prepared to sign the document by appending its hash value (on m bits) and then
encrypting the hash code with its private key
E will generate 2m/2 variations of the message M and computes the hash values for
all of them
E also generates 2m/2 variations of the message M’ that she would really like to have
A authenticating and computes the hash values for all of them
By the birthday paradox, the probability that the two sets of hash values have one
element in common is more than 0.5 – she finds M and M’ with the same hash values
(messages expressing totally different things!)
E will offer M to A for hashing and then signing
E will send instead M’ with the signature A has produced
E breaks the protocol although she does not know A’s private key!
Level of effort for the hash based on DES: 233
February 9, 2012
http://users.abo.fi/ipetre/crypto/
18
Example of composing variations to a message
{This letter is / I am writing} to introduce {you to / to you} {Mr. / } Alfred
{P. / } Barton, the {new / newly appointed} {chief / senior} jewelry
buyer for {our / the} Northern {European / Europe} {area / division}.
He {will take /has taken} over {the / } responsibility for {all / the whole
of} our interests in {watches and jewelry / jewelry and watches} in
the {area/region}. …

Complexity of the attack



Compute the two lists of messages: each requires an effort on the scale
of 2m/2
Sort them: again an effort on the scale of 2m/2
Comparing two sorted tables can be done in linear time!
February 9, 2012
http://users.abo.fi/ipetre/crypto/
19
Two popular hash algorithms


MD5
SHA-1
February 9, 2012
http://users.abo.fi/ipetre/crypto/
20
MD5



Most popular hash algorithm until very recently – concerns for its
security were raised and was proposed to be replaced by SHA-1,
SHA-2
Developed by Rivest at MIT
For a message of arbitrary length, it produces an output of 128 bits


Processes the input in blocks of 512 bits
Idea:



Start by padding the message to a length of 448 bits modulo 512 –
padding is always added even if the message is of required length; the
length of the message is added on 64 bits so that altogether the length
is a multiple of 512 bits
Several rounds, each round takes a block of 512 bits from the message
and mixes it thoroughly with a 128 bit buffer that was the result of the
previous round
The last content of the buffer is the hash value
February 9, 2012
http://users.abo.fi/ipetre/crypto/
21
MD5
February 9, 2012
http://users.abo.fi/ipetre/crypto/
22
MD5 – the algorithm
1.
2.
Padding: add a bit 1 followed by the necessary number of bits 0
Append length – the length is represented on 64 bits
•
3.
4.
Initialize MD buffer with the following 4 values, all on 32 bits:
A=0x01234567, B=0x89ABCDEF, C=0xFEDCBA98,
D=0x76543210
Process each message block of 512 bits in 4 rounds
•
•
5.
If the length is larger than 264, take the 64 least representative bits
Each round takes as input the 512 bits in the input and the content of
the buffer ABCD and updates the buffer ABCD (details on the next
slide)
The four words A,B,C,D in the output of the 4th round are added modulo
232 to the corresponding words A,B,C,D of the input to the first round
Output: the 128 bits in the buffer ABCD after the last round
February 9, 2012
http://users.abo.fi/ipetre/crypto/
23
MD5 processing of a single 512-bit block
• Each round has 16 steps
•T is a table
• F,G,H,I are Boolean functions (tables) on
B,C,D (bit-by-bit operations)
• X has the current 32 bits of the message
•The message has 512 bits, i.e., 16 blocks of 32 bits
•Each of the 16 blocks is used exactly once in each
round
•Round 1: used in consecutive order
•Round 2: used in the order (1+5i) mod 16,
i=0,…,15
•Round 3: used in the order (5+3i) mod 16,
i=0,…,15
•Round 4: used in the order 7i mod 16, i=0,…,15
February 9, 2012
http://users.abo.fi/ipetre/crypto/
24
One single step in MD5
• All operations here are on blocks of 32 bits
• T is a table
• g is one of the functions F,G,H,I (bit-wise function)
• X has the current 32 bits of the message
• CLSs is a circular left shift (rotation) with s bits
• “+” is addition modulo 232
February 9, 2012
http://users.abo.fi/ipetre/crypto/
25
Table T and truth
table of F,G,H,I
February 9, 2012
http://users.abo.fi/ipetre/crypto/
26
Strength of MD5


Every bit of the output is a function of all bits of the input
Rivest’s conjecture:


Vulnerabilities found in 1996, then after 10 years a number of other
weaknesses reported, most serious in 2008



As strong as it can be for a 128-bit hash: birthday attack on the order of
264 and finding a message with a given digest is on the order of 2128
2008: fake certification of SSL was demonstrated based on MD5
currently classified as cryptographically weak
Used in HMAC
February 9, 2012
http://users.abo.fi/ipetre/crypto/
27
Secure Hash Algorithm (SHA)

Developed by NSA and adopted by NIST in FIPS 180-1 (1993)


Part of a family of 3 hashes: SHA-0, SHA-1, SHA-2






SHA-1 specified in RFC 3174 – contains a C code implementation
SHA-1 most widely used
recommendations that SHA-2 should be used because of a potential
math weakness in SHA-1
current competition for a new hash standard to be concluded in
December 2012
Design based on MD4 (previous version of MD5)
Takes as input any message of length up to 264 bits and gives a
160-bit message digest
Same structure as MD5, with block length of 512 bits and buffer of
160 bits
February 9, 2012
http://users.abo.fi/ipetre/crypto/
28
SHA-1 scheme
1.
2.
3.
4.
Append padding bits: message is padded so that length is congruent to
448 modulo 512; padding always added – one bit 1 followed by the
necessary number of 0 bits
Append length: a block of 64 bits containing the length of the original
message is added
Initialize 160-bit MD buffer: this is formed by 32-bit registers A,B,C,D,E.
Initial values: A=0x67452301, B=0xEFCDAB89, C=0x98BADCFE,
D=0x10325476, E=C3D2E1F0
Process message in blocks of 512 bits (i.e., 16 words of 32 bits each)
•
•
5.
Four rounds with 20 steps each (on next slide)
Each round takes as input the current 512-bit input block and the 160-bit
buffer ABCDE and updates the buffer – there is an addition modulo 232
Output: the final content of the buffer gives the message digest
February 9, 2012
http://users.abo.fi/ipetre/crypto/
29
SHA-1 processing of a single 512-bit block
• Each round has 20 steps
• f1,…,f4 are Boolean functions (tables) on b,c,d
• K is a constant changing in each round:
o K1=0x5A827999, K2=0x6ED9EBA1,
o K3=0x8F1BBCDC, K4=0xCA62C1D6
•W[t] is a 32-bit block derived from the current
512-bit input, changing in every step
• show later how W is generated
February 9, 2012
http://users.abo.fi/ipetre/crypto/
30
One single step in SHA-1
• ft is one of the functions f1,…f4 on
B,C,D
•Sk is a circular left shift by k bits
•W is a 32-bit block derived from the
current 512-bit input, changing in every
step
• K is the constant defined earlier
• Addition is modulo 232
February 9, 2012
http://users.abo.fi/ipetre/crypto/
31
Truth tables for functions f1,…,f4
February 9, 2012
http://users.abo.fi/ipetre/crypto/
32
Generating the 32-bit words Wt from the input


Wt=Xt, for 0≤t ≤15, where X is the input
Wt=S1(Wt-16⊕Wt-14 ⊕Wt-8 ⊕Wt-3), for t≥16
February 9, 2012
http://users.abo.fi/ipetre/crypto/
33
Strength of SHA-1



Stronger than MD5 because of longer message digest
Slower than MD5 because of more rounds
No known attacks




Secret design criteria; proposed by NSA
2005: potential math weakness in the design
Variants of SHA-1 with longer message digests have also been
proposed: SHA-256, SHA-384, SHA-512 (n-bit hash for SHA-n)
Used in HMAC
February 9, 2012
http://users.abo.fi/ipetre/crypto/
34
HMAC

Interest in recent years in developing a MAC based on a hash function



MD5 and SHA-1 run faster than symmetric block ciphers such as DES
Code for hash functions widely available
No export restrictions for cryptographic hash functions


Hash values not intended for MAC – they are not protected by secret keys



Cryptographic functions (even those used in MAC) restricted
Some protection needs to be built on top of the hash value
The one approach that gained wide support is HMAC (RFC 2104) included in IP
security and SSL
Requirements for HMAC





Use existing hash functions
The hash function can be easily replaced by another one – treat the hash function as a black
box
Preserve the performance of the hash function
Use and handle keys in a simple way
Well understood cryptographic analysis of the strength of the authentication mechanism
February 9, 2012
http://users.abo.fi/ipetre/crypto/
35
HMAC algorithm

Idea: append a secret key to the message and compute the hash value












To avoid a brute-force attack, apply the hash twice to mangle thoroughly the bits of the
key with those of the message
H=embedded hash function
IV=initial value to the hash function
M=message input to HMAC (including the padding specific to the hash function)
Yi=i-th block of M
L=number of blocks in M
b=number of bits in a block
n=length of the hash code
K=secret key, if its length is greater than b – will be given as input to the hash
function to produce n-bit key
K+=K padded with 0 on the left to make a b-bit key, if the original length of K is
smaller than b
ipad=0x36 repeated b/8 times
opad=0x5C repeated b/8 times
HMACK(M)=H[ (K+⊕ opad) || H[(K+⊕ ipad) || M] ]
February 9, 2012
http://users.abo.fi/ipetre/crypto/
36
HMAC algorithm
• H=embedded hash function
• IV=initial value input to hash function
• M=message input to HMAC (including the padding
specific to the hash function)
• Yi= the i-th block of M
• L=number of blocks in M
• b=number of bits in a block
• n=length of hash code produced by the embedded hash
function
• K=secret key, if its length is greater than b – will be given
as input to the hash function to produce n-bit key
• K+=K padded with 0 on the left to make a b-bit key, if the
original length of K is smaller than b
• ipad=0x36 repeated b/8 times
• opad=0x5C repeated b/8 times
⊕
⊕
HMACK(M)=H[ (K+⊕ opad) || H[(K+⊕ ipad) || M] ]
February 9, 2012
http://users.abo.fi/ipetre/crypto/
37
Strength of HMAC


Brute-force attack requires an effort on the level 2n-1 for a key of
length n
Birthday attack



The main idea in this attack is that Eve can compute the hash values of
many messages and try to find a match
In HMAC she is unable to do that because the hash is protected by a
secret key
Eve will have to rely on messages that she observes on the link: for MD5
she will have to wait in average for 264 messages generated using the
same key



February 9, 2012
On a 1 Gbps-link she needs to observe a continuous stream of messages
with no change in the key for about 250 000 years
With SHA-1 280 messages are needed
For HMAC, using MD5 is secure (and fast)
http://users.abo.fi/ipetre/crypto/
38