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Message Authentication and Hash Functions

Authentication Requirements Authentication Functions Message Authentication Codes Hash Functions Security of Hash Functions and MACs

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Authentication Requirements Kind of attacks (threats) in the context of

communications across a network1. Disclosure2. Traffic analysis3. Masquerade4. Content modification5. Sequence modification6. Timing modification7. Repudiation

Measures to deal with first two attacks: In the realm of message confidentiality, and are addressed with

encryption Measures to deal with items 3 thru 6

Message authentication Measures to deal with items 7

Digital signature

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Message authentication A procedure to verify that messages come from the

alleged source and have not been altered Message authentication may also verify sequencing

and timeliness Digital signature

An authentication technique that also includes measures to counter repudiation by either source or destination

Authentication Requirements

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Authentication Functions

Message authentication or digital signature mechanism can be viewed as having two levels At lower level: there must be some sort of functions producing

an authenticator – a value to be used to authenticate a message

This lower level functions is used as primitive in a higher level authentication protocol


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Authentication Functions Three classes of functions that may be used to produce

an authenticator Message encryption

Ciphertext itself serves as authenticator Message authentication code (MAC)

A public function of the message and a secret key that produces a fixed-length value that serves as the authenticator

Hash function A public function that maps a message of any length into a

fixed-length hash value, which serves as the authenticator


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Message Encryption

Conventional encryption can serve as authenticator Conventional encryption provides authentication as

well as confidentiality Requires recognizable plaintext or other structure to

distinguish between well-formed legitimate plaintext and meaningless random bits

e.g., ASCII text, an appended checksum, or use of layered protocols


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Basic Uses of Message Encryption


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Ways of Providing Structure• Append an error-detecting code (frame check

sequence (FCS)) to each message


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Ways of Providing Structure - 2• Suppose all the datagrams except the IP header is

encrypted.

• If an opponent substituted some arbitrary bit pattern for the encrypted TCP segment, the resulting plaintext would not include a meaningful header


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Confidentiality and Authentication Implications of Message Encryption


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Message Authentication Code Uses a shared secret key to generate a fixed-size

block of data (known as a cryptographic checksum or MAC) that is appended to the message

MAC = CK(M) Assurances:

Message has not been altered Message is from alleged sender Message sequence is unaltered (requires internal

sequencing)

Similar to encryption but MAC algorithm needs not be reversible


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Basic Uses of MAC


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Basic Uses of MAC


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Why Use MACs? i.e., why not just use encryption?

Cleartext stays clear MAC might be cheaper Broadcast Authentication of executable codes Architectural flexibility Separation of authentication check from

message use


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Hash Function Converts a variable size message M into fixed size

hash code H(M) (Sometimes called a message digest) Can be used with encryption for authentication

E(M || H) M || E(H) M || signed H E( M || signed H ) gives confidentiality M || H( M || K ) E( M || H( M || K ) )


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Basic Uses of Hash Function

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Message Authentication Codes

MAC= CK(M)

Key length requirements Sufficient key length to thwart brute force attack

MACs

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Hash Functions

h = H(M) M is a variable-length message, h is a fixed-

length hash value, H is a hash function The hash value is appended at the source The receiver authenticates the message by

recomputing the hash value Because the hash function itself is not

considered to be secret, some means is required to protect the hash value

Hash Functions

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Hash Function Requirements

1. H can be applied to any size data block

2. H produces fixed-length output

3. H(x) is relatively easy to compute for any given x

4. H is one-way, i.e., given h, it is computationally infeasible to find any x s.t. h = H(x)

5. H is weakly collision resistant: given x, it is computationally infeasible to find any y x s.t. H(x) = H(y)

6. H is strongly collision resistant: it is computationally infeasible to find any x and y s.t. H(x) = H(y)

Hash Functions

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Hash Function Requirements

One-way property is essential for authentication

Weak collision resistance is necessary to prevent forgery

Strong collision resistance is important for resistance to birthday attack

Hash Functions

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Simple Hash Functions Operation of hash functions

The input is viewed as a sequence of n-bit blocks The input is processed one block at a time in an iterative fashion

to produce an n-bit hash function

Simplest hash function: Bitwise XOR of every block Ci = bi1 bi2 … bim

Ci = i-th bit of the hash code, 1 i n m = number of n-bit blocks in the input bij = i-th bit in j-th block

Known as longitudinal redundancy check

Hash Functions

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Simple Hash Functions

Hash Functions

• Improvement over the simple bitwise XOR

– Initially set the n-bit hash value to zero

– Process each successive n-bit block of data as follows

» Rotate the current hash value to the left by one bit

» XOR the block into the hash value

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Birthday Attack If the adversary can generate 2m/2 variants of a valid

message and an equal number of fraudulent messages

The two sets are compared to find one message from each set with a common hash value

The valid message is offered for signature The fraudulent message with the same hash value is

inserted in its place

If a 64-bit hash code is used, the level of effort is only on the order of 232

Conclusion: the length of the hash code must be substantial

Birthday Attack

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Generating 2m/2 Variants of Valid Messages

Birthday Attack

• Insert a number of “space-backspace-space” character pairs between words throughout the document. Variations could then be generated by substituting “space-backspace-space” in selected instances

• Alternatively, simply reword the message but retain the meaning

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Brute-Force Attack of Hash Functions Three desirable properties of hash functions

One-way: For any given code h, it is computationally infeasible to find x s.t. H(x) = h

Weak collision resistance: For any given block x, it is computationally infeasible to find y x s.t. H(y) = H(x)

Strong collision resistance: It is computationally infeasible to find any pair (x, y) s.t. H(y) = H(x)

Brute-force attack on n-bit hash code One-way and weak collision require 2n effort Strong collision requires 2n/2 effort If strong collision resistance is required (and this is desirable

for a general-purpose secure hash code), 2n/2 determines the strength of hash code against brute-force attack

Currently, two most popular hash codes, SHA-1 and RIPEMD-160, provide a 160-bit hash code length

Security of Hash Functions and MACs

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