Message Authentication and Hash Functions K. U. Khimani Asst. Prof. IT Dept. VVP Engineering College

What is Authentication?   In the context of computer systems, authentication is a process that ensures and confirms a user’s identity.   For example, ID-Password combination, biometrics(retina, fingerprints…), etc.

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

Message Security Requirements   disclosure   traffic analysis   masquerade   content modification   sequence modification   timing modification   source repudiation   destination repudiation In summary, message authentication is a procedure to verify that received messages come from the alleged source and have not been altered. Message authentication may also verify sequencing and timeliness.

Symmetric Message Encryption   Encryption can also provide 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.

Public-Key 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.   The disadvantage of this approach is that, the public key algorithm, which is complex, must be exercised four times rather than two in each communication.

Message Authentication Code (MAC)   generated by an algorithm that creates a small fixed- sized block   depends on both message and some key   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

MAC  A small fixed-sized block of data  generated from message + secret key  MAC = C(K,M)  M = input message  C = MAC function  K = shared secret key  appended to message when sent

MAC  as shown the MAC provides authentication  can also use encryption for secrecy generally use separate keys for each generally use separate keys for each can compute MAC either before or after encryption can compute MAC either before or after encryption is generally regarded as better done before is generally regarded as better done before  why use a MAC? sometimes only authentication is needed sometimes only authentication is needed  note that a MAC is not a digital signature

Why MAC?  Symmetric Encryption provides authentication and because it is widely used with readily available products, why not simply use this instead of a separate MAC?  We will discuss situations in which a message authentication code is used.

Why MAC? (1)  There are a number of applications in which the same message is broadcast to a number of destinations.  E.g. notifications to users that the network is now unavailable or an alarm signal in a military control centre.  It is cheaper and more reliable to have only one destination responsible for monitoring authenticity.  Thus, the message must be broadcast in plaintext with an associated MAC.  The responsible system has the secret key and performs authentication. If violation occurs, the other destination systems are alerted by general alarm.

Why MAC? (2)  Another possible scenario is an exchange in which one side has a heavy load and cannot afford the time to decrypt all incoming messages.  Authentication is carried out on a selective basis, message being chosen at random for checking.

Why MAC? (3)  Authentication of a computer program in plaintext as an attractive service.  The computer program can be executed without having to decrypt it every time, which would be wasteful of processor resources.  However, if a MAC were attached to the program, it could be checked whenever assurance was required of the integrity of the program.

MAC  a MAC is a cryptographic checksum MAC = C K (M) condenses a variable-length message M condenses a variable-length message M using a secret key K using a secret key K to a fixed-sized authenticator to a fixed-sized authenticator  is a many-to-one function potentially many messages have same MAC potentially many messages have same MAC but finding these needs to be very difficult 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 in the sense that, for two randomly chosen messages, probability that C(K,M) = C(K,M’) is 2^-n, where n is the number of bits in MAC. 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 using IV=0 and zero-pad of final block encrypt message using DES in CBC mode encrypt message using DES in CBC mode and send just the final block as the MAC and send just the final block as the MAC or the leftmost M bits (16≤M≤64) of final blockor the leftmost M bits (16≤M≤64) of final block  but final MAC is now too small for security

Data Authentication Algorithm

Hash Functions  A hash value h is generated by a function H of the form h = H(M) where M is a variable-length message and H(M) is a fixed-length hash value.  The hash value is appended to the message at the source. The receiver authenticates that message by recomputing the hash value.

Requirements of a Hash Function  H can be applied to a block of data of any size.  H produces a fixed-length output.  H(x) is relatively easy to compute for any given x  For any h, it is computationally infeasible to find x such that H(x) = h. It is One-way Property.  For any given block x, it is computationally infeasible to find y ≠ x such that H(y) = H(x). It is called Weak Collision Resistance.  It is computationally infeasible to find any x and y, with x  y such that H(x) = H(y). It is called Strong Collision Resistance.

Basic uses of Hash Function Confidentiality and Authentication Authentication Authentication, Digital Signature

Basic uses of Hash Function Authentication, DS, Confidentiality Authentication (No encryption needed) Authentication, Confidentiality

Simple Hash Function

Security of MACs and Hash  Just as with symmetric and public-key encryption, we can group attacks on hash functions and MACs into two categories: brute-force attacks and cryptanalysis.  brute-force attacks exploiting strong collision resistance hash have cost 2 m / 2 strong collision resistance hash have cost 2 m / bit hash looks vulnerable, 160-bits better128-bit hash looks vulnerable, 160-bits better MACs with known message-MAC pairs MACs with known message-MAC pairs can either attack key space (cf key search) or MACcan either attack key space (cf key search) or MAC at least 128-bit MAC is needed for securityat least 128-bit MAC is needed for security

Security of MACs and Hash  A brute-force attack on a MAC is a more difficult undertaking than a brute-force attack on a hash function because it requires known message-MAC pairs.  A brute-force attack on MAC has cost related to min(2^k,2^n), similar to symmetric encryption algorithms. It is required that min (k, n) >= N, where N is perhaps in the range of 128 bits.

Security of MACs and Hash  cryptanalytic attacks exploit internal structure of f and is based on attempts to find efficient techniques for producing collision for a single execution of f.  Once that is done, the attack must take into account the fixed value of IV. like block ciphers want brute-force attacks to be the best alternative like block ciphers want brute-force attacks to be the best alternative  more variety of MACs so harder to generalize about cryptanalysis.

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

HMAC Design Objectives  use, without modifications, hash functions  allow for easy replaceability of embedded hash function  preserve original performance of hash function without significant degradation  use and handle keys in a simple way.  have well understood cryptographic analysis of authentication mechanism strength

HMAC  specified as Internet standard RFC2104  uses hash function on the message: HMAC K (M)= Hash[(K + XOR opad) || Hash[(K + XOR ipad) || M)] ] o M is the message to be authenticated, o ∥ denotes concatenation, o ⊕ denotes exclusive or (XOR), o K + is the key padded out to size o opad, ipad are specified padding constants  any hash function can be used E.g. MD5, SHA-1, RIPEMD-160, Whirlpool E.g. MD5, SHA-1, RIPEMD-160, Whirlpool

HMAC Overview

HMAC  Append zeros to the left end of K to create a b-bit string K+ (if K is of length 160 bits and b = 512, then K will be appended with 44 zero bytes).

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