![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](https://image.slidesharecdn.com/ch11-241129164030-ac7ba706/85/cryptography-and-network-security-by-william-stallings-19-320.jpg)
![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](https://image.slidesharecdn.com/ch11-241129164030-ac7ba706/85/cryptography-and-network-security-by-william-stallings-21-320.jpg)
cryptography and network security by william stallings
- 1. Cryptography and Network Security Third Edition by William Stallings Lecture slides by Lawrie Brown
- 2. Chapter 11 – Message Authentication and Hash Functions • At cats' green on the Sunday he took the message from the inside of the pillar and added Peter Moran's name to the two names already printed there in the "Brontosaur" code. The message now read: “Leviathan to Dragon: Martin Hillman, Trevor Allan, Peter Moran: observe and tail.” What was the good of it John hardly knew. He felt better, he felt that at last he had made an attack on Peter Moran instead of waiting passively and effecting no retaliation. Besides, what was the use of being in possession of the key to the codes if he never took advantage of it? • —Talking to Strange Men, Ruth Rendell
- 3. 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
- 4. Security Requirements • disclosure • traffic analysis • masquerade • content modification • sequence modification • timing modification • source repudiation • destination repudiation
- 5. 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
- 6. 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
- 7. 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
- 9. Message Authentication Codes • as shown the MAC provides confidentiality • 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
- 10. 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
- 11. 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
- 12. 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
- 13. Hash Functions • condenses arbitrary message to fixed size • 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
- 14. Hash Functions & Digital Signatures
- 15. Hash Function Properties • a Hash Function produces a fingerprint of some file/message/data h = H(M) – condenses a variable-length message M – to a fixed-sized fingerprint • assumed to be public
- 16. 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
- 17. 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)
- 18. 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 MACs
- 19. 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
- 20. 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
- 21. 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
- 22. Summary • have considered: – message authentication using – message encryption – MACs – hash functions – general approach & security
Editor's Notes
- #3: Up till now, have been concerned with protecting message content (ie secrecy) by encrypting the message. Will now consider how to protect message integrity (ie protection from modification), as well as confirming the identity of the sender. Generically this is the problem of message authentication, and in eCommerce applications is arguably more important than secrecy.
- #4: The first two requirements belong in the realm of message confidentiality, and are handled using the encryption techniques already discussed. The remaining requirements belong in the realm of message authentication. At its core this addresses the issue of ensuring that a message comes from the alleged source and has not been altered. It may also address sequencing and timeliness. The use of a digital signature can also address issues of repudiation.
- #12: Can also use block cipher chaining modes to create a separate authenticator, by just sending the last block. However this suffers from being a bit too small for acceptable use today.
- #16: These are the specifications for good hash functions. Essentially it must be extremely difficult to find 2 messages with the same hash, and the hash should not be related to the message in any obvious way (ie it should be a complex non-linear function of the message). There are quite a few similarities in the evolution of hash functions & block ciphers, and in the evolution of the design requirements on both.
- #18: The Birthday Attack exploits the birthday paradox – the chance that in a group of people two will share the same birthday – only 23 people are needed for a Pr>0.5 of this. Can generalize the problem to one wanting a matching pair from any two sets, and show need 2m/2 in each to get a matching m-bit hash. Note that creating many message variants is relatively easy, either by rewording or just varying the amount of white-space in the message.