Cryptography: Digital Signatures Message Digests Authentication Security in Computing Cryptography: Digital Signatures Message Digests Authentication

Digital Signatures Non-repudiation (non-denial) How do you legally prove who actually send you the message? Receiver can verify the claimed identity of sender Sender cannot later repudiate contents of the message Receiver cannot possibly have concocted message by himself/herself

Digital Signatures Purpose Authenticity of legal / financial documents is determined by authorised handwritten signatures Photocopies may be forged and don’t count! Growing need for computing systems to replace physical transport of paper documents The problem is devising a method of “digital signatures” to be used as legal signatures

Digital Signatures Symmetric Scheme A, KA (B, RA, t, M) Trusted Central Authority (CA) is needed CA shares secret key K with sender (Alice) and receiver (Bob): KA and Kb Alice (A)sends message (M)encrypted with her key (KA) to her banker Bob (B) via CA A, KA (B, RA, t, M) A = Alice’s identity; B = Bob’s identity; RA = Random number chosen by Alice; t = timestamp to ensure freshness KA(...) means the message is encrypted using the secret key Alice shares with CA

Digital Signatures CA sees message is from Alice and decrypts it using Alice’s secret key, KA CA then uses Bob’s secret, KB, to encrypt an extended message containing: Alice’s original plaintext message to Bob the “signed message” encrypted with CA’s secret key, KCA(A, t, M) Extended message is then sent to Bob KB (A, RA, t, M, KCA(A, t, M)) KA(...) means the message is encrypted using the secret key Alice shares with CA

Digital Signatures Verification: A case in Court Alice later denies sending message to Bob Bob tells judge that CA will only accept message form Alice if encrypted with her key, KA Bob produces Exhibit 1: KCA(A, t, M)) Judge asks trustworthy CA to decrypt Exhibit I who also testifies that Bob is telling the truth Judge rules in favour of Bob, case dismissed!

Digital Signatures Problems Digital Signature Public key Scheme? Replay attacks: Timestamp; random number Digital Signature Public key Scheme? Using timestamps throughout minimises the problem Based on timestamps old messages are rejected To guard against instant replay attacks Bob checks RA of every incoming message RA((Random number in Alice’s message) is checked to see if any other incoming message contains the same RA. If not then the assumption is that this is new message / request.

Message Digests Integrity One –way Hash function Digital signatures couple together two distinct functions (criticism): “authentication” (i.e. verification) & secrecy “Authentication” is often needed but secrecy is not Message digests provide a more efficient approach to digital signatures

Message Digests Comparing Digital Signature and Message Digests Digital Signature: A, KA(B, RA, t, M) (from Alice to Bob via CA) KB (A, RA, t, P, KCA(A, t, P)) (from CA to BOB) Extended message to Bob

Message Digests Message Digest Public Key Scheme? Message Digest: Instead, consider CA computing a message digest MD(P) by applying MD to P KB ( A, RA, t, P KCA( A, t, MD (P) ) ) Thus, message digest MD(P) is signed and NOT P (computationally faster to do so) Message Digest Public Key Scheme?

Message Digests Applications Message Digest 5 (MD5) / & MD6 are prominent by Ronald Rivest Secure Hash Algorithm (SHA-1) + newer versions of SHA-1 Others (Investigate)

Authentication Authentication Vs Digital Signatures Digital Signatures guarantee non-repudiation at some point in the future Authentication – verifying someone’s identity during communication Authentication – how do you know it’s Alice and not Trudy (imposter) you are ‘talking’ to?

Authentication Authentication Vs Authorisation Authorisation – what a process is permitted to do Server: Is Bob’s process allowed to delete a file ? Authentication – are you actually communicating with the process you think you are? Server: Needs to determine if this is Bob’s process

Authentication Based on shared secret key (symmetric) Commonly known as challenge-response protocols Alice and Bob share secret key, KAB Alice or Bob sends a random number to the other Alice or Bob transforms it in some way and returns the result back to the other

Two way Authentication: challenge –response Alice Bob A RB KAB (RB) RA This protocol contains five messages. Can it be shortened? Alice sends her identity to Bob Bob chooses a challenge to be sure this came from Alice and not Trudy The challenge Bob sends is a large random number RB as plaintext to Alice Alice encrypts message using shared secret key and sends ciphertext KAB(RB) to Bob Bob decrypts ciphertext and checks RB Bob is now sure he is talking to Alice and not Trudy (Trudy does not know KAB) *But Alice does not know she is talking to Bob (Trudy could have sent plaintext RB to Alice!) Therefore, Alice sends Bob her own RA and when Bob returns KAB(RA), Alice knows it’s from him To establish a session key (optional), Alice picks a session kye KS and sends Bob KAB (KS) *As far as Alice is concerned Trudy could have intercepted the first message (see diagram) and sent the random number to her. So Alice does same as what Bob did. KAB (RA) Source: A S Tanenbaum