Digital Signatures and Authentication

1. Digital Signatures and Authentication CSIS 5857: Encoding and Encryption

2. Need for Authentication • Authentication Problem: How can recipient be sure that message was sent by particular person? “Give Darth a $10,000 raise-- Alice” E Masquerading as Alice

3. Authentication • Terminology: • Claimant: Entity desiring to prove their identity(real or fraudulent ) • Verifier: Entity checking identity of claimant • Topics: • Digital Signatures • Challenge/Response Authentication • Replay Attacks

4. Digital Signatures • Based on some signing algorithm • Algorithm applied to message (like message digest) • Message and signature sent to recipient • Recipient uses algorithm to verify signature • Must involve “secret knowledge” known only to signer • Otherwise, adversary could “forge” signature “I can’t create this”

5. Public Keys and Digital Signatures • Signing algorithm involves private key • Public/private key pair generated by sender • Opposite of public key encryption • Sender stores private key, gives public key to recipient • Private key used to sign message • Public key used to verify signature

6. Digital Signatures and Confidentiality • Sender: • Signs message with sender private key • Encrypts message with recipient public key • Recipient • Decrypts message with recipient private key • Verifies signature with sender public key Authentication Confidentiality

7. Signing Message Digests • Problem: • Creating signature from entire message as costly as encrypting entire message with public key algorithm • Solution: • Sender creates message digest (much shorter than message) • Sender creates signature from digest • Recipient creates same message digest from received message • Recipient verifies signature based on message digest

8. RSA Digital Signature Scheme • Encryption/Decryption: • Encryption by sender: C = Pemod n • Decryption by recipient: P = Cdmod n = Pdemod n • Digital signature just reverses order • Key pair generated in same way • Public key: n, e • Private key: d • Signature by sender: S = Mdmod n • Verification by recipient: M = Semod n = Mdemod n • Works since d  e = e  d

9. RSA Digital Signature Scheme • Recipient has sender’s public key • Sent message M and signature S generated from M • Uses key to “decrypt” signature S and compare to M

10. Attacks on Digital Signatures • Known Message Attack • Adversary has intercepted several messages and their corresponding signatures. • Goal: Create fake message M´ and legitimate corresponding signature from those previous messages • Chosen Message Attack • Adversary has ability to make sender sign messages that adversary chooses (“We like kittens”) • Goal: Choose those messages to make it possible to create fake message M´ and legitimate corresponding signature

11. Known Message Attack on RSA • Based on multiplicative property of RSA • Darth intercepts message pairs (M1, S1) and (M2, S2) • Computes M´ = M1M2 • Corresponding signature: S´ = S1S2 • Idea: S´ = S1S2 = (M1dM2d) mod n = (M1M2)d mod n = M´d mod n • Darth now has fake message M´ and matching signature S´ without having to know Alice’s private key!

12. Known Message Attack on RSA • Problem for Darth:Fake message M´ = M1M2 almost certain to be meaningless • Darth can’t control messages M1,M2 • Bob will treat as noise and ignore ???

13. Chosen Message Attack on RSA • Darth chooses messages M1,M2 such that: • M1,M2 appear harmless (and can convince sender to sign) • M1M2 has advantage to Darth • Most serious attack on most digital signature schemes! Alice creates signatures using her private key Darth asks Alice to sign these Darth sends fake message and signature to Bob

14. Chosen Message Attack on RSA Solution: • Sign message digesth(M ) instead of message M • h(M ) must be preimage resistant hash function signature = h(M )Dmod n Why is this effective? • Darth has a fake message M´ • Cancompute its digest h(M´) • Canfind two digests h(M1),h(M2) such that h(M´) = h(M1)  h(M2) • Darth cannot find messages M1,M2 with the desired digests h(M1),h(M2) !

15. Digital Signature Standard • NIST standard (FIPS 186) • Algorithms: • SHA-512 hashing • Schnorr public key encryption scheme (similar to ElGamal)

16. DSS Components • Global public key components (PUG) • p : Large prime (between 512 and 1024 bits) • q : prime divisor of p -1 (approx. 160 bits) • g = h(p-1)/qmod p where h is some integer < p -1 such thath(p-1)/qmod p > 1 • Sender’s private key (PRa) • Random integer < q • Sender’s public key (PUa) • PUa = gPRa mod p

17. Signing a Message • Generate random one-time key k < q • Compute components of message: • r = (gk mod p) mod q • s = [k -1 (H(M) + PUa)] mod q • Signature = (r, s) • Efficiency: only modular exponentiation is gk mod p which can be computed in advance

18. Verifying a Message • w = s -1 mod q • u1 = [H(M) w] mod q • u2 = (rw) mod q • v = [(gu1 PUau2) mod p) mod q • Verifiedifv= r

19. Replay Attacks • Adversary records message from sender to recipient • Resends message to recipient (claiming to be sender) • Any signatures, digests, etc. will be correct! M, h(k, M) M, h(k, M) M = “Give Darth a $1,000 raise -- Alice”

20. Timestamp Solution • Include timestamp in message • Adversary cannot alter if part of digest • Verifier can reject second message with same timestamp • Problems if timestamp not accurate • Clocks not synchronized, no universal time scheme used • Example: daylight savings time could cause multiple legitimate messages with same timestamp! M | time, h(k, M | time) Accept M | time, h(k, M | time) Reject M = “Give Darth a $1,000 raise -- Alice”

21. Nonce Solution • Claimant generates random number not sent before • Verifier keeps list of previousnonces sent by claimant • If current message nonce is in that list, this is a replay M M M | N, h(k, M | N) N New nonce N search Alice’s previous nonces previous nonces

22. Challenge-Response Authentication • Problem with passwords:Claimant is sending a secret to the verifier • May be intercepted or sold • Better idea: • Claimant proves that they know secret without sending it to verifier • Verifier asks question that can only be answered by claimant with that knowledge • Challenge: One-time value sent to claimant • Random number, timestamp, nonce • Response: Result of function applied to value • Function includes secret that only claimant knows Alice’s password $$$

23. Symmetric Key Challenge-Response • Both Alice and Bob verifier know secret symmetric key K • Alice sends request for access • Bob sends nonce RB as challenge • Alice encrypts nonce with symmetric key KA-B • Bob decrypts with KA-B • If result is original nonce RB, then identity verified • Note that actual secret knowledge KA-Bnever sent! “I can’t answer the challenge unless I know KA-B”

24. Public Key Challenge-Response • Alice has public keyKA and corresponding private key • Alice sends request for access • Bob encrypts nonce RB with KAand sendsas challenge • Alice decrypts nonce with her private key, and sends back to Bob • If result is original nonce RB, then identity verified “I can’t answer the challenge unless I know Alice’s private key”

25. Signature Challenge-Response • Alice has public keyKA and corresponding private key • Alice sends request for access • Bob sends nonce RB as challenge • Alice signs nonce with her private key, and sends back to Bob • Bob verifies signature with Alice’s public key and nonce value “I can’t answer the challenge unless I know Alice’s private key”