TamperEvident Digital Signatures Protecting Certification Authorities Against Malware

Tamper-Evident Digital Signatures: Protecting Certification Authorities Against Malware Jong Youl Choi Computer Science Dept. Indiana University at Bloomington Philippe Golle Palo Alto Research Center CA, USA Markus Jakobsson School of Informatics Indiana University at Bloomington

1 Threats to Certificate Authorities • Certificate repudiation – A user chooses weak private key – Intentionally let his private key be leaking discretely forgery • Certificate private key leaking – Malicious attack such as Trojan horse – Leaking CA’s private via covert-channel

2 What is a covert channel? • Hidden communication channel • Steganography – Information hiding Original Image Extracted Image

3 Prisoners' problem [Simmons, ’ 93] • Two prisoners want to exchange messages, but must do so through the warden Plan A • Subliminal channel in DSA What Plan?

4 Leaking attack on RSA-PSS • Random salt is used for padding string in encryption • In verification process, salt is extracted from EM • Hidden information can be embedded in salt value RSA-PSS : PKCS #1 V 2. 1

5 Approaches • Detect leaking • A warden observes outputs from CA Something hidden? • Malicious attack • Replacement of function Pseudo Random Number Generator Certificate Authority mk Sigk

6 Approaches (Cont’d) • Observing is not so easy because random number. . . – looks innocuous – Or, doesn’t reveal any state • A warden (observer) can be attacked Something hidden? Pseudo Random Number Generator mk Certificate Authority Sigk

7 Undercover observer • Signer outputs non-interactive proof as well as signature • Ambushes until verification is invalid Pseudo Random Number Generator mk Sigk

8 Tamper-evident Chain • Predefined set of random values in lieu of random number on the fly • Hash chain verification x 1 Sig 1 Hash() x 2 Hash() x 33 x’ Hash() Sig 2 Sig’ 3 ? X 1=Hash(X 2) ? X 2=Hash(X 3) …. Hash() xn Hash() Sign ? Xn-1=Hash(Xn) Xn+1

9 DSA Signature Scheme • Gen : x y = gx mod p • Sign : m (s, r) where r = (gk mod p) mod q and s = k-1(h(m) + x r) for random value k • Verify : For given signature (s, r), u 1 = h(m) s-1 u 2 = r s-1 and check r=gu 1 yu 2 mod p mod q

10 Hash chain construction k 1 Hash() k 2 Hash() k’ k 33 Hash() r=gk 1 r=gk 2 k 3 r’=g r=gk 3 P 1 P 2 P 3 Sig 1 Sig 2 Sig’ 3 ? X 1=Hash(X 2) ? X 2=Hash(X 3) …. …. …. Hash() kn+1 r=gkn Pn Sign ? Xn-1=Hash(Xn) Pn+1

11 Conclusion • Any leakage from CAs is dangerous • CAs are not strong enough from malicious attacks • We need observers which are under-cover • A small additional cost for proofs Or, Send me email : jychoi@cs. indiana. edu