Tamper-Evident Digital Signatures: Protecting Certification Authorities

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Tamper-Evident Digital Signatures: Protecting Certification Authorities Tamper-Evident Digital Signatures: Protecting Certification Authorities Against Malware Jong Youl Choi Philippe Golle Markus Jakobsson Dept. of Computer Science Palo Alto Research Center School of Informatics Indiana Univ. at Bloomington 3333 Coyote Hill Rd Indiana Univ. at Bloomington Bloomington, IN 47405 Palo Alto, CA 94304 Bloomington, IN 47408 Abstract The threat of covert channels (also called subliminal channels) was first studied by Simmons [18, 19] and later We introduce the notion of tamper-evidence for digi- by, among others, Young and Yung [23, 24]. These authors tal signature generation in order to defend against attacks show how an attacker may leak bits of the private signing aimed at covertly leaking secret information held by cor- key in covert channels present in the randomized key gen- rupted signing nodes. This is achieved by letting observers eration or signing algorithm. For the sake of concreteness, (which need not be trusted) verify the absence of covert let us consider the RSA-PSS signature scheme (known as channels by means of techniques we introduce herein. We RSA's Probabilistic Signature Scheme [7]) as an example. call our signature schemes tamper-evident since any de- The message encoding scheme of RSA-PSS specifies that viation from the protocol is immediately detectable. We the hash of the message to be signed be concatenated with demonstrate our technique for the RSA-PSS (known as a random octet string known as a “salt”. A malicious im- RSA’s Probabilistic Signature Scheme) and DSA signature plementation of RSA-PSS may choose bits of the private schemes and show how the same technique can be ap- key for the salt, instead of a value produced by the pseudo- plied to the Schnorr and Feige-Fiat-Shamir (FFS) signature random number generator. One may argue that this simple schemes. Our technique does not modify the distribution of type of leakage is detectable: a third party could test (for the generated signature transcripts, and has only a mini- each signature) whether the salt is a substring of the secret mal overhead in terms of computation, communication, and key corresponding to the known public key of the signer (the storage. third party would need to be trusted with the secret key). Upon the detection of such an event, the signer would be isolated and decommissioned. However, an attacker could 1 Introduction just as easily leak an encryption of some of the bits of the secret signing key, under a symmetric or public-key encryp- Malware and insider attacks pose an increasing threat to tion scheme for which the attacker knows the decryption our cyber infrastructure. Current protection mechanisms key. For a semantically secure encryption scheme, and ap- against malware rely on the collection of malicious code propriate parameter choices, such a leakage could be made found in the wild. For this protection to be effective, mali- in a truly covert manner. cious code must be detected as quickly as possible after an RSA-PSS is not the only signature scheme that is vulner- attack is mounted. Unfortunately detecting malicious code able to covert channel attacks. To some extent, all signature quickly is difficult, particularly in the case of carefully tar- schemes are vulnerable to these attacks, since they all make geted attacks, such as for example an attack narrowly fo- use of randomness for key generation. Still, covert channel cussed on critical nodes in the infrastructure. attacks pose the greatest threat to signature schemes that use A perfect example of such a target is a certification au- randomness not just once in the initial key generation step, thority. The consequences would be severe if an attacker but for the generation of every signature. Thus discrete-log succeeded in corrupting a certification authority and man- based signatures schemes, such as Schnorr signatures [17] aged to cause it to leak its secret key material. The mere and DSA [20], are particularly vulnerable to covert chan- possibility of such an attack (as opposed to its actual occur- nels given their ongoing use of randomness in the genera- rence) may in fact weaken the trustworthiness of our public tion of each and every signature. Our techniques focus on key infrastructure. This threat is all the more severe as the eliminating covert channels from the signature algorithm of leak may be performed using a covert channel. discrete-log based signature schemes, but they can be com- bined with previously proposed techniques [9] that consider be the values of a hash chain such that si = h(si+1) only covert channels in the key generation phase. (0 ≤ i ≤ n − 1), for some secret seed sn which is known In this paper, we consider the problem of detecting (po- only to the signer. The value s0 is made public by the signer tentially covert) malicious behavior by corrupt certification during a setup phase. Afterward, the signer uses the value authorities and other generators of digital signatures. We si as a salt for signature i = 1; : : : ; n. An observer can propose to solve this problem with tamper-evident digital check the correctness of the salt used in the ith signature signatures. Tamper-evident signatures do not prevent cor- with the equation si−1 = h(si). If this verification fails, the ruption, but they ensure the immediate detection of any cor- observer raises an alarm. ruption that causes a signer to output signatures that are in any way different from those of an honest signer. Tamper- Properties. We describe next two important properties of evident signatures are useful to defend not only against mal- the tamper-evident signature schemes proposed in this pa- ware, but also against insider attacks. A typical insider per. attack [16] is performed by the implementor of a crypto- graphic application, who designs code that operates cor- 1. Undercover observers. In our RSA-PSS example, the rectly while under test, but switches to a corrupt mode of observer can verify the absence of covert channels operation after deployment. Insider attacks are notoriously without interacting with the signer. We say that our hard to prevent, given the difficulty of auditing even small observer is undercover. Undercover observers quietly pieces of software or hardware. Tamper-evident signatures “eavesdrop” on available network traffic to detect ir- do not prevent insider attacks, but ensure that such attacks regularities and need not expose their existence until are immediately detected if they cause a signer to output they raise an alarm. Undercover observers, by virtue of signatures that differ in any way from the signatures of an being hidden, cannot be targets of coercion attacks (un- honest signer. like the signer whose existence is of necessity public). While current security models for digital signatures con- Onwards, we only consider undercover observers, but sider the signer as an oracle, we take a large step towards note that interactive observers may be useful in other a more realistic threat model by allowing – in addition – contexts to design tamper-evident protocols. attackers to corrupt signers and attempt to make them leak 2. Distribution of signatures. In the simple example their secret information to the attacker. When an attacker given above, the distribution of the transcripts gener- corrupts a node, it replaces the code run by that node with ated by tamper-evident RSA-PSS is easily distinguish- code chosen by the attacker. We assume however that the able from that of standard RSA-PSS, given the relation attacker cannot create any new communication channels for of salts. This is undesirable and can easily be avoided. the nodes under its control. The goal of our attacker, as in The tamper-evident signature schemes that we propose the standard definition of security for signature schemes, is in this paper produce a distribution of signature tran- to generate a valid signature on a new message. scripts that is polynomial-time indistinguishable from We assume the existence of one or several observers. An regular transcripts (after removing the proofs consti- observer is an external node whose task is to inspect all sig- tuting evidence of tamper-freeness). nature transcripts produced by a signer and detect any devi- ation from honest signature generation. This task would be Assumptions. The tamper-evident signature schemes trivial if we gave the observer knowledge of all the secrets proposed in this paper make the following assumptions: known to the signer. However, we do not wish to place any trust with observers. Instead, the observers need to detect 1. Unencrypted traffic. We assume that traffic to and the presence of a covert channel given only publicly avail- from the signer is not encrypted. The adaptation of our able information. Once a covert channel is detected, the ob- methods to a model in which traffic is sent over an en- server alerts the public of this fact, and proves the existence crypted communication channel to which the observer of the covert channel to avoid false alarms. This allows cor- does not have decryption abilities is theoretically pos- rupted nodes to be manually disconnected and reconfigured, sible – given well-known results relating to general and minimizes the effects of the attack. multi-party computation. However, an efficient solu- tion that remains compatible with existing VPN tech- Example. To illustrate our techniques, we return to the niques is a challenging open problem. example of RSA-PSS. A small change to the signing al- 2. Timing attacks. Tamper-evident signatures do not pro- gorithm makes RSA-PSS tamper-evident. Let us replace tect against timing attacks. However, by imposing the sequence of random salt used in the message encoding strict requirements on synchronization, one can pro- scheme with successive pre-images of a fixed value by a tect against these as well, at the cost of a reduced (but one-way hash function.
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