Authenticated Key Exchange over Bitcoin

Bitcoin is designed to protect user anonymity (or pseudonymity) in a financial transaction, and has been increasingly adopted by major e- commerce websites such as Dell, PayPal and Expedia. While the anonymity of Bitcoin transactions has been extensively studied, little attention has been paid to the security of post-transaction correspondence. In a commercial ap- plication, the merchant and the user often need to engage in follow-up corre- spondence after a Bitcoin transaction is completed, e.g., to acknowledge the receipt of payment, to confirm the billing address, to arrange the product de- livery, to discuss refund and so on. Currently, such follow-up correspondence is typically done in plaintext via email with no guarantee on confidentiality. Obviously, leakage of sensitive data from the correspondence (e.g., billing ad- dress) can trivially compromise the anonymity of Bitcoin users. In this paper, we initiate the first study on how to realise end-to-end secure communica- tion between Bitcoin users in a post-transaction scenario without requiring any trusted third party or additional authentication credentials. This is an important new area that has not been covered by any IEEE or ISO/IEC se- curity standard, as none of the existing PKI-based or password-based AKE schemes are suitable for the purpose. Instead, our idea is to leverage the Bit- coin’s append-only ledger as an additional layer of authentication between previously confirmed transactions. This naturally leads to a new category of AKE protocols that bootstrap trust entirely from the block chain. We call this new category “Bitcoin-based AKE” and present two concrete protocols: one is non-interactive with no forward secrecy, while the other is interactive with additional guarantee of forward secrecy. Finally, we present proof-of-concept prototypes for both protocols with experimental results to demonstrate their practical feasibility

On the One-Per-Message Unforgeability of (EC)DSA and Its Variants

The American signature standards DSA and ECDSA, as well as their Russian and Chinese counterparts GOST 34.10 and SM2, are of utmost importance in the current security landscape. The mentioned schemes are all rooted in the Elgamal signature scheme and use a hash function and a cyclic group as building blocks. Unfortunately, authoritative security guarantees for the schemes are still due: All existing positive results on their security use aggressive idealization approaches, like the generic group model, leading to debatable overall results. In this work we conduct security analyses for a set of classic signature schemes, including the ones mentioned above, providing positive results in the following sense: If the hash function is modeled as a random oracle, and the signer issues at most one signature per message, then the schemes are unforgeable if and only if they are key-only unforgeable, where the latter security notion captures that the adversary has access to the verification key but not to sample signatures. Put differently, for the named signature schemes, in the one-signature-per-message setting the signature oracle is redundant

Increased Resilience in Threshold Cryptography: Sharing a Secret with Devices That Cannot Store Shares

Threshold cryptography has been used to secure data and control access by sharing a private cryptographic key over different devices. This means that a minimum number of these devices, the threshold $t+1$, need to be present to use the key. The benefits are increased security, because an adversary can compromise up to $t$ devices, and resilience, since any subset of $t+1$ devices is sufficient. Many personal devices are not suitable for threshold schemes, because they do not offer secure storage, which is needed to store shares of the private key. This article presents several protocols in which shares are stored in protected form (possibly externally). This makes them suitable for low-cost devices with a factory-embedded key, e.g., car keys and access cards. All protocols are verifiable through public broadcast, thus without private channels. In addition, distributed key generation does not require all devices to be present

Constructing a pairing-free certificateless proxy signature scheme from ECDSA

Proxy signature is a kind of digital signature, in which a user called original signer can delegate his signing rights to another user called proxy signer and the proxy signer can sign messages on behalf of the original signer. Certificateless proxy signature (CLPS) means proxy signature in the certificateless setting in which there exists neither the certificate management issue as in traditional PKI nor private key escrow problem as in Identity-based setting. Up to now, a number of CLPS schemes have been proposed, but some of those schemes either lack formal security analysis or turn out to be insecure and others are less efficient because of using costly operations including bilinear pairings and map-to-point hashing on elliptic curve groups. In this paper, we formalize the definition and security model of CLPS schemes. We then construct a pairing-free CLPS scheme from the standard ECDSA and prove its security in the random oracle model under the discrete semi-logarithm problem’s hardness assumption as in the provable security result of ECDSA

Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures

In an $\ell$ out of $n$ threshold scheme, $\ell$ out of $n$ members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and further used to retrieve a user\u27s secret key. We combine the notions of threshold scheme and kleptographic attack to construct the first $\ell$ out of $n$ threshold kleptographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models

Short Double- and N-Times-Authentication-Preventing Signatures from ECDSA and More

Double-authentication-preventing signatures (DAPS) are signatures designed with the aim that signing two messages with an identical first part (called address) but different second parts (called payload) allows to publicly extract the secret signing key from two such signatures. A prime application for DAPS is disincentivizing and/or penalizing the creation of two signatures on different payloads within the same address, such as penalizing double spending of transactions in Bitcoin by the loss of the double spender\u27s money. So far DAPS have been constructed from very specific signature schemes not used in practice and using existing techniques it has proved elusive to construct DAPS schemes from signatures widely used in practice. This, unfortunately, has prevented practical adoption of this interesting tool so far. In this paper we ask whether one can construct DAPS from signature schemes used in practice. We affirmatively answer this question by presenting novel techniques to generically construct provably secure DAPS from a large class of discrete logarithm based signatures. This class includes schemes like Schnorr, DSA, EdDSA, and, most interestingly for practical applications, the widely used ECDSA signature scheme. The resulting DAPS are highly efficient and the shortest among all existing DAPS schemes. They are nearly half of the size of the most efficient factoring based schemes (IACR PKC\u2717) and improve by a factor of 100 over the most efficient discrete logarithm based ones (ACM CCS\u2715). Although this efficiency comes at the cost of a reduced address space, i.e., size of keys linear in the number of addresses, we will show that this is not a limitation in practice. Moreover, we generalize DAPS to any N>2, which we denote as N-times-authentication-preventing signatures (NAPS). Finally, we also provide an integration of our ECDSA-based DAPS into the OpenSSL library and perform an extensive comparison with existing approaches

The Random Oracle Model: A Twenty-Year Retrospective

It has been roughly two decades since the random oracle model for security reductions was introduced and one decade since we first discussed the controversy that had arisen concerning its use. In this retrospective we argue that there is no evidence that the need for the random oracle assumption in a proof indicates the presence of a real-world security weakness in the corresponding protocol. We give several examples of attempts to avoid random oracles that have led to protocols that have security weaknesses that were not present in the original ones whose proofs required random oracles. We also argue that the willingness to use random oracles gives one the flexibility to modify certain protocols so as to reduce dependence on potentially vulnerable pseudorandom bit generators. Finally, we discuss a modified version of ECDSA, which we call ECDSA+, that may have better real-world security than standard ECDSA, and compare it with a modified Schnorr signature. If one is willing to use the random oracle model (and the analogous generic group model), then various security reductions are known for these two schemes. If one shuns these models, then no provable security result is known for them

Certificateless Public Key Signature Schemes from Standard Algorithms

Certificateless public key cryptography (CL-PKC) is designed to have succinct public key management without using certificates at the same time avoid the key-escrow attribute in the identity-based cryptography. However, it appears difficult to construct CL-PKC schemes from standard algorithms. Security mechanisms employing self-certified key (also known as implicit certificate) can achieve same goals. But there still lacks rigorous security definitions for implicit-certificate-based mechanisms and such type of schemes were not analyzed formally and often found vulnerable to attacks later. In this work, we first unify the security notions of these two types of mechanisms within an extended CL-PKC formulation. We then present a general key-pair generation algorithm for CL-PKC schemes and use it with the key prefixing technique to construct certificateless public key signature (CL-PKS) schemes from standard algorithms. The security of the schemes is analyzed within the new model, and it shows that the applied technique helps defeat known-attacks against existing constructions. The resulting schemes could be quickly deployed based on the existing standard algorithm implementations. They are particularly useful in the Internet of Things (IoT) to provide security services such as entity authentication, data integrity and non-repudiation because of their low computation cost, bandwidth consumption and storage requirement

Limits in the Provable Security of ECDSA Signatures

Digital Signatures are ubiquitous in modern computing. One of the most widely used digital signature schemes is ECDSA due to its use in TLS, various Blockchains such as Bitcoin and Etherum, and many other applications. Yet the formal analysis of ECDSA is comparatively sparse. In particular, all known security results for ECDSA rely on some idealized model such as the generic group model or the programmable (bijective) random oracle model. In this work, we study the question whether these strong idealized models are necessary for proving the security of ECDSA. Specifically, we focus on the programmability of ECDSA\u27s conversion function which maps an elliptic curve point into its $x$-coordinate modulo the group order. Unfortunately, our main results are negative. We establish, by means of a meta reductions, that an algebraic security reduction for ECDSA can only exist if the security reduction is allowed to program the conversion function. As a consequence, a meaningful security proof for ECDSA is unlikely to exist without strong idealization