(PDF) Weighted threshold ECDSA for securing bitcoin wallet

A Formal Treatment of Hardware Wallets

Cryptology ePrint Archive: Report 2019/034
Date: 2019-01-14
Author(s): Myrto Arapinis, Andriana Gkaniatsou, Dimitris Karakostas, Aggelos Kiayias

Link to Paper

Bitcoin, being the most successful cryptocurrency, has been repeatedly attacked with many users losing their funds. The industry's response to securing the user's assets is to offer tamper-resistant hardware wallets. Although such wallets are considered to be the most secure means for managing an account, no formal attempt has been previously done to identify, model and formally verify their properties. This paper provides the first formal model of the Bitcoin hardware wallet operations. We identify the properties and security parameters of a Bitcoin wallet and formally define them in the Universal Composition (UC) Framework. We present a modular treatment of a hardware wallet ecosystem, by realizing the wallet functionality in a hybrid setting defined by a set of protocols. This approach allows us to capture in detail the wallet's components, their interaction and the potential threats. We deduce the wallet's security by proving that it is secure under common cryptographic assumptions, provided that there is no deviation in the protocol execution. Finally, we define the attacks that are successful under a protocol deviation, and analyze the security of commercially available wallets.

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Currently Bitcoin uses secp256k1 with the ECDSA algorithm, though the same curve with the same public/private keys can be used in some other algorithms such as Schnorr. secp256k1 was almost never used before Bitcoin became popular, but it is now gaining in popularity due to its several nice properties. Bitcoin uses the ECDSA algorithm to produce the above-mentioned keys. The purpose of our work is to present some useful motifs for the domain parameters of base point (P) and the order (n) of the subgroup produced by it, while choosing the elliptic curve and the Galois field on which we formulate the algorithm, in order to obtain safer private ... Secp256k1 refers to ECDSA parameters of the curve used in Bitcoin and is defined in Standards for Efficiency Cryptography (SEC) [6]. Secp256k1 has almost never been used before Bitcoin became popular, Python ECDSA has deployed RFC 6979 instead of generating a random number since September 9, 2013 6 Bitcoin Knots is a derivative of Bitcoin Core, which also generates the number k with nonce_function_rfc6979(). 7 Bitcoinjs-lib, a pure JavaScript Bitcoin library for node.js and browsers, also has deployed RFC 6979 by deterministicGenerateK ... The Bitcoin system’s signature algorithm is based on elliptic curves , and their scheme is to prevent double-spending attacks through ECDSA signature vulnerabilities . That is, if the signature uses the same random number twice, the private key of the signature will be exposed.

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