ECDSA Private Keys Study of Security

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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submitted by dj-gutz to myrXiv [link] [comments]

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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. Most commonly-used curves have a random structure, but secp256k1 was constructed in a ... ECDSA Security in Bitcoin and Ethereum: a Research Survey Hartwig Mayer {hartwig.mayer} CoinFabrik Revised June 28, 2016 Abstract ... Bitcoin security draws more and more attention recently. One of Bitcoin vulnerabilities is caused by ECDSA weak randomness. A random number is not cryptographically secure, which leads to private key leakage and even fund theft. This security problem has been well known in Bitcoin community and fixed by applying RFC 6979 update in 2013. Secondly, we describe how the ECDSA is used in Bitcoin technology. Bitcoin is a type of crypto-currency that has been in existence since 2009. It was introduced by Satoshi Nakamoto (possibly a pseudonym) in their much cited paper [8]. Its design and distribution is not controlled by any central organization. Despite this, Bitcoin has de ed all odds to become a phenomenal currency widely ... 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 ...

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