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07-23 22:52 - 'BUY BITCOINS!' (self.Bitcoin) by /u/benger_alert removed from /r/Bitcoin within 37-47min

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BUY BITCOINS!
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07-18 23:12 - 'is bitfury Chinese? If yes then the beginning of stabbing starts!!!' by /u/benger_alert removed from /r/Bitcoin within 13-23min

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is bitfury Chinese? If yes then the beginning of stabbing starts!!!
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Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies

Cryptology ePrint Archive: Report 2019/023
Date: 2019-01-08
Author(s): Joachim Breitner, Nadia Heninger

Link to Paper


Abstract
In this paper, we compute hundreds of Bitcoin private keys and dozens of Ethereum, Ripple, SSH, and HTTPS private keys by carrying out cryptanalytic attacks against digital signatures contained in public blockchains and Internet-wide scans. The ECDSA signature algorithm requires the generation of a per-message secret nonce. This nonce must be generated perfectly uniformly, or else an attacker can exploit the nonce biases to compute the long-term signing key. We use a lattice-based algorithm for solving the hidden number problem to efficiently compute private ECDSA keys that were used with biased signature nonces due to multiple apparent implementation vulnerabilities.

References
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  6. Boneh, D., Venkatesan, R.: Hardness of computing the most significant bits of secret keys in diffie-hellman and related schemes. In: Koblitz, N. (ed.) Advances in Cryptology — CRYPTO ’96. pp. 129–142. Springer Berlin Heidelberg, Berlin, Heidelberg (1996)
  7. Bos, J.W., Halderman, J.A., Heninger, N., Moore, J., Naehrig, M., Wustrow, E.: Elliptic curve cryptography in practice. In: Christin, N., Safavi-Naini, R. (eds.) Financial Cryptography and Data Security. pp. 157–175. Springer Berlin Heidelberg, Berlin, Heidelberg (2014)
  8. Brengel, M., Rossow, C.: Identifying key leakage of bitcoin users. In: Bailey, M., Holz, T., Stamatogiannakis, M., Ioannidis, S. (eds.) Research in Attacks, Intrusions, and Defenses. pp. 623–643. Springer International Publishing, Cham (2018)
  9. Brown, D.R.L.: SEC 2: Recommended elliptic curve domain parameters. http://www.secg.org/sec2-v2.pdf (2010)
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  13. Courtois, N.T., Emirdag, P., Valsorda, F.: Private key recovery combination attacks: On extreme fragility of popular bitcoin key management, wallet and cold storage solutions in presence of poor rng events. Cryptology ePrint Archive, Report 2014/848 (2014), https://eprint.iacr.org/2014/848
  14. Dall, F., De Micheli, G., Eisenbarth, T., Genkin, D., Heninger, N., Moghimi, A., Yarom, Y.: Cachequote: Efficiently recovering long-term secrets of SGX EPID via cache attacks. IACR Transactions on Cryptographic Hardware and Embedded Systems 2018(2), 171–191 (May 2018). https://doi.org/10.13154/tches.v2018.i2.171-191, https://tches.iacr.org/index.php/TCHES/article/view/879
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Compact Multi-Signatures for Smaller Blockchains

Cryptology ePrint Archive: Report 2018/483
Date: 2018-06-10
Author(s): Dan Boneh, Manu Drijvers, Gregory Neven

Link to Paper


Abstract
We construct new multi-signature schemes that provide new functionality. Our schemes are designed to reduce the size of the Bitcoin blockchain, but are useful in many other settings where multi-signatures are needed. All our constructions support both signature compression and public-key aggregation. Hence, to verify that a number of parties signed a common message m, the verifier only needs a short multi-signature, a short aggregation of their public keys, and the message m. We give new constructions that are derived from Schnorr signatures and from BLS signatures. Our constructions are in the plain public key model, meaning that users do not need to prove knowledge or possession of their secret key.
In addition, we construct the first short accountable-subgroup multi-signature (ASM) scheme. An ASM scheme enables any subset S of a set of n parties to sign a message m so that a valid signature discloses which subset generated the signature (hence the subset S is accountable for signing m). We construct the first ASM scheme where signature size is only O(k) bits over the description of S, where k is the security parameter. Similarly, the aggregate public key is only O(k) bits, independent of n. The signing process is non-interactive. Our ASM scheme is very practical and well suited for compressing the data needed to spend funds from a t-of-n Multisig Bitcoin address, for any (polynomial size) t and n.

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