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[89.247.102.137]) by smtp.googlemail.com with ESMTPSA id i16sm4038060wmd.28.2018.11.28.08.43.12 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 28 Nov 2018 08:43:13 -0800 (PST) From: Jonas Nick X-Google-Original-From: Jonas Nick To: Anthony Towns , Bitcoin Protocol Discussion References: <20181128104946.bftgbclno6gzzji4@erisian.com.au> Openpgp: preference=signencrypt Autocrypt: addr=jonasd.nick@gmail.com; prefer-encrypt=mutual; keydata= xsFNBFQ2o3oBEACv5N5WajlYk+i/4B8FmniipCB4biIKg38spMNt1EYM6RzTu+hbOrVOlJW8 fq/ih+dvlpreGxRPQlX4jr75kwoJCykd3geywTUl3KPLeJ/JRQJ8fVkine4Wr5qB5Jwo3+wt inDVooaaF32Y0HolNacXVzT1x9uwn83Bz/ifg+iGATn/e1Si3ga/ytY5wYDzFz6aUDRW8ulu DcG8ARMAgtzmi66EuyQyIWwSyoWFU8wJ98slU9LKuTu23r6HdxFuV+P2H1omJm+z8cd4QBMj I23uHst0Wx1MyTeVhZCnQAghyasA3oopwzqRf5wwECAui1oZhr59R4R1DHJjn0PeWZXBSnOo XPQ1ERjz4nQrODiIDEabD5DClPHZ1bte0tswm1aYBtD8/me9ck+SJdoH5r0DJrXCTtNl1XG1 9TTUINQe0eaQUOTakZmVaneCeSrw/pKOknkzudOCNCbmngKa2oJQOynrdsBuoigIYY+NQdot fk1nJljrBzyTh4sFktbHyA24x/hCykMX6FnIQxDnsGR+S3I+vzADBLBBMQQtZsUA+xnvPu4l 6You5SZMVhgprQy38bKybeIGxSZtmPNtBf8ouKhAUpbIfOaq6BoP4EtueXk/vyieFxXiIkbF N6b3pjhkG7wVG17HqCqeVeHz1ZAQJUPcqDQAPaelBf38RXPbeQARAQABzSJKb25hcyBOaWNr IDxqb25hc2Qubmlja0BnbWFpbC5jb20+wsF/BBMBAgApAhsDBwsJCAcDAgEGFQgCCQoLBBYC AwECHgECF4AFAlu1I0QFCQtA5soACgkQsacOT43NA2Y5zA/9G1kt1ECa6zPhpEBV5iqD1omt ABdrZSxD8gBsZOMt2nLE1f4J0Oqy9LfMzKFzC8Kyd7usu6HVA8XM3fjVgqi+cDlEhaE+RqFi FVJjai7Fo1EqQGoD8QKTHDpGMNAmkfiQI7yc7OOxJ7X/nRpI8EnUsHG0slw3ieG6krrwLMfi rdJz5xA3P0tjdz/gRsG1IkwaB1bWnrIyh4oS9MiTSO1GZzHdRrhYZPFnJa7XiQsDWTvtTf4o fkbDAxqsKSqJhh99Gl79dXjJ1X9c6YfmxdOWuHZwtpJRgTFXSavaojkjPdnx4/f8lsgQg0tI BEaZnfroAvJCkYCqxNAPS5pSCaRaZbm+eoBl9848eFQztds/xfG3xIpn6VaOSdDNCD0+kSiO LrqghKLN3nPWOfCU0zPlkFuNsWX0ALvAJj6UKGbvMRfR6uj5NPZuHbA2FK9/1pOfKLjm6bHI 2HtXeS5B0+eoAjHzoF9w/2DM4+DLU8Qbn63CpDZ3dodqK3Z7PHLv9oiiCVUFxia0J9YUZJru 1jFHc3BA/Ado4LSxjyUbG0kDQjddvBEmQIkW5c2VrkczYv8gCOLwiUF+RPqc8PxGRs5I5SqJ RzcEN9nIaFcP5MTPrabbkXKLw6ZhHqc3J85qMOLoxThP5SCWM7I1SwLYIGgcWGFtL27U9IXe /wzNH4aerKfOwU0EWVEx3gEQAMH7dVvWR+idYEe3OVDY/SVV80wjfOe1zTDTOQ+qB8D5Fin8 7v3Rpt8y0RxW3Y4Fbljoi635jhJo3/MoTHvZSes61LbnPzUjReYmIqMYprJ5HSF+IkskW9E5 P078G6wI2hxwjRXXg4y+Z+oYk3C8GBH1Ejjs2i3lmYIPACMUKDba26ZIuxkjK5OB3tZHmTOu YRJ9eP5KltSD4P6Y6ZTgDlvUpQeJa0w52A4dOQARmyKDiGJ5z+x8gSeCK3IrYWyt79et364R SWZG4pFj34fnHIcHPebwOMX6gMZdPIyKNxaTwA62gnQp5loJoJJUTsgSTSOW1Dzvjjxm/4iW M2HlS6NT0f80fSw1GnfIxSSPrx2F4Iwg8ckAWzy/EYcGr7+pHJ28AVVN4q0EG/9WvTsL9iM9 Zqbw9cI9faDTDuJfYtcxIorMgkmDF4u14GFdzSsx5loTO+/7VFZhFDLLCC1eHCzOvLjHFg+9 XpR0N7eArpDiYBWPFWBVthHtb6JuXqAWyZ+0LZZw2JGM4/gzUdFr+1FznJX1MqtlwtrAggM4 xrPlnIf4qwL6B074tr00vzr4YIzl0FUGti9Qx+xozqeO2NmKltXmfBYfBJZdnfanVHp8XMDS +z7CVKCzMkmnuyJ0QrY0jJVAxOvlwLQy363Nk5pRprrHna2R2+ZsTqf8Cw3dABEBAAHCwXwE GAEIACYWIQQ2xxo3ydmIveglCNmxpw5Pjc0DZgUCWVEx3gIbDAUJA8JnAAAKCRCxpw5Pjc0D ZgeWEACfP52WfyPUWMg8mZax834TW/RGBaUi9KQZc0tRX8lDrsD42aunTF+8va8t4/vw4Cfy kloL+5mcz9orWzp+9YVO98U0O2s76zDTxBIJC5pp8ZRoqCZbRhD2w7DBNxgazeChCmsSmADn /3ktkAztTI99I/xa/i7/PhVKn/MQJZ/vzFOwdvxaVar8W7jsWnzw43DFMVIVyWrwXeBaKVFe vBwvnltvbmNyvx8L+3W0dPP4biVsCbT6Fteki++c3XoAooCut7ld9wP0oNiYUUFMSd2rEErd QHPnaTGil/KAO2BMQEbcCXbDX7L9PX6rjonPwQIbaP3zNbuRfZj8LRKzz7ih+gOJRMPGGYX1 eMUVXwoi8EQeofLM7wmOQikXlDbVR0a3+kKj/g6yKsBFvRbtSx73DeLg2Zp4EodoUnF/0W3V JqZCWeI794kfk6NFvKKn1GLfxdyj82wiqzzCNFnYe6H4l78kGCZ7E0yg0u0M0kCjtDfBlxHJ r1FDbWf3e4yX76QwxsQwR5yiY9mpWWo6Z6XFDT2Jz6HQX7y9oJhV/cLyAMzVz3Y7BSLm9tX5 /pX1TjOC7jsEBBPYFk1XyLQ+Ip6ZT0TZx7nXNoF08GhTXFLLx7tSNzx1IE+Go0FXcA0vmYUy Ex981QeJInExpznDYCvx7pHU1PzImXcSLzWzqR8Anw== Message-ID: Date: Wed, 28 Nov 2018 16:43:12 +0000 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Thunderbird/60.3.1 MIME-Version: 1.0 In-Reply-To: <20181128104946.bftgbclno6gzzji4@erisian.com.au> Content-Type: text/plain; charset=utf-8 Content-Language: en-US-large Content-Transfer-Encoding: 8bit X-Spam-Status: No, score=-2.0 required=5.0 tests=BAYES_00,DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, FREEMAIL_FROM, RCVD_IN_DNSWL_NONE autolearn=ham version=3.3.1 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on smtp1.linux-foundation.org X-Mailman-Approved-At: Wed, 28 Nov 2018 23:33:04 +0000 Subject: Re: [bitcoin-dev] Multi party Schnorr Rust implementation X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 28 Nov 2018 16:43:17 -0000 > For deterministic nonces, you generate r=H(p,m) based on the message > being signed and your private key, so can only start this process when > you start signing, and the sharing rounds mean interactivity. It's not your point but it should be noted that this is not secure unless all other signers give you zero knowledge proof that they've generated their nonce in the same way. Otherwise, if your asked to sign the same message you'll use the same nonce for two different challenges. In your example you'd compute s=r+H(R',P',m)*p and s'=r+H(R'',P',m)*p from which an observer can compute the secret key p. On 11/28/18 10:49 AM, Anthony Towns via bitcoin-dev wrote: > On Tue, Nov 27, 2018 at 10:33:30PM -0800, Devrandom via bitcoin-dev wrote: >> Are there any candidates for non-interactive threshold signatures?  Interactive >> signatures are not very suitable for air-gapped use cases. > > I think you can work around this to some extent by "batching" signing > requests. > > (Background: > > For interactive multisignatures (threshold or not), the protocol is: > > produce secret nonce r, calculate public nonce R=r*G > everyone shares H(R) > everyone shares R, checks received values match received hashes > everyone calculates s=r+H(R',P',m)*p, shares s > > For deterministic nonces, you generate r=H(p,m) based on the message > being signed and your private key, so can only start this process when > you start signing, and the sharing rounds mean interactivity. > > ) > > But you don't strictly need deterministic nonces, you just have to never > use the same nonce with a different message. If you arrange to do that > by keeping some state instead, you can calculate nonces in advance: > > phase 1: > produce secret nonces r1..r1024, calculate R1..R1024 > share H(R1)..H(R1024) > > phase 2: > store other parties hashes, eg as H1..H1024 > share R1..R1024 > > phase 3: > check received nonces match, ie H(R1)=H1, etc > > phase 4: > request to sign msg m, with nonce n > if nonce n has already been used, abort > mark nonce n as having being used > lookup other signer's nonces n and sum them to get R' > calculate s = rn + H(R',P',m)*p > share s > > That way you could do phases 1-3 once, and then do 1024 signatures during > the month on whatever your current timetable is. > > You could also combine these phases, so when you get a signing request you: > > * receive msg to sign m, n=4; everyone else's R4, H(R5) > > * check H(R4) = previously received "H(R4)" > * calculate R4' by summing up your and everyone's R4s > * bump state to n=5 > * do the signature... > > * send sig=(s,R4), R5, H(R6) > > which would let you have an untrusted app that does the coordination and > shares the nonces and nonce-hashes, and getting all the needed air-gapped > communication in a single round. (This is effectively doing phase 3 and > 4 for the current signature, phase 2 for the next signature, and phase > 1 for the signature after that all in one round of communication) > > That seems almost as good as true non-interactivity to me, if your signing > hardware is capable of securely storing (and updating) a few kB of state > (which is probably not quite as easy as it sounds). > > Cheers, > aj > > _______________________________________________ > bitcoin-dev mailing list > bitcoin-dev@lists.linuxfoundation.org > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev >