From mboxrd@z Thu Jan 1 00:00:00 1970 Delivery-date: Fri, 04 Apr 2025 09:34:43 -0700 Received: from mail-oi1-f186.google.com ([209.85.167.186]) by mail.fairlystable.org with esmtps (TLS1.3) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (Exim 4.94.2) (envelope-from ) id 1u0k0A-0002wu-2v for bitcoindev@gnusha.org; Fri, 04 Apr 2025 09:34:43 -0700 Received: by mail-oi1-f186.google.com with SMTP id 5614622812f47-3fab1478893sf593981b6e.2 for ; Fri, 04 Apr 2025 09:34:42 -0700 (PDT) ARC-Seal: i=2; a=rsa-sha256; t=1743784476; cv=pass; d=google.com; s=arc-20240605; b=cyE/u/0MCI+aOFoB8dcVvkG/A8wE11Xi6c2U4dAG8MH02xgbwbAct8ngMHsYaR1for 67IIxvr0srxF6ViYSf0XrP6Kj78B676xkl3NMZLsDQpDbW/EoAFfxtddEXRHdGI0+Vwm I5Qc8n+eaIgIk95yRTyOt5NkuA//YmpiV1UF2UedWTzNNGoSh9WOxfJhKb27pxW8jASM w4uDdUVZaaquNioMiXLL5RkBZQtOVj0bsGQEirC8UuekpQa0g47rJUlpx8i6ZmhdeGgq QZwwp8zc17yRR56uiok6dIgAapNSWroRAAeD3JAnQv6vccRmW6TJxk7UNFStBRw0Bieg 216w== ARC-Message-Signature: i=2; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20240605; h=list-unsubscribe:list-subscribe:list-archive:list-help:list-post :list-id:mailing-list:precedence:content-transfer-encoding:to :subject:message-id:date:from:mime-version:sender:dkim-signature :dkim-signature; bh=UHt/ru/4xE27oDrHSmtbY1S8C2DRcZZMO0geH1h9/0k=; fh=Hc8uL8m6NW9bZgKqTlSAL7RCSoHDwtRJ0m0PYqC5EH8=; b=jPfqt5o06wp9EgFyqWR5mqPtMCWZKP7BdapxS1vP7Z6mO7f4R681SRgVHooSzcsIl4 z/4DeYd+vm9Cfx1orsbgq2/wz9uPWof7pWxBSaFvU4BqMGQ5hhth21sFoc7iHKQI9Xcv wqjGo4PPIpc2bS0QI3Z41kH4ygEP/M5Jrf822wCjTZHyWQpQUjGyStPJPyUiXP2X9+Gh D1RWiLIfbMJ0J2fdLG7RzDYCryY2+gu14lKZBpBDgDi3AJOn5H0BonTJJeQ77U1AMNwI QmRTs+fOMP9zY0OCLRYqQW/g43dhMDwC44/HRnsrrQR6o3L2mTJghEfym6PIOTharow1 QvuQ==; darn=gnusha.org ARC-Authentication-Results: i=2; gmr-mx.google.com; dkim=pass header.i=@gmail.com header.s=20230601 header.b=Tbzh9gKm; spf=pass (google.com: domain of eth3rs@gmail.com designates 2a00:1450:4864:20::52d as permitted sender) smtp.mailfrom=eth3rs@gmail.com; dmarc=pass (p=NONE sp=QUARANTINE dis=NONE) header.from=gmail.com; dara=pass header.i=@googlegroups.com DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20230601; t=1743784476; x=1744389276; darn=gnusha.org; h=list-unsubscribe:list-subscribe:list-archive:list-help:list-post :list-id:mailing-list:precedence:x-original-authentication-results :x-original-sender:content-transfer-encoding:to:subject:message-id :date:from:mime-version:sender:from:to:cc:subject:date:message-id :reply-to; bh=UHt/ru/4xE27oDrHSmtbY1S8C2DRcZZMO0geH1h9/0k=; b=b8Xf/O6tlvF+UM4KL2xEdXYoDXI4TNiiHaNbIjk9Rsd+6W6iz8oKWfeNh1lK291v95 xAvUBP1MUL2N8M04UVlEufPQse4m4kA0oopjRpQQ2QwlHz8cwg0Z+oe2vwWnk3pVOhlS ZuLnMT03q/BxkIsDRlcoyITS8DnoaE7/hSY0BgeSoPNiflN9L3mTB/TNQxV2x1Oyrd/D mN68ZrZ9HOy7rfupIZmOgpyzF6Khqr4itumqnyWgKffe9painpjjfxAVDoEbbuaOPZl3 vbBRylIvSwseNs8jwhDCo6xWTUvNbQhxG+zLXZm6h8nN5XO2ULWm6XlNVNKad4ArawL3 6e6Q== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20230601; t=1743784476; x=1744389276; darn=gnusha.org; h=list-unsubscribe:list-subscribe:list-archive:list-help:list-post :list-id:mailing-list:precedence:x-original-authentication-results :x-original-sender:content-transfer-encoding:to:subject:message-id :date:from:mime-version:from:to:cc:subject:date:message-id:reply-to; bh=UHt/ru/4xE27oDrHSmtbY1S8C2DRcZZMO0geH1h9/0k=; b=biuuLHFfLJo8cBrwAzj+KFk7uWQ8lcvLdEWINakrxlU+LW9OaVBfq54xtcLKgssDCY P1/M8c2D3oLi0mYdtjkO30DU1LISTqrcxZ5yJeU0WBQB+rPI5jcQ5/q0P6VTlMW6AHFU Uzi5r+C/hZgJv6VCwgCqcfF4Lv70cz1keMGUpVZ1uJ7idxPFXUsmy+wxZrUEOKuabL92 Gzsk/62chgeHlJ6HBeN3BBzVTTEpr1qtA5YyHC98m2eKxZojPPWs+CWXCRLnUzZJknVW vZ6fqfHmK9zriuoO6woRTV5Au+Ovk8ZIrzK0Bx0Hso6z74OrB/PzzOAXFM7hb+DhwEx5 CZdg== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20230601; t=1743784476; x=1744389276; h=list-unsubscribe:list-subscribe:list-archive:list-help:list-post :list-id:mailing-list:precedence:x-original-authentication-results :x-original-sender:content-transfer-encoding:to:subject:message-id :date:from:mime-version:x-beenthere:x-gm-message-state:sender:from :to:cc:subject:date:message-id:reply-to; bh=UHt/ru/4xE27oDrHSmtbY1S8C2DRcZZMO0geH1h9/0k=; b=aZNoT5noYrgxIZE44jwvuptbD9z7RHinghzkVlRfa3MP7UWYxMshBpsqr7nJPz7qQx vJbTSMOvo5tBL+xTJM17E8+Pag/Ue6yT5093hvf1YeuwBnsEwaw6wvgA6LSOJRzH6Kmk ROPSQSHd85wL93kxrWqSUBucaFf3LEXRxmXCzwFMjSViaXWU9HYUNq0GHHnZmXYhuaDP 9tyDFhf9wenD0hsJWsgfU1c1VOUQsDQuKflmdiH1OrbfsrKLu3lvRglg2sOBJHzYpFUz acH1S8IKZX83Ix4YvNVX3uyVgtq718WCFi3RYrMD2P1cMFzbEZRQn38h13+cpFO0TkLp iOBw== Sender: bitcoindev@googlegroups.com X-Forwarded-Encrypted: i=2; AJvYcCVuRvTzWRvxH+bdXO9F4RlRTGSzr3K7uTAIsB9qhbGCg0R5VrZoiQmTaO5ypetavnL9E+ODv1SsO7Z6@gnusha.org X-Gm-Message-State: AOJu0Yxigs/8R3JFysYMdU9WwTn/QrC/t6dSaKNrBE/fUAnZSjx2l5Th bH1Rf7UIBa+V+A6rNbYC+JeCbkhtwrUMaM0lAhfR/728z0XLcZot X-Google-Smtp-Source: AGHT+IFMmmdx9OhDd945JQunUNxNfvKkhbyfuDzYd4VJsiBy731A/esf3ltmniaVB9ktvlGO2VZFbw== X-Received: by 2002:a05:6808:6a96:b0:3fb:7114:4ba7 with SMTP id 5614622812f47-4004562003dmr2263969b6e.25.1743784476014; Fri, 04 Apr 2025 09:34:36 -0700 (PDT) X-BeenThere: bitcoindev@googlegroups.com; h=ARLLPAJbyPx2U2KIduA1OFLqedv/cILoxyLRHXP2tf6OQFhmgw== Received: by 2002:a4a:e904:0:b0:602:40ed:5c6f with SMTP id 006d021491bc7-60409e7069dls603214eaf.0.-pod-prod-06-us; Fri, 04 Apr 2025 09:34:32 -0700 (PDT) X-Received: by 2002:a05:6808:3989:b0:3f9:aeb6:6eac with SMTP id 5614622812f47-40045620058mr2545655b6e.30.1743784472372; Fri, 04 Apr 2025 09:34:32 -0700 (PDT) Received: by 2002:a05:600c:1c8e:b0:43d:85ca:231a with SMTP id 5b1f17b1804b1-43eb34435d3ms5e9; Fri, 4 Apr 2025 09:30:25 -0700 (PDT) X-Received: by 2002:a05:600c:450d:b0:439:6118:c188 with SMTP id 5b1f17b1804b1-43ed0c6e894mr35410095e9.19.1743784223810; Fri, 04 Apr 2025 09:30:23 -0700 (PDT) ARC-Seal: i=1; a=rsa-sha256; t=1743784223; cv=none; d=google.com; s=arc-20240605; b=MtnY8HsXXsEJVR3Bw3HhzMeYiJlSfobP0Sa1aKpeHh5ng/RSfMpgsWcjrlxqQ1AX30 AmKAd6IebBKXyx5/yvVd4VlAhpCjWZQ2uiHSgOwkFU6lX0Jvv9iMmQLWgdUvGgm445Vf hM40ttsER3eJIt84K4d1nbzuN3NBosC2C5JVZqALXXEj6K2W6UdY8BXrz47+z7SE2dys +S/GP6r9Gb/lndWImd5ozXGfwj4xRBou5lMe+MqhtwlbmJR8b/6BvA4Ujoed8zc7pfZv v1O8+BKKw3kK0mYsL9mMpZqKPY8zbuI4jXBELZSgzAAwU5fnqqwqbLD1JFCnPpxT3IWp Hd2w== ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20240605; h=content-transfer-encoding:to:subject:message-id:date:from :mime-version:dkim-signature; bh=ycS484WHqyAQcdS80E4ZFGI3VJaOhDgqveSoiGnDt/k=; fh=DMP0F9ULS1guKiqimntQRCN8ZraraesEgQuVcn7F0Z0=; b=Nrn/IOBvKQFdHe4eW4b1vAcbwMFoJ1QGqtKqGVj95YRVS72jSNSGE1vn2vOuNj1gI1 Zvw/wuF9ctQm4htbjHo6iWMtD3mCvgKTNLRdq8MPDHzHGwSd/WEkldm1UwExFCqwsEWA m9/v/UO2MqEYQwv3bYbobUFOW2HACQdATFKnlUf+ksOEggxG87uWogDFvVlNfBZsd20F kuS9j3KA0bGsBoh+UKJKmX8I34u2aLbuXOY1wc1P/ZsoLcJxtyhppaPJKfKQWn2svUEe cTBJnx3EKXq5uPysNbfIvCh1bFyIwVNxVHkpRUsMkw3nJbwg18EMV4rQ3Z1IzjPiMpR0 Tp1g==; dara=google.com ARC-Authentication-Results: i=1; gmr-mx.google.com; dkim=pass header.i=@gmail.com header.s=20230601 header.b=Tbzh9gKm; spf=pass (google.com: domain of eth3rs@gmail.com designates 2a00:1450:4864:20::52d as permitted sender) smtp.mailfrom=eth3rs@gmail.com; dmarc=pass (p=NONE sp=QUARANTINE dis=NONE) header.from=gmail.com; dara=pass header.i=@googlegroups.com Received: from mail-ed1-x52d.google.com (mail-ed1-x52d.google.com. [2a00:1450:4864:20::52d]) by gmr-mx.google.com with ESMTPS id 5b1f17b1804b1-43ea97959f7si6709335e9.1.2025.04.04.09.30.23 for (version=TLS1_3 cipher=TLS_AES_128_GCM_SHA256 bits=128/128); Fri, 04 Apr 2025 09:30:23 -0700 (PDT) Received-SPF: pass (google.com: domain of eth3rs@gmail.com designates 2a00:1450:4864:20::52d as permitted sender) client-ip=2a00:1450:4864:20::52d; Received: by mail-ed1-x52d.google.com with SMTP id 4fb4d7f45d1cf-5e5c9662131so3632690a12.3 for ; Fri, 04 Apr 2025 09:30:23 -0700 (PDT) X-Gm-Gg: ASbGncsCfgPKZ9JAw1XG91I4Jz7/+6RrwTEkwYSHeZJfrhkW7c1RrX2oT6FY5faeV9S UbNusHUMo1l52okdvSN0Rt6f4H5wBkN005DBnlF7XVMWgVtuAE8GC6RCdUXAlh718XIOS2O5+dQ mO+K4MqEe3wX3KpXqEN8Hh1et14oE= X-Received: by 2002:a17:907:3e10:b0:ac3:8790:ce75 with SMTP id a640c23a62f3a-ac7d6cbd72bmr312830966b.10.1743784222758; Fri, 04 Apr 2025 09:30:22 -0700 (PDT) MIME-Version: 1.0 From: Ethan Heilman Date: Fri, 4 Apr 2025 12:29:46 -0400 X-Gm-Features: ATxdqUFX8GEo2aDHYpM_T81yVkwXSV3DSd11guvPY7fSwP6YEtkD9fwmBdbc83I Message-ID: Subject: [bitcoindev] Post Quantum Signatures and Scaling Bitcoin To: Bitcoin Development Mailing List Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Original-Sender: eth3rs@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; dkim=pass header.i=@gmail.com header.s=20230601 header.b=Tbzh9gKm; spf=pass (google.com: domain of eth3rs@gmail.com designates 2a00:1450:4864:20::52d as permitted sender) smtp.mailfrom=eth3rs@gmail.com; dmarc=pass (p=NONE sp=QUARANTINE dis=NONE) header.from=gmail.com; dara=pass header.i=@googlegroups.com Precedence: list Mailing-list: list bitcoindev@googlegroups.com; contact bitcoindev+owners@googlegroups.com List-ID: X-Google-Group-Id: 786775582512 List-Post: , List-Help: , List-Archive: , List-Unsubscribe: , X-Spam-Score: -0.5 (/) I strongly believe Bitcoin will need to move to PQ signatures in the near future. The rest of this email is premised on this belief. PQ (Post Quantum) signatures present a problem for Bitcoin: First, they are large. Of the three proposed in BIP-360 [0], the smallest is 1.5kb for the public key + signature [1]. Without a discount this represents a massive reduction in Bitcoin's transaction volume due to the increase in transaction size of Bitcoin payment using such signatures. - Second, even if we discount PQ signatures and public keys so that the maximum number of transactions that can fit in a block is unchanged we still have the problem that these blocks and transactions will be an order of magnitude bigger. If it is the case that we can handle these extra bytes without degrading performance or decentralization, then consider the head room we are giving up that could be used for scalability. Beyond this there is also the risk that techniques could be developed to encode JPEGs and other data in these discounted PQ signatures or public keys. BIP-360 takes steps to make an abuse of this discount more difficult by requiring that a PQ signature and public key can only be written to the blockchain if they verify. We do not need PQ Signatures to be completely =E2=80=9CJPEG resistant=E2=80=9D, they just nee= d PQ signatures to not enable significantly cheaper storage than payments. The degree to which the proposed PQ signature algorithms resist being repurposed as a storage mechanism is an open question and worth investigating. If it turned out PQ signatures could be used to encode data very cheaply, then Bitcoin faces the dilemma that if you discount PQ signatures, you make the JPEG problem worse and may price out the payment use case. If you don't discount PQ, you price out most people from sending payments in Bitcoin since non-PQ witness data can be used for storage I want to draw the community's attention to a solution that could not only address these problems but also increase Bitcoin=E2=80=99s scalability (and privacy): Non-interactive Transaction Compression (NTC) for Transactions supporting PQ signatures. This is sometimes called Non-Interactive Witness Aggregation (NIWA) [2]. This would require a new transaction type supporting PQ signatures. The miner of a block would then pull out the signatures and hash pointers from transactions to compress transaction data and non-interactively aggregate all the PQ signatures in all the transactions in a block, replacing them with one big STARK (STARKS are a form of SNARK which is PQ). This would make PQ signatures significantly smaller and cheaper than ECDSA and schnorr signatures. Consider the following back of the envelope math: 2 bytes per Input =3D 2 bytes per TXID, 0 bytes per signature 37 bytes per output =3D 32 bytes pubkey hash + 5 bytes value (max 2.8m BTC per output) 1-input-2-output transaction would be: 2 + 2*37 =3D 76 bytes (4,000,000/76)/(60*10) =3D ~87 txns/sec You could shave some bytes off the value, or add some bytes to the TXID. [3] provides a more detailed estimate, proposing 113.5 weight units (WU) for a 1-input-2-output transaction with no address reuse. However it does not consider TXID compression. If desired an account-based model could push this even further to 12 bytes per transaction per block [4]. This would enable approximately 4,000,000/(12*60*10) =3D 555 txns/second. A secondary benefit of having on-chain PQ payments only be ~76 bytes in size is that it fundamentally changes the pricing relationship between payments and on-chain JPEG/complex contracts. The problem with on-chain JPEGs is not that they are possible, but that they are price competitive with payments. At ~76 bytes per payment or better yet ~76 bytes per LN channel open/close, JPEGs no longer present the same fee competition to payments as payments become much cheaper. Such a system would present scaling issues for the mempool because prior to aggregation and compression, these transactions would be 2kb to 100kb in size and there would be a lot more of them. It is likely parties producing large numbers of transactions would want to pre-aggregate and compress them in one big many input, many output transactions. Aggregating prior to the miner may have privacy benefits but also scalability benefits as it would enable cut-throughs and very cheap consolidation transactions. ~87/txns a second does not include these additional scalability benefits. Consider an exchange that receives and sends a large number of transactions. For instance between block confirmations customers send the exchange 10 1-input-2-output transactions in deposits and the exchange sends out 10 1-input-2-output transactions in withdrawals. The exchange could consolidate all of the outputs paying the exchange, including chain outputs, into one output and do the same for inputs. This would reduce not just size, but also validation costs. (10 * 2 + 20 * 2 * 37) + (10 * 2 + 20 * 2 * 37) =3D 3000 bytes becomes (10 * 2 + 11 * 2 * 37) + (2 + 11 * 2 * 37) =3D 1650 bytes If constructing these proofs turned out to be as expensive as performing POW, it would make block generation not progress free. Essentially you'd have a two step POW: proof generation and then the actual POW. Such a scenario would be very bad and cause the biggest miner to always be the one that generates blocks. A critical assumption I am making is that such proof generation is not particularly expensive in the scheme of POW. I am optimistic that proof generation will not be this expensive for two reasons There are PQ signature schemes which support non-interactive aggregation such as LaBRADOR [5]. Thus, the STARK wouldn=E2=80=99t need to perform the block-wide signature aggregation and would only need to perform transaction compression, cut throughs and consolidation. We could make use of recursive STARKs [8] to allow miners to parallelize proof generation to reduce latency or to decentralize proof generation. Users creating transactions could perform non-interactive coinjoins with other users or settlement/batching. This would not only take proof generation pressure off of the miners and reduce the strain on the mempool but in some circumstances it would provide privacy if used with payjoin techniques like receiver side payment batching [7]. The approach we are proposing treats the STARK the miner produces as free from a blocksize perspective. This is important for bootstrapping because it means that fees are significantly cheaper for a transaction, even if it is the only compressed transaction in the block. This encourages adoption. Adoption helps address the chicken and egg problem of wallets and exchanges not investing engineering resources to support a new transaction type if no one is using it and no one wants to use it because it isn't well supported. By having a single format, built into the block we both accelerate the switch over and prevent a fragmented ecosystem that might arise from doing this in Bitcoin script. Fragmentation reduces the scalability benefits because validators have to validate multiple STARKs and reduces the privacy benefits because there are many coinjoins, rather than each being a coinjoin. Even if our approach here turns out to be infeasible, we need a way to reduce the size of PQ signatures in Bitcoin. The ability to move coins, including the ability to move coins that represent JPEGs, is the main functionality of Bitcoin. If we make storage/JPEG too price competitive with the ability to transfer coins, we destroy that essential functionality and decrease the utility of Bitcoin for everyone. Currently moving coins securely requires at least one 64 byte signature, which is an unfortunate tax on this most vital of all use cases. I believe removing that tax with signature aggregation will be beneficial for all parties. Consider the world of PQ signatures in Bitcoin without STARKs: - The large size of PQ signatures will make it more expensive for users to use them prior to the invention of a CRQC (Cryptographically Relevant Quantum Computer). This means that most outputs will not be protected by PQ signatures. Once a CRQC arises there will be a rush to move funds under the protection of PQ signatures but due to the large size of PQ signatures the fees will be too expensive for most outputs. Users will instead need to move their funds to centralized custodial wallets that can use a small number of outputs. In such a world it will be much harder and expensive to self-custody. - Without a solution here the large sizes of PQ signatures will limit Bitcoin's functionality to move coins using on-chain payments. This will also favor centralized custodians and erode the decentralized nature of Bitcoin. None of this is an argument against adopting BIP-360 or other PQ signatures schemes into Bitcoin. On the contrary, having PQ signatures in Bitcoin would be a useful stepping stone to PQ transaction compression since it would allow us to gain agreement on which PQ signature schemes to build on. Most importantly, in the event of a CRQC being developed it will be far better to have uncompressed PQ signatures in Bitcoin than none at all. Acknowledgements: These ideas arose out of correspondence with Hunter Beast. I want to thank Neha Narula, John Light, Eli Ben-Sasson for their feedback, Jonas Nick for his feedback and his idea to use LaBRADOR for signature aggregation, Tadge Dryja for suggesting the term =E2=80=9CJPEG resistance= =E2=80=9D and his ideas around its feasibility. I had a number of fruitful discussions over lunch with members of the MIT DCI and on the Bitcoin PQ working group. These acknowledgements should not be taken as an agreement with or endorsement of the ideas in this email. [0]: Hunter Beast, BIP-360: QuBit - Pay to Quantum Resistant Hash (2025) https://github.com/bitcoin/bips/pull/1670/files# [1]: Benchmark Report: Post-Quantum Cryptography vs secp256k1 https://github.com/cryptoquick/libbitcoinpqc/blob/main/benches/REPORT.md [2]: Ruben Somsen, SNARKs and the future of blockchains (2020) https://medium.com/@RubenSomsen/snarks-and-the-future-of-blockchains-55b820= 12452b [3]: John Light, Validity Rollups on Bitcoin (2022) https://github.com/john-light/validity-rollups/blob/main/validity_rollups_o= n_bitcoin.md [4] Vitalik Buterin, An Incomplete Guide to Rollups (2021) https://vitalik.eth.limo/general/2021/01/05/rollup.html [5]: Aardal, Aranha, Boudgoust, Kolby, Takahashi, Aggregating Falcon Signatures with LaBRADOR (2024) https://eprint.iacr.org/2024/311 [6]: Gidi Kaempfer, Recursive STARKs (2022) https://www.starknet.io/blog/recursive-starks/ [7]: Dan Gould, Interactive Payment Batching is Better (2023) https://payjoin.substack.com/p/interactive-payment-batching-is-better [8] John Tromp, Fee burning and Dynamic Block Size (2018) https://lists.launchpad.net/mimblewimble/msg00450.html --=20 You received this message because you are subscribed to the Google Groups "= Bitcoin Development Mailing List" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to bitcoindev+unsubscribe@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/= CAEM%3Dy%2BXMLuGH-MAfkYanfbU3Ynduw54jDVguKxgO2xEtnSEkZg%40mail.gmail.com.