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原始链接: https://news.ycombinator.com/item?id=39976225

为了全面了解 256 位 ECDSA 密钥的强度，让我们考虑一些计算。破解此类密钥所需的平均尝试次数约为 2^128。目前，在 FPGA 上计算 ECDSA 签名最快的已知方法的运行速度约为每秒 1,315 个事务 (TPS)。高端 FPGA 的成本约为 10,000 美元。假设一个实体可以以一半的价格购买 2022 财年生产的所有 Xilinx FPGA，并持续免费运行它们，其计算能力将等于 2.65 万亿 TPS。然而，即使如此巨大的容量也无法在宇宙年龄（估计约为 12.8e+23 秒）内破解 256 位 ECDSA 密钥。如果我们进一步假设该实体能够获得地球的全部经济产出（202.6万亿美元），理论上他们的处理能力可以提高2.66e+28 TPS；仍然不足以在人类寿命内破解单个比特币私钥。这些计算提供的证据表明，当前的加密方法仍然可以安全地抵御使用现有技术的暴力攻击，除非有任何重大的技术进步。

Just for fun, because it's hard to appreciate how strong a 256bit ECDSA key is.

Base Numbers:

- 2*128 guesses on average

- public state of the art for ECDSA on an FPGA is 1315tps [0]

- retail price of said fpga $10,000 [1]

- total net income for xilinx from advanced FPGAs FY2022 (936M * 0.74 + 879M * 0.72) = 1325M [2]

Ballpark numbers, we'll assume that attacker can buy 10x every FPGA xilinx made in 2022 for a 50% discount and can run them non stop for zero cost.

We'll also assume they have a bunch of secret math geniuses and have a faster ECDSA implementation that can do 1,000,000,000 tps ( or 1,000,000x SOTA)

- (1325,000,000 / 5,000) * 10 = 2,650,000 FPGAs

- 2,650,000 * 100,000,000,000 = 2,650,000,000,000,000tps

- 2*128 / 2,650,000,000,000,000 = 1.28e+23s

- 1.28e+24 / 60 / 60 / 24 / 365 = 4,080,000,000,000,000 years

- ~4 quadrillion years

- or 4x the time until every planet has been ejected from every star system and the sun has cooled to 5K [3]

But why stop there, lets assume that the attacker can use the entire planets GDP to buy chips and has a 1,000,000,000,000,000x faster ECDSA implementation.

- World GDP (2022): 101.3 trillion

- (101,300,000,000,000 / 5000) = 20,260,000,000

- 100,000,000,000,000,000 * 20,260,000,000 = 2.66419e+28tps

- 2*128 / 2.66419e+28 = 12,772,451,173s

- 12,772,451,173 / 60 / 60 / 24 / 365 = 405 years

So even then, we wouldn't see a single BTC key broken within our lifetime.

(Unless you believe that 3 letter agencies have successfully built a quantum computer that practically implement shore's algorithm, in which case you should probably be more worried about the fact that they can break public key encryption globally)

[0]: https://arxiv.org/pdf/2112.02229.pdf

[1]: https://www.colfaxdirect.com/store/pc/viewPrd.asp?idproduct=...

[2]: https://web.archive.org/web/20211203065624/https://investor....

[3]: https://en.wikipedia.org/wiki/Timeline_of_the_far_future

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