Compare this with another eight-word phrase: "rebel twenty hotel solve zone arena dad east". These words were selected randomly and uniformly from a list of 2048 words using a secure RNG (you could use coins, dice, cards instead or in conjunction). Unlike "There is no new thing under the sun", I can be confident that this precise string of words did not exist anywhere until this moment. Before I revealed this precise passphrase it had, provably, 88 bits of entropy (so I'd guess it to have been about 300 billion billion times stronger).
Even then, I would recommend using something stronger still for a brainwallet. While I occasionally use brainwallets with as little as 96 bits of entropy, I recommend a minimum of 128 bits to anyone that's not confident in doing the calculations themselves. For reference:
- Casascius coin addresses have 128 bits of entropy and they're holding out well.
- A typical address as generated by Bitcoin Core contains 160 bits of entropy (about 4 billion times stronger than 128 bits).
Diceware, mentioned in tspacepilot's link, gives you about 12.92 bits of entropy per word so you'll want 10 words as a minimum and 13 words for maximum security.
Final note: Now that I've posted "rebel twenty hotel solve zone arena dad east" online, it would make a poor brainwallet passphrase. I wouldn't care to guess at its strength but it's certainly far, far less than 88 bits.
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