I have seen an image about brute forcing Bitcoin cryptography saying even a perfect computer which uses all the power of star system, and still wont succeed. 
How strong is Monero cryptography against such an attack?
asked Oct 8, 2016 at 17:53
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That image is wrong. Although brute force takes 256 bits, the best available attacks on elliptic curve cryptography is equivalent to bruteforcing something with half the key size, or 128-bits (which is still pretty strong).– PyRulezOct 9, 2016 at 22:09
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2 Answers
This image says that all the energy of the sun would not be enough to try all the Bitcoin private keys (256-bit keys).
The elliptic curve that Monero uses works with 255-bit private keys, and trying all of them would not be feasible either.
One weakness that Bitcoin and Monero both share are from quantum computing. With quantum computing, significantly less energy would be required to crack private keys.
Therefore Monero is (essentially) equally secure, withstanding that quantum computation is not available.
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1Quantum computing is not more than a theoretical threat right now and Bitcoin keys and Monero keys are not the same, so the threat models differ. However, Op didn't ask about Quantum threats, so no reason to go into that.– pl55Oct 9, 2016 at 14:38