ECC keys vulnerable to brute force attack? I have started learning about Elliptic Curve Cryptography (ECC). Since the key size required in ECC is relatively smaller than the key size in RSA (to provide the same encryption strength), I wonder whether the smaller key size of ECC makes it vulnerable to brute force attack.  Does it?

I'm not very knowledgeable about the ways in which a key can be cracked.  But, basically, fewer bits means the number of possibilities can be more quickly guessed or tried!
Yes a brute force key-guessing attack would be faster, but:


It would be ridiculously slow for either. E.g. see this for 256-bit keys.
There are faster attacks on both and those attacks break larger RSA sizes than ECC sizes.


Related: Why can ECC key sizes be smaller than RSA keys for similar security?