I didn't mean to suggest you would have any interest in doing any such thing but I think you misunderstood what the paper was describing.
There are ways of using the encrypted messages in signature schemes to send extra information that is not detectable. This applies not only to elliptic curve signature schemes but other discrete logarithm schemes such as such Schnorr and EIGamal.
This paper is not really something you have to worry about unless you were trying to send yourself information in secret from the wallet that you could read from the blockchain. It is not any weakness in the signature scheme.
If you were trying to send yourself information then you would in effect have to brute force the encryption.
Think of it this way. Each time I sign a message with ECDSA I use a random number and iI come up with the signed message.
Now if I have a cipher that I have prearranged, say a simple substitution cipher so a->b, c->d etc. (this is our prearranged mapping function)
Now I want to transmit the message theeaglehaslanded this becomes uiffbhmfibtmboefe.
So I can keep trying different random numbers until the first part of the signed message says uiffbhmfibtmboefe. When the signed message is published then anyone with the substitution cipher can decrypt it.
Now it will probably take quite a few tries with random numbers to come up with this combination of letters. Look at the problem of generating vanity addresses and how much more difficult it gets as they get longer.
So you can split the message in to sections and send it bit by bit so you drastically reduce the amount of resources for encryption at the expense of sending more messages.
By the way this is not supposed to be a technical explanation so hopefully I won't get too many critical comments from Wikipedia experts. I'm sure someone on the forum will publish a white paper about it soon anyway.
So, yea, don't worry about it.