The thesis that reusing an address is not "using Bitcoin correctly", is kind of weird, to say the least.
I'll just repost relevant part of my post from another forumEven proper reuse of ECDSA private key makes it less secure. Satoshi did very good work protecting Bitcoin from possible future advances in cryptography - new addresses are created whenever it is appropriate, before first (and, ideally, the last) use public key is secret, only hash of it (address) is exposed to the public. But Satoshi did not forbid intentional address reuse, thus making key reuse possible.
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CURVE the elliptic curve field and equation used
G elliptic curve base point, a generator of the elliptic curve with large prime order n
n integer order of G, means that n * G = O
Calculate e = \textrm{HASH}(m), where HASH is a cryptographic hash function, such as SHA-1.
Let z be the L_n leftmost bits of e, where L_n is the bit length of the group order n.
Select a random integer k from [1, n-1]. - This is what counts
Calculate the curve point (x_1, y_1) = k * G.
Calculate r = x_1 \pmod{n}. If r = 0, go back to step 3.
Calculate s = k^{-1}(z + r d_A) \pmod{n}. If s = 0, go back to step 3.
The signature is the pair (r, s).
And every (r, s) pair derived from the same dA and exposed to the public means more food for hyperlinearization and SAT-solvers. (Some day those two beasts will meet together and produce fertile offspring G elliptic curve base point, a generator of the elliptic curve with large prime order n
n integer order of G, means that n * G = O
Calculate e = \textrm{HASH}(m), where HASH is a cryptographic hash function, such as SHA-1.
Let z be the L_n leftmost bits of e, where L_n is the bit length of the group order n.
Select a random integer k from [1, n-1]. - This is what counts
Calculate the curve point (x_1, y_1) = k * G.
Calculate r = x_1 \pmod{n}. If r = 0, go back to step 3.
Calculate s = k^{-1}(z + r d_A) \pmod{n}. If s = 0, go back to step 3.
The signature is the pair (r, s).
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