How can address' hash160 be used to determine information for malicious purposes? (Ie reusing of the same address)

Question

I've been playing around with Richard Kiss's Pycoin app which is clarifying how P2PK works. I see that the hash160 of the value: (0x04) (x-coordinate) (y-coordinate) (for an uncompressed Testnet private key in this instance) gives a hash160 value used to prove ownership of the private key.

How is this detrimental for reuse of private keys if there is no issue with PRNGs providing low entropy? I understand how the Android bug was exploited (to a degree, it reused "random values"), but I fail to understand why only sharing the hash160 in a single transaction can be maliciously exploited. To clarify, I'm not talking about privacy concerns of tracking addresses through the Blockchain.

EDIT: The vulnerabilities in question (as specified in the answer are related to quantum computing and/or EDCSA weaknesses, neither of which exist)

Answer 1

The potential security issue is that an an EC public key might one day be reversible into a private key using (for example) Shor's algorithm[1]. This does not apply to a hash of a public key (aka address).

Since the public key of a Bitcoin address is revealed in the first transaction spending from that address, it is therefore considered a bad practice to reuse that address (also for privacy reasons)

[1] See https://security.stackexchange.com/a/34942/16036

Answer 2

If your PRNGs are good, you don't lose any security by using the same address any number of times. Some websites claim that addresses should not be reused because that will make your bitcoins vulnerable to quantum computers and/or some newly discovered weaknesses in ECDSA. However, both of these scenarios are unrealistic at the moment, and I think that if they do become realistic, this will be such a big problem for the world's cryptography that you won't be the first victim (unless you are Satoshi Nakamoto).