[Ethereum] Is it safe to reuse Ether addresses

Currently, Ethereum uses elliptic curve cryptography (ECDSA), the same as Bitcoin. So whatever "unsafe" concerns there are with how Bitcoin transactions are signed, would be the same with Ethereum currently.

In Bitcoin and Ethereum, sending from an address will reveal the public key easily. Quantum computers compromise ECDSA and would make it easy to deduce the private key from the public key: this is usually the concern about revealing the public key. Lamport signatures are believed to be quantum resistant.

Update May 2019: Account abstraction described below has not been implemented due to complexity, and is planned as part of sharding.

Future release of Ethereum, will have Abstraction of transaction origin and signature:

The goal of these changes is to set the stage for abstraction of account security. Instead of having an in-protocol mechanism where ECDSA and the default nonce scheme are enshrined as the only "standard" way to secure an account, we take initial steps toward a model where in the long term all accounts are contracts, contracts can pay for gas, and users are free to define their own security model.

Accounts will be able to specify their own scheme for validating transactions. This opens the door for Lamport signatures (or other algorithms desired by the user) which improves security against quantum computers in Ethereum.

Custom cryptography: users can upgrade to ed25519 signatures, Lamport hash ladder signatures or whatever other scheme they want on their own terms; they do not need to stick with ECDSA.