Monero has 4 keys associated with each address:
- public view key
- public spend key
- private view key
- private spend key
Can you sweep all coins from an address if you only have the private spend key?
Yes. In a nutshell, the spend key is deterministic and therefore you'd be able to derive the private view key. Subsequently, you can generate the public counterparts by multiplying the private keys with the base point (G). Lastly, using the public spend key and public view key, you can construct the public address.
Thus, to answer your question. Yes, you can sweep all coins from an address if you merely have the private spend key.
A more theoretical explanation about how "How Cryptonote Addresses Are Created" (and thus why you are able to sweep all coins from an address if you merely have the private spend key) can be found here. To quote:
Cryptonote Public Addresses differ in several ways compared to Bitcoin. First, Cryptonote uses two keypairs, known as the spend keypair and the view keypair. Furthermore, these keys are EdDSA (specifically ed25519) keys, whereas Bitcoin uses ECDSA (specifically secp256k1) keys. Finally, Cryptonote Public Addresses are direct representations of the pair of public keys, whereas Bitcoin (and clones) uses a hash of the single public key. EdDSA keys (both private and public) are 256 bits long, or 64 hexadecimal characters. Not every 256-bit integer is a valid EdDSA scalar (private key); it must be less than the "curve order". The function to do this is labeled sc_reduce32.
To add to the confusion, there are presently at least three different methods of private key derivation in existence for Monero (and other Cryptonotes), though Bitcoin also has many:
Original (non-deterministic) Style – The Private Spend Key and Private View Key are both independently and randomly chosen to form an account. You can simulate this above by pressing the "Random" buttons next to fields 3. and 4., then pressing "Gen 5.", "Gen 6.", and "Gen 7.", in that order. There is no good way to back up a non-deterministic account other than keeping copies of the files; you need to have a copy of both private keys, but presently only MyMonero will accept the two keys as input instead of a seed/wallet file. For these reasons, it is not recommended to use an account of this type.
Mnemonic (Electrum or Deterministic) Style – In this style, the Private View Key is derived from the Private Spend Key, so you only need to remember one thing: the seed, which is actually just a representation of the Private Spend Key itself. This 256-bit scalar can be easily converted to a "24-digit" Base1626 "number" in the form of a mnemonic seed, which is 25 words long with the last word being used as a checksum. Mnemonics convert on a ratio of 4:3 minimum: four bytes creates three words, plus one checksum word; eight bytes creates six words, plus one checksum word; and so on. The "seeds" created by this method will always be valid scalars as they are sent to sc_reduce32 first. The Private View Key is derived by hashing the Private Spend Key with Keccak-256, producing a second 256-bit integer, which is then sent to sc_reduce32. You can test out this style above by pressing the "Random" button on the upper right, or by pressing either of the "Random" buttons next to fields 1. and 2., then the various "Gen x." buttons. You can backup accounts of this type by writing down or otherwise saving the 25 word deterministic seed; you can easily restore using both Simplewallet and MyMonero.
MyMonero Style – This is similar to 2., but uses a 13 word seed instead of a 25 word seed. The 13 words convert to a 128-bit integer that is used for both spend and view key derivation, in the following form: the 128-bit integer is hashed with Keccak-256 to produce a 256-bit integer, a. a is sent to sc_reduce32, which returns the Private Spend Key. a is hashed once more with Keccak-256 to produce a second 256-bit integer, b. b is then sent to sc_reduce32, which returns the Private View Key. You may have noticed a critical difference between this style and the Electrum Style: MyMonero's Private View Key derivation is done by hashing random integer a, while Electrum Style derivation is done by hashing the Private Spend Key. This means that 13 and 25 word seeds are not compatible – it is not possible to create an Electrum Style seed (and account) that matches a MyMonero Style seed (and account) or vice versa; the view keypair will always be different. You can test out this style above with the "Random MyMonero" button. To backup MyMonero accounts, save the 13 word seed; you can currently "restore" using MyMonero only (you're really just logging in) – Simplewallet does not currently support 13-word seeds.
Above we discussed the different ways private keys are derived; the rest of the address generation process is the same in all three cases. The Private Spend Key and Private View Key are sent to the ed25519 scalarmult function to create their counterparts, the Public Spend Key and Public View Key. To create the actual Public Address, the following is performed:
- The pair of public keys are prepended with one network byte (the number 18, 0x12, for Monero). It looks like this: (network byte) + (32-byte public spend key) + (32-byte public view key).
- These 65 bytes are hashed with Keccak-256.
- The first four bytes of the hash from 2. are appended to 1., creating a 69-byte Public Address.
- As a last step, this 69-byte string is converted to Base58. However, it's not done all at once like a Bitcoin address, but rather in 8-byte blocks. This gives us eight full-sized blocks and one 5-byte block. Eight bytes converts to 11 or less Base58 characters; if a particular block converts to <11 characters, the conversion pads it with "1"s (1 is 0 in Base58). Likewise, the final 5-byte block can convert to 7 or less Base58 digits; the conversion will ensure the result is 7 digits. Due to the conditional padding, the 69-byte string will always convert to 95 Base58 characters (8 * 11 + 7).
- This 95-character result is the (obscenely long) Cryptonote Public Address!
- If you're creating an integrated address, simply append the 64-bit payment ID to step 1 and continue; everything else is the same except for the lengths (77 bytes total, 106 Base58 digits) and the prepended byte (19, 0x13).