Create encryption key from decryption key (password)?

Question

Alice has a password that she would like to use for decryption. Alice isn't able to store any other information, but she has access to any program/mechanism you choose. How can she create an encryption key for Bob, so Bob will be able to encrypt messages, but won't be able to decrypt them and Alice will be able to decrypt them using password? Following applies:

• Bob is able to provide Alice any data alongside with the encrypted messages.
• Communication of Alice and Bob is already secured. Purpose of this isn't to secure the communication.

What have I tried
First I thought about general RSA and password protected ssh keys. But Alice won't be able to remember private key. But she could provide both pub and priv key to Bob. Bob would be using pub key to encrypt message, sending the priv key alongside each message. Alice would use priv key and password to decrypt the message... questionmark? Im not sure if ssh keys can be used this way. Also it doesn't feel like right tool to use.

I'm not trying to reinvent the wheel. I think such a mechanism has been implemented already, I'm just not aware of its existence (or maybe Im aware of the tool, but do not reallize it can be used this way).

Answer 1

One way to do this is to use elliptic curve (EC) cryptography. Alice could start by taking a SHA256 hash of her password, which would result in a 256-bit value which she could use as her private key. Then, she can multiply this value by an EC generator point, to create a public key, which she could give Bob.

Answer 2

0. Alice possesses a secret password that only she knows.

1. Alice optionally hashes her password (e.g. with SHA-256) to distill its entropy or prevent guessing (e.g. PBKDF2).

2. Alice takes the password or hash and uses it to seed a cryptographically secure random number generator (CSRNG).

3. Alice uses the CSRNG to deterministically generate an RSA public-private key pair. The result will always be the same given the same password; Alice does not need to store the public or private key.

4. Alice gives the public key to Bob.

5. When Bob wants to send a message to Alice, he creates a new AES symmetric encryption key, encrypts the key by RSA using the aforementioned public key, and encrypts the message with the AES key.

6. Alice uses her secret password to re-create the private key to decrypt the AES symmetric key, and uses that to decrypt the message.

Note:

But she could provide both pub and priv key to Bob.

Bob would be using pub key to encrypt message, sending the priv key alongside each message.

Alice absolutely must not give her private key to Bob! That would let Bob decrypt other people's messages to Alice, and also let any eavesdropper decrypt Bob's messages to Alice.