Combined Signature and Encryption Schemes.

So, lets say I want to create a secure messaging system based on public
key crypto. I start with something like PGP. Peoples may or not have a
Key Pair, so there are 4 ways to send a message:

1) Not signed, Not encrypted (neither sender or recipient has keys)
2) Signed, Not encrypted (recipient doesnt have key)
3) Not Signed, Encrypted (sender doesnt have key)
4) Signed, Encrypted (both have keys)

So now, I decide I'm going to have an Signature Scheme, and an
Encryption Scheme. For now those are independant Schemes.

My Signature Scheme is basically going to be a Hash on the Plaintext,
and then a signature primitive, such as RSA or ECDSA, on this hash.

Now I want my Encryption Scheme to be safe against Chosen Ciphertext
Attacks, so it includes a MAC on the Ciphertext.

So now basically I have three operations that operate on the full
message data:

1) A Hash on the Plaintext
2) A block cipher on the Plaintext, this gives me the CipherText
3) A Mac on the Ciphertext

So I'm wondering if it is possible to optimize this so that I only need
2 passes on the full data ? In particular I'm thinking there might be a
way to combine the Signature and Encryption schemes to achieve this.

Thanks

.

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