Add definitions for key agreement schemes.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

protocol/protocol.tex

@@ -194,8 +194,12 @@
 \newcommand{\zkSNARKs}{\term{zk-SNARKs}}
 \newcommand{\memo}{\term{memo field}}
 \newcommand{\Memos}{\titleterm{Memo Fields}}
+\newcommand{\keyAgreementScheme}{\term{key agreement scheme}}
+\newcommand{\KeyAgreementScheme}{\titleterm{Key Agreement Scheme}}
 \newcommand{\keyDerivationFunction}{\term{Key Derivation Function}}
 \newcommand{\KeyDerivationFunction}{\titleterm{Key Derivation Function}}
+\newcommand{\symmetricEncryptionScheme}{\term{symmetric authenticated encryption scheme}}
+\newcommand{\SymmetricEncryptionScheme}{\titleterm{Symmetric Authenticated Encryption Scheme}}
 \newcommand{\pseudoRandomFunction}{\term{Pseudo Random Function}}
 \newcommand{\pseudoRandomFunctions}{\term{Pseudo Random Functions}}
 \newcommand{\PseudoRandomFunctions}{\titleterm{Pseudo Random Functions}}
@@ -289,6 +293,11 @@
 \newcommand{\KDF}{\mathsf{KDF}}
 \newcommand{\kdftag}{\mathsf{kdftag}}
 \newcommand{\kdfinput}{\mathsf{kdfinput}}
+\newcommand{\AsymPublic}{\mathsf{AsymPublic}}
+\newcommand{\AsymPrivate}{\mathsf{AsymPrivate}}
+\newcommand{\AsymSharedSecret}{\mathsf{AsymSharedSecret}}
+\newcommand{\KeyAgreementGen}{\mathsf{KeyAgreementGen}}
+\newcommand{\KeyAgreement}{\mathsf{KeyAgreement}}
 \newcommand{\SymEncrypt}[1]{\mathsf{SymEncrypt}_{#1}}
 \newcommand{\SymDecrypt}[1]{\mathsf{SymDecrypt}_{#1}}
 \newcommand{\SymSpecific}{\mathsf{AEAD\_CHACHA20\_POLY1305}}
@@ -735,15 +744,18 @@ and $\SymEncrypt{\Key}(P) \neq C$.
 %an encryption algorithm $\AuthEncEncrypt \typecolon \Nonce \times ...$,
 %and a decryption algorithm $\AuthEncDecrypt$.
 
-\nsubsubsection{Key Agreement Scheme}
+\nsubsubsection{\KeyAgreementScheme}
 
-\todo{abstract functionality of Curve25519}
+A \keyAgreementScheme is a cryptographic protocol in which two parties agree
+a shared secret, each using their private key and the other party's public key.
+Such a scheme defines a type of public keys $\AsymPublic$, a type of private
+keys $\AsymPrivate$, and a type of shared secrets $\AsymSharedSecret$.
 
-\nsubsubsection{\KeyDerivationFunction}
+Let $\KeyAgreementGen \typecolon () \rightarrow \AsymPublic \times \AsymPrivate$
+be a randomized algorithm generating a (public, private) key pair.
 
-$\KDF \typecolon \setofNew \times GeneralCRHOutput \times AsymPrivate \times AsymPublic \times AsymPublic
-\rightarrow \Keyspace$ is a \keyDerivationFunction, suitable for use
-with ... and deriving keys for $\SymEncrypt{}$.
+Let $\KeyAgreement \typecolon \AsymPrivate \times \AsymPublic \rightarrow \AsymSharedSecret$
+be the agreement function.
 
 
 \nsubsection{\JoinSplitTransfers{} and Descriptions} \label{pourdesc}