While reading a literature on signature schemes, I came across the concept of Existential Unforgeability of signature scheme against Adaptive Chosen Message Attack. Can anyone point me to the paper where this notion was introduced first? Otherwise, may I ask for a paper/reference where the above-mentioned game is properly defined?
These are standard terms in the cryptographic literature. Refer to Goldwasser's Lecture Notes on Cryptography, particularly section 10.3.1 where the definitions of forgery of digital signatures are introduced:
Existential Forgery: The adversary succeeds in forging the signature of one message, not necessarily of his choice.
Selective Forgery: The adversary succeeds in forging the signature of some message of his choice.
Universal Forgery: The adversary, although unable to find the secret key of the The forger, is able to forge the signature of any message.
Total Break: The adversary can compute the signer’s secret key.
The exact use of these definitions can be seen later in the notes in which some proofs are discussed.