The issues of privacy of electronic currency faced researchers and developers for a long time, long before Bitcoin. In 1991, Tatsuaki Okamoto and Kazuo Ohta from the NTT research laboratory (Japan's largest telecommunications company) introduced
6 criteria for an ideal e-currency, including privacy: "relationship between the user and his purchases must be untraceable by anyone". Nicholas van Saberhagen, an anonymous author behind the work on the CryptoNote protocol, which formed the basis of Monero, in December 2012 summarized
these 6 criteria to two specific properties: Untraceability
: for every incoming transaction, all possible senders are equally likely. Unlinkability
: for any two outgoing transactions, it is impossible to prove that they were sent to the same person.
None of the other properties are characteristic of Bitcoin, since all transactions are broadcasted publicly. Of course, by the time this work was written, various tumblers made it possible to combine outputs of several transactions and send them through some intermediate address. Also, by that time, some protocols based on the zero-knowledge proof were known, but at that time such evidence was large enough to make them impractical to use.
What was proposed to tackle the issues: firstly, each transaction was signed on behalf of the group, not the individual, as in BTC. To do this, we used the option of an electronic digital signature called "Ring Signature" (further development of the so-called "Group Signature"). However, when implementing a completely anonymous ring signature, a (very high) probability of double spending of coins arose, and therefore the so-called linkable anonymity
primitive was taken, which was implemented through a one-time-key mechanism (i.e., when creating each new transaction, the group key changes).
Essentially, although it's certainly worth noting that the CryptoNote implementation used a different scheme of elliptical curves (EdDSA instead of ECDSA, as a result, an elliptic curve with a different equation was used, etc.).