This is not how friends operate, "friend." Please do not piss on our legs and then infer something about the weather.

Edited to add:


Please see above quote for irony.

The notation in the whitepaper and what you've seen here is proper notation. I = x*H_p(P) means x times H_p(P) where H_p is a hash function, H_p(P) is the hash function evaluated at a point, and * denotes elliptic curve multiplication which is NOT normal multiplication. Just like matrix multiplication is not the same as usual multiplication, elliptic curve multiplication takes place in a different manner than what you learned in, say, elementary algebra class. This is an abstract multiplicative notion, it is quite usual and proper to see it used this way.

For further reading, I would not begin necessarily with fluffypony's wall of links, but with Daepp and Gorkin's "Reading, Writing, and Proving" to learn a little bit about formal mathematics, and then maybe move onto Trappe and Washington's "Introduction to Cryptography." In that order. Be sure to try all the exercises in both books before asking any more questions.

Edit: I a word.

First impressions of the paper: there are some good insights, and it's written well.

But... time stamps can be manipulated by dishonest actors (addressed in the CryptoNote whitepaper) and hence can not be trusted to prevent double spending. Which is one motivation behind Nakamoto's development of the Blockchain-by-Proof-of-Work solution to the Byzantine General problem.

Proof-of-work methods had been utilized before for various applications, most notably, to mitigate spam e-mail, but, Nakamoto was the first to solve the problem of coming to a concensus about order-of-events in a distributed, peer-to-peer way without timestamps. Even Nakamoto's solution is not a true solution, but simply a method that converges to a solution probabilistically over time. It's provable that a one-time, 2-General problem requires a countable number of verifications for a closed solution. The only other alternative Blockchain-by-Proof-of-X method that has been proposed since Nakamoto's solution has been Blockchain-by-Proof-of-Stake (and it's variant, the Blockchain-by-Proof-of-Stake-Velocity). Other Proof-of-X methods, such as Proof-of-Burn and Proof-of-Publication, have not been proposed to verify transactions, but to bootstrap value from one cryptocurrency to another and to verify the existence of a file by some point in time on the blockchain, respectively.  If either of these methods can be utilized to verify transactions, no method has been proposed to my knowledge.  

Recent rigorous security analyses of Blockchain-by-Proof-of-Stake methods are troubling: unless some Proof-of-Work component is included, a dedicated attacker can "kill" a coin with no cost http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2393940, but the attack requires a vast amount of capital, requires rational behavior on the part of a market (ha!), and requires the actor to enact a PR campaign trying to kill the coin. It's is unlikely to generate profit for the attacker (i.e. it's a strictly malicious attack). Notice, however, this may not apply to Blockchain-by-Proof-of-Stake-Velocity, I'm not sure. This core solution to generating an order of events without time stamps, the Blockchain-by-Proof-of-Work (BPOW) has essentially remained unchanged since it's original inception by Nakamoto. This is the primary strength of any cryptocurrency protocol. Variants in measuring the blockchain, such as following the heaviest subtree, not the longest chain, have been proposed, and are the best hope at improving that basic piece of the protocol. https://eprint.iacr.org/2013/881.pdf