Zero to Monero


(azw3,epub,mobi,pdf)



Cryptography. It may seem like only mathematicians and computer scientists have
access to this obscure, esoteric, powerful, elegant topic. In fact, many kinds of
cryptography are simple enough that anyone can learn their fundamental concepts.
It is common knowledge that cryptography is used to secure communications,
whether they be coded letters or private digital interactions. Another application is
in so-called cryptocurrencies. These digital moneys use cryptography to assign and
transfer ownership of funds. To ensure that no piece of money can be duplicated
or created at will, cryptocurrencies usually rely on ‘blockchains’, which are public,
distributed ledgers containing records of currency transactions that can be verified
by third parties [97].

It might seem at first glance that transactions need to be sent and stored in
plain text format to make them publicly verifiable. In fact, it is possible to conceal
a transaction’s participants, as well as the amounts involved, using cryptographic
tools that nevertheless allow transactions to be verified and agreed upon by
observers [136]. This is exemplified in the cryptocurrency Monero.
We endeavor here to teach anyone who knows basic algebra and simple com-
puter science concepts like the ‘bit representation’ of a number not only how
Monero works at a deep and comprehensive level, but also how useful and beautiful
cryptography can be.

For our experienced readers: Monero is a standard one-dimensional distributed
acyclic graph (DAG) cryptocurrency blockchain [97] where transactions are based
on elliptic curve cryptography using curve Ed25519 [38], transaction inputs are
signed with Schnorr-style multilayered linkable spontaneous anonymous group
signatures (MLSAG) [108], and output amounts (communicated to recipients
via ECDH [52]) are concealed with Pedersen commitments [88] and proven in a
legitimate range with Bulletproofs. Much of the first part of this report is
spent explaining these ideas.