What papers should I read to understand the mathematics behind Monero?
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An excellent overview of most aspects of Monero (excluding subaddresses and bulletproofs) is here: https://github.com/kurtmagnus/Monero-RCT-report/blob/master/main.pdf
Learn about Elliptic Curve Cryptography here: https://steemit.com/monero/@luigi1111/understanding-monero-cryptography-privacy-introduction
Learn about Monero's proof of work algorithm, stealth addresses and Monero's original ring signatures (LSAG) in the cryptonote white paper https://cryptonote.org/whitepaper.pdf
Learn about how confidential transactions hide transaction amounts (including what range proofs are) here: https://people.xiph.org/~greg/confidential_values.txt
Learn about blockchain transaction structures here: https://cryptonote.org/standards/
Learn about the MLSAG upgrade to Monero's ring signatures here: https://lab.getmonero.org/pubs/MRL-0005.pdf
Learn about Bulletproofs, which will be replacing Monero's existing range proofs, here: https://github.com/AdamISZ/from0k2bp/blob/master/testzkp.pdf and here: https://eprint.iacr.org/2017/1066.pdf
Learn about ring signatures in a more general sense here: http://diyhpl.us/~bryan/papers2/bitcoin/Borromean%20ring%20signatures.pdf
Learn about subaddresses here: https://lab.getmonero.org/pubs/MRL-0006.pdf
See all of the Monero Research Lab publications here: https://lab.getmonero.org/
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