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New protocol designed by the Monero Research Labs combining ring signatures from CryptoNote with Confidential transactions. RingCT transactions are not only untraceable (ring signature) but also keep the transaction amount private (confidential transaction).

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The other two answers are good in that they cover the part about Pedersen commitments, and how those are used to check that the sum of the amounts in the outputs created doesn't exceed that of the sum …
answered Apr 25 '17 by user141
11
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a set of n other outputs on the blockchain, indistinguishable with respect to their amounts, which are all the same (currently), or all hidden (under ringCT, see below). This is already working, with … minimum n = 2 enforced on the protocol level, and soon to be raised to 4; Stealth addresses: obscure the destination of funds (already working); RingCT: hides transaction amounts as well. This …
answered Oct 18 '16 by user141