In cryptography, a ring signature is a type of digital signature that can be performed by any member of a group of users who each have keys. Thus, a message signed with a ring signature is endorsed by someone in a particular group of people. One of the security properties of a ring signature is that it should be computationally impossible to determine which of the group members' keys was used to produce the signature.
For example, a ring signature could be used to provide an anonymous signature from "a high-ranking White House official," without revealing which official signed the message. Ring signatures are suitable for this application because the anonymity of a ring signature cannot be revoked and because the group for a ring signature can be improvised (no pre-configuration required).
Application a Dynastycoins
A ring signature uses your account keys and a number of public keys (also known as outputs) pulled from the blockchain using a triangular distribution method. Over time, past results could be used again and again to train possible signatory participants. In a "ring" of possible signatories, all members of the ring are equal and valid. There is no way for an outside observer to tell which of the possible signers in a group of signatures belongs to your account. Therefore, ring signatures ensure that transaction outputs are untraceable. Also, there are no fungibility issues with Dynastycoins given that every transaction output has plausible deniability (for example, the network cannot tell which outputs are spent or unspent).
To read how Dynastycoins offers you privacy by default (non-connectability), see the hidden addresses. (stealth address)