Abstract: Systems and methods are described for encrypting amounts and asset types of a verifiable transaction on a blockchain ledger. For each asset, an asset tag is blinded, multiplied by the amount of the asset, and the product is blinded again to create an encrypted amount of the asset. Both encrypted amount of the asset and a corresponding generated output value are within a value range, and the sum of the encrypted input value and the encrypted output value equals zero. Rangeproofs for each of the encrypted output values are associated with a different public key. Each public key is signed with a ring signature based on a public key of a recipient. A second ring signature is used to verify each asset tag, where the private key of the second ring signature for each asset is a difference between a first blinding value and an output coefficient.

Abstract: Systems and methods are described for transferring an asset from a parent chain to a sidechain. A simplified payment verification (SPV) proof associated with the parent chain asset may be generated. The SPV proof may include a threshold level of work. The SPV proof associated with the parent chain asset may be validated, and a sidechain asset corresponding to the parent chain asset may be generated. If no reorganization proof is detected, the sidechain asset is released. To redeem the sidechain asset in the parent chain, a SPV proof associated with the sidechain asset may be generated. The parent chain may validate the SPV proof associated with the sidechain asset. The parent chain asset associated with the sidechain asset may be held for a second predetermined contest period. The parent chain asset may then be released if no reorganization proof associated with the sidechain asset is detected.