Abstract: In various embodiments, methods and systems for erasure coding with enhanced local protection groups are provided. An erasure coding scheme can be defined based on a Vertical Local Reconstruction Code (VLRC) that achieves high storage efficiency by combining the Local Reconstruction Code and conventional erasure coding, where the local reconstruction code (LRC) is carefully laid out across zones. Thus, when a zone is down, remaining fragments form an appropriate LRC. Further, an inter-zone erasure coding scheme—Zone Local Reconstruction Code (ZZG-2 code)—is provided having both local reconstruction within every zone and a-of-b recovery property across zones. An inter-zone adaptive erasure coding (uber code) scheme is provided, the uber code is configurable to produce near optimal performance in different environments characterized by intra and inter-zone bandwidth and machine failure rates.

Abstract: In various embodiments, methods and systems for erasure coding with enhanced local protection groups are provided. An erasure coding scheme can be defined based on a Vertical Local Reconstruction Code (VLRC) that achieves high storage efficiency by combining the Local Reconstruction Code and conventional erasure coding, where the local reconstruction code (LRC) is carefully laid out across zones. Thus, when a zone is down, remaining fragments form an appropriate LRC. Further, an inter-zone erasure coding scheme—Zone Local Reconstruction Code (ZZG-2 code)—is provided having both local reconstruction within every zone and a-of-b recovery property across zones. An inter-zone adaptive erasure coding (uber code) scheme is provided, the uber code is configurable to produce near optimal performance in different environments characterized by intra and inter-zone bandwidth and machine failure rates.

Abstract: First biometric parameters are acquired from a user. Input data are encrypted according to the biometric parameters to produce ciphertext. The biometric parameters are encoded using a syndrome encoder to produce a syndrome code. The ciphertext and the syndrome code are associated with each other and stored in a computer readable media so that only the same user can subsequently decrypt the cipher text.