Generation and verification of erasure encoded fragments

A system to verify an integrity of a generated specified erasure encoded fragment related to a data file, the specified erasure encoded fragment being generated from a plurality of erasure encoded fragments related to the data file, the system comprising:

• a processor;
• and
• a memory, accessible by the processor and storing instructions that are executable by the processor, the instructions, when executed by the processor, causing the processor to:
• apply an erasure encoding scheme to the data file;
• generate the specified erasure encoded fragment a first time by multiplying a first composite matrix and a first set of erasure encoded fragments of the plurality of erasure encoded fragments, the first set not including the specified erasure encoded fragment, wherein the first composite matrix is based on the erasure encoding scheme and the first set;
• generate the specified erasure encoded fragment a second time by multiplying a second composite matrix and a second set of erasure encoded fragments of the plurality of erasure encoded fragments, wherein the second composite matrix is based on the erasure encoding scheme and the second, and wherein the second set is identical to the first set except for the second set including at least one erasure encoded fragment of the plurality of erasure encoded fragments which is different from the erasure encoded fragments of the first set, the at least one different erasure encoded fragment not being the specified erasure encoded fragment;
• compare the specified erasure encoded fragment generated the first time with the specified erasure encoded fragment generated the second time;
• and
• indicate that an error has occurred if the specified erasure encoded fragment generated the first time and the specified erasure encoded fragment generated the second time are not identical.

A system to verify an integrity of a specified erasure encoded fragment related to a data file, the specified erasure encoded fragment being generated from a plurality of erasure encoded fragments related to the data file, the system comprising:

• a plurality of servers which:
• apply an erasure encoding scheme to the data file;
• generate the specified erasure encoded fragment a first time by multiplying a first composite matrix and at least a first set of erasure encoded fragments of a plurality of erasure encoded fragments related to the data file, the at least first set not including the specified erasure encoded fragment, wherein the first composite matrix is based on the erasure encoding scheme and the at least first set;
• generate the specified erasure encoded fragment a second time by multiplying a second composite matrix and a second set of erasure encoded fragments of the plurality of erasure encoded fragments, wherein the second composite matrix is based on the erasure encoding scheme and the second set, and wherein the second set is identical to the at least first set except for the second set including at least one erasure encoded fragment which is different from the erasure encoded fragments of the at least first set, the at least one different erasure encoded fragment not being the specified erasure encoded fragment;
• compare the specified erasure encoded fragment generated the first time with the specified erasure encoded fragment generated the second time;
• and
• declare that an error has occurred if the specified erasure encoded fragment generated the first time and the specified erasure encoded fragment generated the second time are not identical.