Encoding data utilizing a zero information gain function

A dispersed storage (DS) module of a dispersed storage network (DSN) comprises:

• a first module, when operable within a computing device, causes the computing device to:
• dispersed storage error encode in accordance with distributed data storage parameters, a data segment of data to produce a set of encoded data slices and a set of zero information gain (ZIG) encoded data slices, wherein the set of encoded data slices is encoded in accordance with a dispersed storage error encoding scheme and wherein the set of ZIG encoded data slices is encoded using a ZIG function, wherein a first ZIG encoded data slice of the set of ZIG encoded data slices is generated by matrix multiplying a first decoding matrix and a first encoded data slice of the set of encoded data slices and wherein the generating the first ZIG encoded data slice includes:
• generating a first partial encoded data slice based on the first decoding matrix, the first encoded data slice and a row of the encoding matrix corresponding to the first encoded data slice;
• generating a second partial encoded data slice based on a second decoding matrix, a second encoded data slice and a row of the encoding matrix corresponding to the second encoded data slice, wherein the second encoded data slice is an encoded data slice of the set of encoded data slices and not included in the subset of encoded data slices;
• and
• combining the first and second partial encoded data slices to produce the first ZIG encoded data slice;
• select a first subset of encoded data slices from the set of encoded data slices, wherein the first subset of encoded data slices includes less than a threshold number of encoded data slices, and further wherein the threshold number of encoded data slices is required to recreate the data segment;
• and
• a second module, when operable within the computing device, causes the computing device to:
• send, via an interface of the computing device, the subset of encoded data slices to a first memory within the DSN for storage therein;
• and
• send, via the interface, the set of ZIG encoded data slices to a second memory within the DSN for storage therein.