Nodes may leak whole field elements or collections of smaller-subfield elements. Static leakage repeats one linear view, while dynamic leakage can change transformations between refresh epochs, including through incomplete erasure of intermediate state.

1. claim

   Static partial leakage defeats a whole-share threshold

   proved under model

   Proposition 1 quantifies how full-share and subfield leakage reduce the remaining Reed-Solomon repair information needed to reconstruct the secret, even when fewer than the nominal threshold of whole shares leak in an epoch.

   Static and dynamic leakage attacks · Repair background and missing proofs
2. claim

   Dynamic leakage accumulates across epochs

   proved under strong model

   Proposition 2 gives an efficient adversary that gathers enough subfield information across epochs to reconstruct the secret when leakage functions vary and affected nodes store nonzero values; the paper labels this a strong but plausible implementation model.

   Static and dynamic leakage attacks · Repair background and missing proofs

Two theorems preserve storage and repair parameters across translations, but the reverse direction requires a linear MDS regenerating code and the baseline forward encoding has a low rate unless linearity or batching is exploited.

1. claim

   PSS implies an erasure regenerating code

   proved

   A (t,n) PSS storing alpha bits per node and recovering through d helpers sending beta bits yields an erasure regenerating code with n nodes, reconstruction dimension t plus 1, and the same storage and repair parameters.

   PSS-to-RC and RC-to-PSS translations · Repair background and missing proofs
2. claim

   Linear MDS RC implies PSS

   proved with conditions

   Every specified linear MDS regenerating code with n plus 1 nodes and dimension k plus 1 yields a (k,n) PSS whose recovery contacts the same d helpers for beta bits each.

   PSS-to-RC and RC-to-PSS translations · Repair background and missing proofs

GRC replaces one uniform threshold with monotone decoding sets and allowed error patterns, requiring Decode to correct every permitted error set and every erasure pattern leaving some decoding set intact.

1. claim

   Linear GRC existence for Q2 error structures

   existence theorem

   Theorem 3 maps a Q2 general adversary structure into a linear GRC over a finite field, while explicitly leaving parameter optimization and achievable rates open.

   Generalized-decoding regenerating codes