You may also be interested in the rich literature on the subject of algorithmic fault tolerance. This includes the old assignment: Write a sort that correctly sorts its input when a constant number of comparisons will fail (or, the slightly more evil version, when the asymptotic number of failed comparisons scales as log(n)
for n
comparisons).
A place to start reading is Huang and Abraham's 1984 paper "Algorithm-Based Fault Tolerance for Matrix Operations". Their idea is vaguely similar to homomorphic encrypted computation (but it is not really the same, since they are attempting error detection/correction at the operation level).
A more recent descendant of that paper is Bosilca, Delmas, Dongarra, and Langou's "Algorithm-based fault tolerance applied to high performance computing".