1. A method for replacing anode storing distributed data, the method comprising: receiving, by a first storage node, a first set of shares generated from a data file wherein each share in the first set includes a linear combination of pieces of the data file along with a set of coefficients used to generate the linear combination; receiving, by the first storage node, an indication of a new storage node replacing a failed node, the failed node including a second set of shares generated from the data file; generating, by the first storage node, a first replacement share responsive to the indication, wherein the first replacement share is generated by: multiplying each share in the first set and the set of coefficients by a random scaling value; and combining the multiplied first set of shares and the multiplied set of coefficients; and transmitting, by the first storage node, the generated first replacement share to the new storage node; wherein the first replacement share and at least one other replacement share form the second set of shares at the new storage node, the other replacement share generated by a second storage node.