Embodiments of the invention discloses a system and a method for determining an encrypted edit distance as an encryption of a minimum cost of transformation of a first sequence into a second sequence based on an insertion cost, a deletion cost, and a substitution cost. The method determines recursively a current element of the matrix as an encryption of a minimum of a first element, a second element, and a third element to produce the dynamic programming solution, wherein the first element represents the insertion cost, the second element represents the deletion cost, and the third element represents the substitution costs, and wherein the current element, the first element, the second element, and the third element are homomorphically encrypted with a public key; and selects the dynamic programming solution as the encrypted edit distance, wherein steps of the method are performed by a first processor and a second processor.