In one embodiment, a method, system, and apparatus are described, the method, system, and apparatus including generating metadata to be associated with each block of a series of blocks, the generating including, except for an initial block, receiving: a first block, including a signed block, and a second block to be signed, retrieving a first value including a square of a random number, R′2, multiplying R′2 by a nonce, r, and setting r·R′2 to be a square of a first random number, denoted R2, for the second block, retrieving a second value from the first block, the second value including K-bit vector, E′, determining a bit string value of the second block, M, computing E=hash(R2∥M∥E′), and determining a signature, Sig, for the second block by calculating Sig=r Sig′ SE-E′. Related methods, systems, and apparatuses are also described.