A computer-implemented method of generating an elliptic curve cryptosystem (ECC) signature includes the steps of: generating a first random key (k1) having n bits, where n is a natural number; calculating a first ECC point (V) from k1 and a base point; and storing k1 and V securely in a computer-readable medium. To digitally sign electronic data, the method further includes the steps of generating a second random key (k2), where k2 has fewer than n bits; calculating a second ECC point (Q) from V and k2; and digitally signing electronic data using Q.