In the field of cryptography, using space-time tradeoff, the attacker is decreasing the exponential time required for a brute force attack. use partially precomputed values in the hash space of a cryptographic hash function to crack passwords in minutes instead of weeks. Decreasing the size of the rainbow table increases the time required to iterate over the hash space. The meet-in-the-middle attack attack uses a space-time tradeoff to find the cryptographic key in only formula_1 encryptions (and formula_2 space) compared to the expected formula_3 encryptions (but only formula_4 space) of the normal attack. 