How does your chain get the back-step value when a new block is calculated? A specially protected back-step generator was invented to calculate the required values. Of course we cannot break the rules of mathematics, but with a few ideas you can pre-calculate the required value just in time.
The back-step blockchain produces a finite number of blocks. The number is a configuration parameter and you can define before you run the chain the first time. This number can be very, very huge. A blockchain for a bank may run for 20 years and generate 5000 blocks every second before it runs out of values.
Before you use the chain the first time it runs through all values, using a dedicated hardware. At certain points checkpoint values are recorded in a non-volatile memory. When the generator reaches the end, just after the last checkpoint a cleverly designed volatile back-step cache is used to cache the values soon needed. While blocks are generated, the generator refills the cache automatically.
A reference design uses 32 kB of volatile cache RAM and 3 MB of flash. The recipe includes a FPGA chip with our specially programmed hardware logic. A dedicated security chip and a low power CPU with USB controller completes our recipe. Now comes a lot of programming to implement a lot of logic into a small piece of hardware. As long as back-step values are not used in blocks they are secret. Security and speed were the motivation why we produce the Back-Step Blockchain as a hardware product.
See how we stop the bad guy.