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Well, I'd like to let you do the necessary web research for the protocol and documentation to flash the user program and other memory regions. If you find something, please edit your question to add the URLs.
Instead of looking for a way to crack the communication, did you consider to crack the read-out protection of the 8052's flash memory? An astonishing high number of MCUs can be cracked.
Welcome to SE/RE! Please edit your question to add links to any documentation (descriptions, images, whatever you have) of the board and the sensors. -- What did you try for now? Did you record raw data or waves? Did you start to draw a (partial) schematic? What kind of device uses this board for what purpose?
If the input is longer than the hash, there need to be multiple different inputs resulting in the same output. However, finding them is deliberately most costly.
Are you aware that hash value do not contain the input data? A hash function maps the input data to a number, in this case 256 bits wide. SHA was invented to make finding data with the same hash value most difficult. What did your own web research reveal, and why did it not help you? What is the underlying actual problem you try to solve?
@DaveInPA What 4 pins do you mean? There are (beside ground) "select" (could be optimized away), "clock", and "data." The clock frequency can be anything. But SPI transmits commonly multiples of 8 bits, so this might indeed not be SPI.
If you are still after this, please edit your question to add a link to the MCU's programmer's manual and the waves from your scope. These "non-digital" signals might just be caused by the R-C networks.
Did you try these? 1) Depending on the format of the image file: Since you (need to) know the target, you can research the offset of the firmware image. 2) Assume that the image begins with the first mapped code. -- I'd think that a map file will show absolute addresses, not offsets.
In the case shown in the question it is not .data but .rodata. The data type does not have any effect of the segment, it depends on being writable or not.