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Which BigInteger is needed for implementing SHA-256? SHA-256 has 64 hex symbols as output. I could use the data structure "string" to calculate the SHA-256 or a BigInteger.

Do I need uint256_t in the programming language C++ because I have 256 bits (0 and 1) and so the numbers from 0 to $2^{256} - 1$?

I first implemented SHA-256 with strings as variables and implemented functions for addition of two strings and so on. But maybe it is faster to implement SHA-256 with BigIntegers?

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SHA-256 operates on 32-bit integers, with each 32-bit integer mapping to 4 bytes (big-endian). The 64-byte input block is turned into 16 32-bit integers (uint32_t[16]), the 32-byte state/output represents 8 32-bit integers (uint32_t[8]). At no point does SHA-256 use big integers.

SHA-512 is similar, but uses 64-bit integers instead.

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