Given a set of SHA1 hash code, if we knew a portion of the plaintext for each particular hash code, and also the remaining portion of the plaintext is a constant value for each hash code. Is it possible for us to recover what is the constant value?
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Yes, but unless there is a significant break through in the crypto-analysis of SHA-1, the only way to retrieve the constant value is by brute forcing it. In other words, trying all the values, calculating the SHA-1 over the plaintext and the constant and comparing it with the given hash value.