EXERCISE 1 — Hashing and the avalanche effect
==============================================

Commands:
  echo "transfer 100 dollars" | sha256sum
  echo "transfer 900 dollars" | sha256sum

Example output:
  9e2... (64 hex characters)   <- for "100 dollars"
  41a... (64 hex characters)   <- for "900 dollars"

(openssl equivalent, if sha256sum isn't present):
  echo "transfer 100 dollars" | openssl dgst -sha256
  echo "transfer 900 dollars" | openssl dgst -sha256

WHAT YOU OBSERVE:
  - Both digests are EXACTLY 64 hex characters (256 bits) — the output
    size is fixed regardless of input length. Hash a 1-line string or a
    1 GB file: still 64 hex chars.
  - Changing just "1" -> "9" produces a COMPLETELY different digest, with
    no resemblance to the first. That is the AVALANCHE EFFECT: a one-bit
    input change flips, on average, half the output bits.

WHY THIS MATTERS FOR INTEGRITY:
  - If you know the expected digest of some data, you can re-hash what you
    actually received and compare. Even the tiniest alteration (one digit
    in a payment amount) yields a totally different digest, so tampering
    is impossible to hide by making a "small, similar" change.
  - This is the basis of integrity checking — but remember (Chapter 2
    warning): because the hash function is public and keyless, an attacker
    who changes the data can also recompute a matching digest. A bare hash
    only protects integrity if the digest itself reaches you untampered.
    Binding integrity to a sender needs a key -> a MAC.

NOTE: piping `echo` includes a trailing newline in the input, so your
exact digits will differ from any reference — what matters is the two
properties (fixed length, total change), not the specific hex value.