BLOCKCHAIN & WEB3 FUNDAMENTALS - Chapter 2, Exercise 2 Solution
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Correcting "A Signature Is Just Encrypting With Your Private Key"

PROBLEM
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A colleague says: "A digital signature works like encrypting the
message with your private key so only you could have sent it."
Identify exactly what's wrong with this description and correct it
using this chapter's own actual sign/verify process.

SOLUTION
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The colleague has the right general instinct - the private key really
is what proves you sent something - but the specific mechanism
described is backwards and, for a real scheme like ECDSA, not
technically accurate.

What's wrong:
1. Digital signing is not simply "encrypting the message." A signature
   is produced by running the message (or, more precisely, its hash)
   together with the private key through a signing algorithm - the
   output is a signature value, not an encrypted, unreadable version of
   the original message. Anyone can still read the original message in
   plain form; the signature is a separate, attached piece of proof.
2. "Only you could have sent it" also skips a step: it's not the act of
   signing alone that proves this, it's the fact that anyone can then
   take your public key and independently check the signature against
   the message. If that check passes, it's mathematically infeasible
   for anyone who doesn't know your private key to have produced a
   signature that would pass.

Corrected process, per this chapter:
- The signer uses their PRIVATE key together with the message to
  produce a signature.
- Anyone holding the signer's PUBLIC key can verify that signature
  against the message, without ever needing the private key themselves.
- Nobody lacking the private key can forge a signature that will pass
  verification.

ANSWER: A digital signature isn't the message encrypted with the
private key - it's a separate value computed from the message and the
private key together, which anyone can then verify against the signer's
public key. The message itself stays fully readable throughout; only
the ability to produce a passing signature is restricted to whoever
holds the private key.

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WHY THIS WORKS AS AN ANSWER

This catches a genuinely common informal misconception about how
signatures work (conflating "signing" with "encrypting") and replaces
it with the chapter's own precise three-step sign/verify/forge-resistant
description.