BLOCKCHAIN & WEB3 FUNDAMENTALS - Chapter 2, Exercise 3 Solution
==========================================================
Why ECDSA Over RSA for Bitcoin

PROBLEM
-------
Using this chapter's own RSA-vs-ECDSA comparison, explain why
Bitcoin's designers might have chosen ECDSA over RSA specifically, even
though both are legitimate ways to build a public/private key pair.

SOLUTION
--------
Both RSA and ECDSA give you the same basic capability this chapter
describes - a public/private key pair where signing is easy with the
private key and verification is easy with the public key, but forging
a signature without the private key is computationally infeasible.
They just get there through different hard mathematical problems: RSA
through the difficulty of factoring a large number back into its two
secret prime factors, and ECDSA through the elliptic curve discrete
logarithm problem.

The practical difference this chapter highlights is key size versus
security level. ECDSA reaches the same real-world security strength as
RSA while using dramatically shorter keys. For a general-purpose system
that just needs to sign one thing occasionally, this difference might
not matter much. But Bitcoin is a network processing and permanently
storing millions of signed transactions, forever, on every single full
node that chooses to keep a complete copy of the chain.

Shorter keys and shorter signatures under ECDSA directly translate to:
- less data that has to be transmitted with every transaction,
- less permanent storage every node needs to hold onto,
- faster verification, since there's simply less mathematical work to
  check per signature.

At Bitcoin's real scale - a shared, replicated, permanently-growing
ledger - those savings compound across millions of transactions and
thousands of independent nodes, in a way they wouldn't for a one-off
signed document.

ANSWER: RSA and ECDSA are both legitimate, secure ways to build the
same kind of key pair, but ECDSA achieves equivalent security with
much shorter keys and signatures - a real, practical efficiency
advantage that matters enormously at the scale of a blockchain network
storing and verifying huge numbers of signatures forever, which is
almost certainly why Bitcoin's designers chose it over RSA.

----
WHY THIS WORKS AS AN ANSWER

This applies the chapter's own stated efficiency advantage (shorter
keys, same security) to the actual real-world constraint a blockchain
network faces (permanent, replicated storage of huge numbers of
signatures), rather than treating the RSA/ECDSA choice as arbitrary.