She then calculates a "shared secret" by point-multiplying her ephemeral private key (e) with Bob's public key (P). This gives a shared point (known as "Z"). Here's the magic... this shared point (Z) is the SAME as if she had multiplied her private key (e), Bob's private key (p) and the cryptographic Generator point (G). But she calculated it using Bob's PUBLIC key. image

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Having calculated the shared secret and blinded the public keys using it, she then send Bob the ecash token, including the ephemeral PUBLIC KEY (E) that she created. image