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xkcd #2912: Cursive Letters
(imgs.xkcd.com)
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Although cursive has a unified design, everyone writes cursive a little differently. The idea is that cursive is designed to write whole words in a single stroke. The concept of a secure signature in cursive is that the more work a single stroke is, the more uniquely a person writes it.
That is to say, even though you may have the same name as someone else, it's extremely unlikely that a person can copy your nuances precisely enough to forge your signature on the fly. It isn't a perfect system, but it's easy enough to verify a signature that people could do it before technology was around to aid that process.
That concept is also why they say the actual design of your signature is less important than the consistency of doing it the same every time.
There was some guy years and years ago who tried to see how ridiculous he could make his signature and have a store still accept it. As I recall he got to the point of drawing pictures on the receipt. Eventually he tried to buy something expensive like a TV for +1000 bucks before someone finally said something.
Of course now that search engines suck I'm having trouble finding the writeup he did.
At one time illiterate people could just mark an X. The security of a signature isn't really in it's uniqueness or it's relationship with your name. Security of a signature is down to the fact that you could to prison for forgery if you fake someone else's signature.