# Ecash - Probability of catching a user using secret splitting who duplicates the coin

For detecting double spending, secret splitting is used. If a user duplicates the coin, then there will be two different transaction items in transaction list. What is the probability of catching a user who duplicates the coin using this technique?

To clarify:

https://www.cs.bham.ac.uk/~mdr/teaching/modules03/security/students/SS4/DigitalCash.pdf shows on slide 13 of 17 that the probability of catching a user is $1-(\frac{1}{2})^n$ where $n$ is the number of identity pairs used in the transaction item. But how do you calculate it?

• "How do you calculate it" Calculate $1 - (1/2)^n$ ? Or do you mean how do you detect the double spending? – cypherfox Mar 10 '18 at 15:19
• If you're still interested in e-cash, here is something modern: ia.cr/2015/972 – cypherfox Mar 10 '18 at 15:21