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A simple mobile e-cash system with observers satisfying e-cash divisibility, partial anonymity, off-line payment, transferability and double-spending prevention requirements is presented. The proposed e-cash system is based on two well-known cryptographic primitives, namely ElGamal signature along with Schnorr identification protocols. Therefore, it can be considered simple in the sense of implementation and security considerations. The traditional and elliptic curve realizations of e-money system are presented. The system employs observers, i.e. cryptographic bank chips implemented in customer's payment device (e.g. smart phone) in order to avoid the increase in the size of transferred e-cash data, which is a major flaw of most divisible, anonymous, off-line and transferable e-cash systems. The security of the proposed e-money system is based on discrete logarithm problems in cyclic and elliptic curve groups. The system's security against chosen message attack is provided.

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In our previous paper we presented an offline e-cash system with observers. We have shown that the proposed system satisfies basic requirements for e-cash schemes. We also covered such security issues as chosen message attack resistance and forgery of protocols data. However, in that paper we focused more on the system itself, rather than its analysis.Hence, here we present cryptanalysis of our system. We aim to prove that existential forgery of data is not possible due to complexity of the discrete logarithm problem. Furthermore, we perform the analysis of trustworthiness of the system using the so-called BAN logic. Also, we consider effectivity of the proposed e-cash system in observers with limited computational resources.