Space efficient method of verifying electronic payments

A method of using a machine to verify electronic payments generated by a customer using a private key, the machine including a memory storing instructions of the method in machine readable form, the method comprising:

• receiving from a bank a first set of k electronic verifiers for a first set of k electronic payments from the customer and a conversation key, each verifier allowing authentication of its associated electronic payment without revealing the private key;
• receiving from the bank a summary verifier for a second group of electronic payments;
• transmitting payment information to the customer for use in generating electronic payments;
• the payment information including an initializing payment and a first value of a payment index, each value of the payment index associating an electronic payment with a verifier;
• receiving a request from the customer and an electronic payment;
• receiving from the customer along with the electronic payment having a second value of the payment index a verifier having a third value of the payment index, the third value being greater than the second value;
• storing the verifier;
• authenticating the electronic payment using one of the verifiers by comparing a first hash of a first string including the electronic payment to a verifier having an associated value of the payment index equal to the second value of the payment index;
• and
• responding to the request if the electronic payment is authenticated.

An article of manufacture comprising:

• a memory;
• and
• instructions stored in the memory in machine readable form for a method of verifying electronic payments generated by a customer using a private key, the method comprising:
• receiving from a bank a first set of electronic verifiers for a first set of electronic payments from the customer, each verifier allowing authentication of an associated electronic payment without revealing the private key;
• selecting from the first set of verifiers a random subset of verifiers and storing in the memory only the random subset of verifiers;
• transmitting to the customer payment information for use in generating electronic payments;
• receiving a request from the customer and an electronic payment;
• determining whether the electronic payment will be authenticated by searching the memory for an associated verifier;
• authenticating the electronic payment using an associated verifier;
• and
• responding to the request if the electronic payment is authenticated.

An article of manufacture comprising:

• a memory;
• and
• instructions stored in the memory in machine readable form for a method of verifying electronic payments generated by a customer using a private key, the method comprising:
• receiving from a bank a first set of electronic verifiers for a first set of electronic payments from the customer, each verifier allowing authentication of an associated electronic payment without revealing the private key;
• receiving from the bank a summary verifier for a second group of electronic payments;
• transmitting to the customer payment information for use in generating electronic payments;
• receiving a request from the customer and an electronic payment;
• receiving from the customer along with the electronic payment a verifier for a third electronic payment;
• storing the verifier in the memory;
• authenticating the electronic payment using an associated verifier;
• and
• responding to the request if the electronic payment is authenticated.