Methods and apparatuses for providing cryptographic assurance based on ranges
as to whether a particular data item is on a list. According to one computer-implemented
method, the items on the list are sorted and ranges are derived from adjacent pairs
of data items on the list. Next, cryptographically manipulated data is generated
from the plurality of ranges. At least parts of the cryptographically manipulated
data is transmitted onto a network for use in cryptographically demonstrating whether
any given data item is on the list. According to another computer-implemented method,
a request message is received requesting whether a given data item is on a list
of data items. In response, a range is selected that is derived from the pair of
data items on the list that define the smallest range that includes the given data
item. A response message is transmitted that cryptographically demonstrates whether
the first data item is on the list using cryptographically manipulated data derived
from the range. According to another computer-implemented method, a request message
requesting an indication as to whether a first data item is on a list of data items
is transmitted. In response, a message is received that cryptographically demonstrates
whether the first data item is on the list, where the response message identifies
a range that is derived from the pair of data items on the list that defines the
smallest range that includes the first data item.
