Avoid A Message To Be Validated Differently
One problem which arises especially for small M is, that the number of incorrect keys different recipients measure differ with probability. So to define only one threshold is not enough, because it would cause a message to be validated differently, when the number of incorrect keys r is very close to the defined threshold.
This can be prevented by defining more than one threshold. Because the number of errors increase proportional with M, the thresholds are defined like
- Acceptance
- Rejection
- If the number of incorrect keys r is below, then the bit is valid with high probability
- If the number of incorrect keys r is above, then the bit is faked with high probability
- If the number of incorrect keys r is in-between both thresholds, then the recipient cannot be sure, if another recipient gets the same outcome, when validating the bit. Furthermore he can't be even sure, if he validated the message right.
If we assume perfect channels without noise, so the bit can't be changed due to the transfer, then the threshold can be set to zero, because the swap test passes always, when the compared states are the same
Read more about this topic: Quantum Digital Signature
Famous quotes containing the words avoid, message, validated and/or differently:
“While I do not suggest that humanity will ever be able to dispense with its martyrs, I cannot avoid the suspicion that with a little more thought and a little less belief their number may be substantially reduced.”
—J.B.S. (John Burdon Sanderson)
“I believe in Michael Angelo, Velasquez, and Rembrandt; in the might of design, the mystery of color, the redemption of all things by Beauty everlasting, and the message of Art that has made these hands blessed.”
—George Bernard Shaw (1856–1950)
“Unlike femininity, relaxed masculinity is at bottom empty, a limp nullity. While the female body is full of internal potentiality, the male is internally barren.... Manhood at the most basic level can be validated and expressed only in action.”
—George Gilder (b. 1939)
“The new concept of the child as equal and the new integration of children into adult life has helped bring about a gradual but certain erosion of these boundaries that once separated the world of children from the word of adults, boundaries that allowed adults to treat children differently than they treated other adults because they understood that children are different.”
—Marie Winn (20th century)