Search results
Results from the WOW.Com Content Network
Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] Euclid proved c. 300 BCE that every Mersenne prime M p = 2 p − 1 has a corresponding perfect number M p ...
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
However, starting in the mid-1990s, crypto protocols were analyzed in operational models (assuming perfect cryptography) using model checkers, and numerous bugs were found in protocols that were "verified" with BAN logic and related formalisms.
This is an accepted version of this page This is the latest accepted revision, reviewed on 7 January 2025. Practice and study of secure communication techniques "Secret code" redirects here. For the Aya Kamiki album, see Secret Code. "Cryptology" redirects here. For the David S. Ware album, see Cryptology (album). This article needs additional citations for verification. Please help improve ...
Computational hardness assumptions are of particular importance in cryptography. A major goal in cryptography is to create cryptographic primitives with provable security. In some cases, cryptographic protocols are found to have information theoretic security; the one-time pad is a common example. However, information theoretic security cannot ...
In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k , a number n is called k -perfect (or k -fold perfect) if the sum of all positive divisors of n (the divisor function , σ ( n )) is equal to kn ; a number is thus perfect if and ...
This concept is the computational complexity analogue to Shannon's concept of perfect secrecy. Perfect secrecy means that the ciphertext reveals no information at all about the plaintext, whereas semantic security implies that any information revealed cannot be feasibly extracted. [2] [3]: 378–381
An example of an information-theoretically hiding commitment scheme is the Pedersen commitment scheme, [18] which is computationally binding under the discrete logarithm assumption. [19] Additionally to the scheme above, it uses another generator h of the prime group and a random number r. The commitment is set =. [20]