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Does anyone know any cryptographic methods that do not use prime numbers? If so, which ones?

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  • $\begingroup$ A little bit more seriously.. Prime numbers are involved in some trapdoor functions (base for asymmetric cryptography such as RSA or ECC) . Other crypto primitives are not related to primes (well - there is non-negligible probability you will stump on a prime number) $\endgroup$
    – gusto2
    Dec 21, 2017 at 9:28
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    $\begingroup$ A better question might be are there any(asymetric) cryptographic primitives which do not rely on (continue with one of these): a. arithmetic over prime field, arithmetic over finite field. b. Discrete logarithm hardness. c. Number theory. $\endgroup$
    – Meir Maor
    Dec 21, 2017 at 9:41
  • $\begingroup$ Thank you or this. Please see the scenario: One of the first items on your agenda is the restoration of online fiscal transactions, more specifically credit card transactions (though you can assume that, along with modification to your solution, this will be used for online stock trading). In this specific scenario there are three players in said transaction, the customer, the seller and the bank. For simplification, the seller and customer will be holding accounts at the same bank which is/ can be queried for verification. Can anyone suggest? $\endgroup$
    – Axioms
    Dec 21, 2017 at 22:36
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    $\begingroup$ I cannot see any relation between this scenario and the question you asked... $\endgroup$
    – Geoffroy Couteau
    Dec 22, 2017 at 0:47
  • $\begingroup$ @MeirMaor Not really sure if that actually makes a “better question“, but here goes… ;) $\endgroup$
    – e-sushi
    Dec 27, 2017 at 17:01

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There is none. All cryptography involves the number 2, which is prime, whenever dealing with information in strings of bits—or in esoteric cases like ROT13, well, there's a prime number right there, 13, not to mention that 26, the size of the alphabet on which ROT13 works, is the product of primes 2 and 13.

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    $\begingroup$ (Note in addition that the total number of characters in your answer plus in my comment is the number 431, which is prime) $\endgroup$
    – Geoffroy Couteau
    Dec 20, 2017 at 23:38
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    $\begingroup$ Every possible alphabet size is obtained as a product of primes; that's not a particularly remarkable property. $\endgroup$
    – Federico Poloni
    Dec 27, 2017 at 18:58

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