Cryptography in an unbounded computational model

Abstract

We investigate the possibility of cryptographic primitives over nonclassical computational models. We replace the traditional finite field F*n with the infinite field Q of rational numbers, and we give all parties unbounded computational power. We also give parties the ability to sample random real numbers. We determine that secure signature schemes and secure encryption schemes do not exist.We then prove more generally that it is impossible for two parties to agree upon a shared secret in this model. This rules out many other cryptographic primitives, such as Diffie-Hellman key exchange, oblivious transfer and interactive encryption.