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On real quadratic number fields suitable for cryptography. (English) Zbl 1207.11107

Summary: We present empirical results that suggest that there are real quadratic fields with properties similar to imaginary quadratic fields in terms of size and structure of the class group. Therefore, these class groups can also be used for encryption schemes such as the ElGamal scheme, where up to now, only class groups of imaginary quadratic fields have been considered. Some security aspects are also addressed.

MSC:

11R11 Quadratic extensions
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
11Y40 Algebraic number theory computations
94A60 Cryptography
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