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Book Chapter10.1007/978-3-322-84957-1_30

A Survey of Cryptosystems Based on Imaginary Quadratic Orders

Detlef Hühnlein-2000-01-01
2

TL;DRAbstract

Since nobody can guarantee that popular public key cryptosystems based on factoring or the computation of discrete logarithms in some group will stay secure forever, it is important to study different primitives and groups which may be utilized if a popular class of cryptosystems gets broken. A promising candidate for a group in which the DL-problem seems to be hard is the class group’ Cl(Δ) of an imaginary quadratic order, as proposed by Buchmann and Williams [BuWi88].Recently this type of group has obtained much attention, because there was proposed a very efficient cryptosystem based on non-maximal imaginary quadratic orders [PaTa98a], later on called NICE (for New Ideal Coset Encryption) with quadratic decryption time. To our knowledge this is the only scheme having this property. First implementations show that the time for decryption is comparable to RS A encryption with e = 216 +1. Very recently there was proposed an efficient NICE-Schnorr type signature scheme [HuMe99] for whic

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Since nobody can guarantee that popular public key cryptosystems based on factoring or the computation of discrete logarithms in some group will stay secure forever, it is important to study different primitives and groups which may be utilized if a popular class of cryptosystems gets broken. A promising candidate for a group in which the DL-problem seems to be hard is the class group’ Cl(Δ) of an imaginary quadratic order, as proposed by Buchmann and Williams [BuWi88].Recently this type of group has obtained much attention, because there was proposed a very efficient cryptosystem based on non-maximal imaginary quadratic orders [PaTa98a], later on called NICE (for New Ideal Coset Encryption) with quadratic decryption time. To our knowledge this is the only scheme having this property. First implementations show that the time for decryption is comparable to RS A encryption with e = 216 +1. Very recently there was proposed an efficient NICE-Schnorr type signature scheme [HuMe99] for whic

Keywords

CryptosystemHybrid cryptosystemDiscrete logarithmMathematicsThreshold cryptosystemQuadratic equationThe ImaginaryQuadratic field

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