Threshold Cryptography based on class groups of imaginary quadratic fields
Guilhem Castagnos  1  
1 : Université de Bordeaux
Université de Bordeaux (Bordeaux, France)

More than 30 years ago, Buchmann and Williams proposed to use ideal class groups of imaginary quadratic fields in cryptography, with a key exchange protocol similar to Diffie-Hellman. After several twists and turns, there has been a renewed interest in this field in recent years. This renaissance is mainly due to two characteristics. First, these class groups allow the design of cryptographic protocols that do not require a trusted third party for the generation of public parameters. Second, these groups allow the instantiation of a general-purpose encryption scheme, CL, linearly homomorphic modulo a prime number, which has found many applications. In this talk, I will give an overview of threshold linearly homomorphic encryption, give a brief introduction to class groups and CL and present a threshold variant.


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