  Since ML algorithms have proven their success in many different applications,
there is also a big interest in privacy preserving (PP) ML methods for building
models on sensitive data. Moreover, the increase in the number of data sources
and the high computational power required by those algorithms force individuals
to outsource the training and/or the inference of a ML model to the clouds
providing such services. To address this, we propose a secure 3-party
computation framework, CECILIA, offering PP building blocks to enable complex
operations privately. In addition to the adapted and common operations like
addition and multiplication, it offers multiplexer, most significant bit and
modulus conversion. The first two are novel in terms of methodology and the
last one is novel in terms of both functionality and methodology. CECILIA also
has two complex novel methods, which are the exact exponential of a public base
raised to the power of a secret value and the inverse square root of a secret
Gram matrix. We use CECILIA to realize the private inference on pre-trained
RKNs, which require more complex operations than most other DNNs, on the
structural classification of proteins as the first study ever accomplishing the
PP inference on RKNs. In addition to the successful private computation of
basic building blocks, the results demonstrate that we perform the exact and
fully private exponential computation, which is done by approximation in the
literature so far. Moreover, they also show that we compute the exact inverse
square root of a secret Gram matrix up to a certain privacy level, which has
not been addressed in the literature at all. We also analyze the scalability of
CECILIA to various settings on a synthetic dataset. The framework shows a great
promise to make other ML algorithms as well as further computations privately
computable by the building blocks of the framework.
