  Homomorphic encryption (HE) has found extensive utilization in federated
learning (FL) systems, capitalizing on its dual advantages: (i) ensuring the
confidentiality of shared models contributed by participating entities, and
(ii) enabling algebraic operations directly on ciphertexts representing
encrypted models. Particularly, the approximate fully homomorphic encryption
(FHE) scheme, known as CKKS, has emerged as the de facto encryption scheme,
notably supporting decimal numbers. While recent research predominantly focuses
on enhancing CKKS's encryption rate and evaluation speed in the context of FL,
the search operation has been relatively disregarded due to the tendency of
some applications to discard intermediate encrypted models. Yet, emerging
studies emphasize the importance of managing and searching intermediate models
for specific applications like large-scale scientific computing, necessitating
robust data provenance and auditing support. To address this, our paper
introduces an innovative approach that efficiently searches for a target
encrypted value, incurring only a logarithmic number of network interactions.
The proposed method capitalizes on CKKS's additive and multiplicative
properties on encrypted models, propagating equality comparisons between values
through a balanced binary tree structure to ultimately reach a single
aggregate. A comprehensive analysis of the proposed algorithm underscores its
potential to significantly broaden FL's applicability and impact.
