Security of Multi-Adjustable Join Schemes: Separations and Implications

Database management systems (DBMS) are one of cloud services with major applications in industry and business. In the use of such services, since the cloud service provider cannot be entrusted with the plain data, the databases are typically encrypted prior to outsourcing. One of the most challenging issues in designing these services is supporting SQL join queries on the encrypted database. The multi-adjustable join scheme (M-Adjoin) [Khazaei-Rafiee 2020], an extension of Adjoin [Popa-Zeldovich 2012 and Mironov-Segev-Shahaf 2017], is a symmetric-key primitive that supports the join queries for a list of column labels on an encrypted database. In previous works, the following security notions were introduced for
$\text{Adjoin}$
and
$\text{M-Adjoin}$
schemes:
$\mathtt {3Partition}$
,
$\mathtt {M3Partition}$
and
$\mathtt {M3P}_{k}$
, for every integer
$k$
. In this article, we first extend the simulation-based and indistinguishability-based security notions for
$\text{Adjoin}$
, defined by Mironov
et al.
, to
$\text{M-Adjoin}$
. Then, we study the relations between all these security notions for
$\text{M-Adjoin}$
. In particular, some non-trivial relations are proved which resolve some open problems raised by Mironov
et al.