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Advances, Systems and Applications

Table 1 The description of symbol

From: Privacy-preserving cloud-edge collaborative learning without trusted third-party coordinator

Symbols

Description

\(\boldsymbol{m}\)

A vector of messages \([ m_0, \cdots , m_{\frac{N}{2}-1} ]\)

\(\boldsymbol{m}{[j]}\)

The j-th message of \(\boldsymbol{m}\)

\([\![ \boldsymbol{m} ]\!]\)  

A ciphertext of \(\boldsymbol{m}\)

\(\textrm{M}\)

A list of vectors \(\{ \boldsymbol{m}_0, \cdots , \boldsymbol{m}_{n-1} \}\)

\(\textrm{M}{[j]}\)

The j-th vector of \(\textrm{M}\)

\(\textrm{M}{[i][j]}\)

The j-th message of the i-th vector of \(\textrm{M}\)

\(\mathbf{{M} }\)

A set of lists \(\{ \textrm{M}_0, \cdots , \textrm{M}_{n-1} \}\)

\(\mathbf{{M} }{[j]}\)

The j-th list of \(\mathbf{{M} }\)

\(\mathbf{{M} }{[i][j]}\)

The j-th vector of the i-th list of \(\mathbf{{M} }\)

\([\![ \textrm{M} ]\!]\)  

A list of ciphertexts \(\{[\![ \boldsymbol{m}_0 ]\!], \cdots , [\![ \boldsymbol{m}_{n-1} ]\!] \}\)  

\([\![ \textrm{M} ]\!]{[j]}\)  

The j-th ciphertext of \([\![ \textrm{M} ]\!]\)  

\([\![ \mathbf{{M} } ]\!]\)  

A set of lists \(\{[\![ \textrm{M}_0 ]\!], [\![ \textrm{M}_1 ]\!], \cdots , [\![ \textrm{M}_{n-1} ]\!] \}\)  

\([\![ \mathbf{{M} } ]\!]{[j]}\)  

The j-th list of \([\![ \mathbf{{M} } ]\!]\)  

\([\![ \mathbf{{M} } ]\!]{[i][j]}\)  

The j-th ciphertext of the i-th list of \([\![ \mathbf{{M} } ]\!]\)  

\(\boldsymbol{m}_0 + \boldsymbol{m}_1\)

Component-wise addition

\(\boldsymbol{m}_0 * \boldsymbol{m}_1\)

Component-wise multiplication

\(\boldsymbol{m}_0 - \boldsymbol{m}_1\)

Component-wise subtraction