Table 2 Summary of notations

m

Original message

\({M}_{0}\), \({M}_{1}\)

Left and right half of a codeword

\({\textsf{M}}_{L}\), \({\textsf{M}}_{R}\)

Left and right half of the memory

\({\mathcal {O}}^{T}_{cnmc}(.,.)\)

Tampering oracle

\(\delta _{0}[]\), \(\delta _{1}[]\)

Stores tampering queries data

\(f_{0}\), \(f_{1}\)

Tampering functions

\({\mathcal {K}}\)

Key set

poly(n)

Polynomial function on input n

\(k \xleftarrow \$ {\mathcal {K}}\)

A key is selected

n

Security parameter

\({\mathcal {O}}^{l}(s, .)\)

Leakage oracle with s and \(\tau \) as input

\(\mu _{0}[]\), \(\mu _{1}[]\)

Stores leakage queries data

\(\alpha\)

Common reference string

\(\epsilon (n)\)

A negligible function

P(x; r)

A randomized algorithm

\({\mathbb {E}} \underset{s}{\approx }\ {\mathbb {F}}\)

Statistical indistinguishability

\({\mathcal {H}}_{\infty }(X)\)

Min-entropy

\(\tilde{{\mathcal {H}}}_{\infty }(X|Y)\)

Conditional average min-entropy

\(\tau ()\)

Arbitrary leakage function

\(\lambda\)

Label

\(\pi\)

Proof of a statement

\(S_{0}\), \(S_{1}\)

Two simulators

pk, sk

Public and private key pair

r

Randomness

\({\mathcal {R}}(m,w)\)

Relation

\({\mathfrak {D}}_{k}()\)

Block cipher decryption algorithm

\({\mathfrak {E}}_{k}()\)

Block cipher encryption algorithm

\(Enc_{k}()\)

CNMC encoding algorithm

\(Dec_{k}()\)

CNMC decoding algorithm

\({\mathcal {O}}_{prp}()\)

Pseudorandom permutation oracle

\({\mathcal {O}}_{R}()\)

Random permutation oracle

\(\mathfrak {Enc}^{lrs}\), \(\mathfrak {Dec}^{lrs}\)

lrs encoding and decoding algorithm