1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
use super::engine_error;
use crate::specification::engines::AbstractEngine;
use crate::specification::entities::{LweCiphertextEntity, LweKeyswitchKeyEntity};
engine_error! {
LweCiphertextDiscardingKeyswitchError for LweCiphertextDiscardingKeyswitchEngine @
InputLweDimensionMismatch => "The input ciphertext LWE dimension and keyswitch key input LWE \
dimensions must be the same.",
OutputLweDimensionMismatch => "The output ciphertext LWE dimension and keyswitch output LWE \
dimensions must be the same."
}
impl<EngineError: std::error::Error> LweCiphertextDiscardingKeyswitchError<EngineError> {
/// Validates the inputs
pub fn perform_generic_checks<KeyswitchKey, InputCiphertext, OutputCiphertext>(
output: &OutputCiphertext,
input: &InputCiphertext,
ksk: &KeyswitchKey,
) -> Result<(), Self>
where
KeyswitchKey: LweKeyswitchKeyEntity,
InputCiphertext: LweCiphertextEntity,
OutputCiphertext: LweCiphertextEntity,
{
if input.lwe_dimension() != ksk.input_lwe_dimension() {
return Err(Self::InputLweDimensionMismatch);
}
if output.lwe_dimension() != ksk.output_lwe_dimension() {
return Err(Self::OutputLweDimensionMismatch);
}
Ok(())
}
}
/// A trait for engines keyswitching (discarding) LWE ciphertexts.
///
/// # Semantics
///
/// This [discarding](super#operation-semantics) operation fills the `output` LWE ciphertext with
/// the keyswitch of the `input` LWE ciphertext, using the `ksk` LWE keyswitch key.
///
/// # Formal Definition
///
/// ## LWE Keyswitch
///
/// This homomorphic procedure transforms an input
/// [`LWE ciphertext`](`crate::specification::entities::LweCiphertextEntity`)
/// $\mathsf{ct}\_{\mathsf{in}} =
/// \left( \vec{a}\_{\mathsf{in}} , b\_{\mathsf{in}}\right) \in \mathsf{LWE}^{n\_{\mathsf{in}}}\_
/// {\vec{s}\_{\mathsf{in}}}( \mathsf{pt} ) \subseteq \mathbb{Z}\_q^{(n\_{\mathsf{in}}+1)}$ into an
/// output [`LWE ciphertext`](`crate::specification::entities::LweCiphertextEntity`)
/// $\mathsf{ct}\_{\mathsf{out}} =
/// \left( \vec{a}\_{\mathsf{out}} , b\_{\mathsf{out}}\right) \in
/// \mathsf{LWE}^{n\_{\mathsf{out}}}\_{\vec{s}\_{\mathsf{out}}}( \mathsf{pt} )\subseteq
/// \mathbb{Z}\_q^{(n\_{\mathsf{out}}+1)}$ where $n\_{\mathsf{in}} = |\vec{s}\_{\mathsf{in}}|$ and
/// $n\_{\mathsf{out}} = |\vec{s}\_{\mathsf{out}}|$. It requires a
/// [`key switching key`](`crate::specification::entities::LweKeyswitchKeyEntity`).
/// The input ciphertext is encrypted under the
/// [`LWE secret key`](`crate::specification::entities::LweSecretKeyEntity`)
/// $\vec{s}\_{\mathsf{in}}$ and the output ciphertext is
/// encrypted under the [`LWE secret key`](`crate::specification::entities::LweSecretKeyEntity`)
/// $\vec{s}\_{\mathsf{out}}$.
///
/// $$\mathsf{ct}\_{\mathsf{in}} \in \mathsf{LWE}^{n\_{\mathsf{in}}}\_{\vec{s}\_{\mathsf{in}}}(
/// \mathsf{pt} ) ~~~~~~~~~~\mathsf{KSK}\_{\vec{s}\_{\mathsf{in}}\rightarrow
/// \vec{s}\_{\mathsf{out}}}$$ $$ \mathsf{keyswitch}\left(\mathsf{ct}\_{\mathsf{in}} , \mathsf{KSK}
/// \right) \rightarrow \mathsf{ct}\_{\mathsf{out}} \in
/// \mathsf{LWE}^{n\_{\mathsf{out}}}\_{\vec{s}\_{\mathsf{out}}} \left( \mathsf{pt} \right)$$
///
/// ## Algorithm
/// ###### inputs:
/// - $\mathsf{ct}\_{\mathsf{in}} = \left( \vec{a}\_{\mathsf{in}} , b\_{\mathsf{in}}\right) \in
/// \mathsf{LWE}^{n\_{\mathsf{in}}}\_{\vec{s}\_{\mathsf{in}}}( \mathsf{pt} )$: an [`LWE
/// ciphertext`](`LweCiphertextEntity`) with $\vec{a}\_{\mathsf{in}}=\left(a\_0, \cdots
/// a\_{n\_{\mathsf{in}}-1}\right)$
/// - $\mathsf{KSK}\_{\vec{s}\_{\mathsf{in}}\rightarrow \vec{s}\_{\mathsf{out}}}$: a
/// [`key switching key`](`crate::specification::entities::LweKeyswitchKeyEntity`)
///
/// ###### outputs:
/// - $\mathsf{ct}\_{\mathsf{out}} \in \mathsf{LWE}^{n\_{\mathsf{out}}}\_{\vec{s}\_{\mathsf{out}}}
/// \left( \mathsf{pt} \right)$: an
/// [`LWE ciphertext`](`crate::specification::entities::LweCiphertextEntity`)
///
/// ###### algorithm:
/// 1. set $\mathsf{ct}=\left( 0 , \cdots , 0 , b\_{\mathsf{in}} \right) \in
/// \mathbb{Z}\_q^{(n\_{\mathsf{out}}+1)}$
/// 2. compute $\mathsf{ct}\_{\mathsf{out}} = \mathsf{ct} -
/// \sum\_{i=0}^{n\_{\mathsf{in}}-1} \mathsf{decompProduct}\left( a\_i , \overline{\mathsf{ct}\_i}
/// \right)$
/// 3. output $\mathsf{ct}\_{\mathsf{out}}$
pub trait LweCiphertextDiscardingKeyswitchEngine<KeyswitchKey, InputCiphertext, OutputCiphertext>:
AbstractEngine
where
KeyswitchKey: LweKeyswitchKeyEntity,
InputCiphertext: LweCiphertextEntity,
OutputCiphertext: LweCiphertextEntity,
{
/// Keyswitch an LWE ciphertext.
fn discard_keyswitch_lwe_ciphertext(
&mut self,
output: &mut OutputCiphertext,
input: &InputCiphertext,
ksk: &KeyswitchKey,
) -> Result<(), LweCiphertextDiscardingKeyswitchError<Self::EngineError>>;
/// Unsafely keyswitch an LWE ciphertext.
///
/// # Safety
/// For the _general_ safety concerns regarding this operation, refer to the different variants
/// of [`LweCiphertextDiscardingKeyswitchError`]. For safety concerns _specific_ to an engine,
/// refer to the implementer safety section.
unsafe fn discard_keyswitch_lwe_ciphertext_unchecked(
&mut self,
output: &mut OutputCiphertext,
input: &InputCiphertext,
ksk: &KeyswitchKey,
);
}