---
title: "BGV-multiply"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{BGV-multiply}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(polynom)
library(HomomorphicEncryption)
```

Set some parameters.
```{r params}
d  =   4
n  =   2^d
p  =   (n/2)-1
t  =   p
q  = 868
pm = GenPolyMod(n)
```

Set a working seed for random numbers
```{r}
set.seed(123)
```

Create the secret key and the polynomials a and e, which will go into the public key
```{r}
# generate a secret key
s = GenSecretKey(n)

# generate a
a = GenA(n, q)

# generate the error
e = GenError(n)
```

Generate the public key.
```{r}
pk0 = GenPubKey0(a, s, e*p, pm, q)
pk1 = GenPubKey1(a)
```

Create a polynomial message
```{r}
# create a message
m1 = polynomial( coef=c(1, 1, 1) )
m2 = polynomial( coef=c(0, 1   ) )
```

Create polynomials for the encryption
```{r}
# polynomials for encryption
e1 = GenError(n)
e2 = GenError(n)
u  = GenU(n)
```

Generate the ciphertext
```{r}
m1_ct0 = pk0*u + p*e1 + m1
m1_ct0 = m1_ct0 %% pm
m1_ct0 = CoefMod(m1_ct0, q)
  
m1_ct1 = pk1*u + p*e2
m1_ct1 = m1_ct1 %% pm
m1_ct1 = CoefMod(m1_ct1, q)

m2_ct0 = pk0*u + p*e1 + m2
m2_ct0 = m2_ct0 %% pm
m2_ct0 = CoefMod(m2_ct0, q)
  
m2_ct1 = pk1*u + p*e2
m2_ct1 = m2_ct1 %% pm
m2_ct1 = CoefMod(m2_ct1, q)
```

EvalMult
```{r}
multi_ct0 = m1_ct0 * m2_ct0
multi_ct0 = multi_ct0 %% pm
multi_ct0 = CoefMod(multi_ct0, q)
multi_ct0 = round(multi_ct0)

multi_ct1 = (m1_ct0 * m2_ct1 + m1_ct1 * m2_ct0)
multi_ct1 = multi_ct1 %% pm
multi_ct1 = CoefMod(multi_ct1, q)
multi_ct1 = round(multi_ct1)

multi_ct2 = (m1_ct1 * m2_ct1)
multi_ct2 = multi_ct2 %% pm
multi_ct2 = CoefMod(multi_ct2, q)
multi_ct2 = round(multi_ct2)
```

Decrypt
```{r}
decrypt = (multi_ct2 * s^2) + (multi_ct1 * s) + multi_ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)
decrypt = CoefMod(round(decrypt), p)
print(decrypt)
```
