Dungeon Master's tables of FHE things When using a plain modulus large enough for batching, generating relin keys fails at N=1024,2048.
Noise budget impact at minimum plain modulus to support batching of a single operation
n
Add
Mul+relin
1024
N/A
N/A
2048
N/A
N/A
4096
~0
~26
8192
~0
~28
16384
~0
~29
32768
~0
~30
Noise budget at minimum plain modulus to support batching
n
1024
2048
4096
8192
16384
32768
bits
N/A
N/A
49
149
365
800
Precise sizes may vary with RNG.
Some keys fail to generate for some poly degrees (marked as N/A).
Coefficient modulus is default for 128-bit security.
Plain modulus = 1,000,000. (Should have no effect)
Poly degree
1024
2048
4096
8192
16384
32768
secret key
4.17 kiB
15.15 kiB
68.60 kiB
264.46 kiB
1,004.55 kiB
3.77 MiB
public key
8.41 kiB
30.19 kiB
130.92 kiB
529.19 kiB
1.96 MiB
7.53 MiB
compact public key
4.27 kiB
15.22 kiB
68.69 kiB
264.50 kiB
1,004.58 kiB
3.77 MiB
relin keys
N/A
N/A
270.42 kiB
2.07 MiB
15.69 MiB
113.02 MiB
compact relin keys
N/A
N/A
131.21 kiB
1.03 MiB
7.85 MiB
56.51 MiB
Galois keys
N/A
N/A
5.79 MiB
49.65 MiB
408.23 MiB
3.09 GiB
compact Galois keys
N/A
N/A
N/A
N/A
N/A
N/A
Precise sizes may vary with RNG.
Coefficient modulus is default for 128-bit security.
Plain modulus = 1,000,000. (Should have no effect)
Poly degree
1024
2048
4096
8192
16384
32768
secret key
8.42 kiB
30.19 kiB
86.45 kiB
422.24 kiB
1.74 MiB
7.06 MiB