tools

HE Tools

The tools for hekit consist of useful commands for finding HE parameters based on user constraints. The following sections describe their details and usage.

Dependencies

• python >= 3.8

gen-primes

The command hekit gen-primes generates a list of sorted primes in range [n, m] where n and m are positive integers.

Options

The gen-primes command can be executed with the following options.

Option	Meaning
-h, help	Show the help message.
start	start number.
stop number	stop number.

Running

To run the tool, simply provide start and stop arguments. For example:

hekit gen-primes 1 100

algebras

The command hekit algebras given the plaintext prime p and the required number of p-boxes d returns the available algebras.

Options

The algebras command can be executed with the following options.

Option	Meaning
-h, help	Show the help message.
-p	Define plaintext prime. Default value is 2.
-d	Define number of coefficients in a slot. Default value is 1.
--no-corrected	Include corrected d orders.
--no-header	Do not print headers.

The primes that can be used are only those provided in the ~/.hekit/primes.txt file. If the file is not created by the user, it will be autogenerated with primes in range [2, 140 000]

Running

To run the tool, simply provide a single prime or a range where primes may be, or a combination of the two. For example, searching for algebras where the prime is 2, those between 11 and 25 inclusive, and 31.

hekit algebras -p 2,11-25,31

Searching for algebras that give d larger than 1 simply pass the flag and argument in a similar manner to p. For example, searching algebras with the same p, but with d values of 2 and between 4 to 5, inclusive.

hekit algebras -p 2,11-25,31 -d 2,4-5

For more information run

hekit algebras -h

Result

The table retuned by the searches have the following column headers shown below with their meanings,

Header	Meaning
p	plaintext prime
d	number of coefficients in a slot (a.k.a. p-boxes)
m	order of the cyclotomic polynomial
phi(m)	the Euler totient of m which is the degree of the ciphertext and plaintext polynomial
nslots	the number of slots in a ciphertext and plaintext polynomial (phi(m) / d)