MiMC with general degree e polynomial (MiMCGe)

This is a Computer Science Project for MSci. Mathematics and Computer Science degree at University of Birmingham.

The tool built for the project is a CLI which implements MiMC cipher but instead of x^3, taking a general polynomial x^e with an arbitrary exponent e. The tool allows to test diffusion, confusion and cipher efficiency. It also allows to run encryption/decryption for the cipher itself. Additionally, AES and original MiMC are implemented for comparison.

The full report for the project can be found here.

Running the script

First, you need to have rust with cargo installed.

Then build the optimized binary:

cargo build --release

This will create ./target directory with the compiled code. Now you can run the CLI tool to see all available options:

./target/release/mimcge --help

Options

The tool allows to test cipher:

• diffusion: additionally mean, sample standard deviation are provided for null hypothesis testing (chapter 3.2).
• confusion: additionally mean, sample standard deviation are provided for null hypothesis testing (chapter 3.2).
• enc-time: encrypting test-size number of plaintexts sample-size amount of times.
• dec-time: decrypting test-size number of ciphertexts sample-size amount of times.
• cipher-test: encrypts and decrypts random or given plaintext.
• generate-test-samples: provides an encrypted sequence from 0 to test-size for NIST STS testing.
• start-bit-stream: starts printing an encrypted sequence from 0 of 32-bit numbers for Dieharder testing.

Implemented ciphers for testing are AES, MiMC and MiMCGe which is the second argument for the tool.

Note: only a number of block sizes are implemented. This is because cipher operations are in GF(2^n) field, thus, for every different block size n, irreducible polynomial need to be provided. Moreover, AES implementation is provided by the crate, which allows only 128 bit block size.

Important remark

MiMCGe ciphers with powers of two exponent (x^2, x^4, etc.) are not secure. This is discussed in chapter 3.3 of the report.

Examples

• To test MiMCGe with polynomial x^5, block size of 17 and random plaintext:

./target/release/mimcge cipher-test mimcge 17 --exponent 5

• To provide specific round constants (this will determine number of rounds), key and plaintext. This way the ciphertext will always be the same. In this case, ciphertext will be 580:

./target/release/mimcge cipher-test mimcge 11 -e 5 -p 201 -k 11 -R 0 3 443 221 50

• To get MiMCGe with polynomial x^5 diffusion statistic of block_size 17 and 1000 plaintexts. This will also provide sample standard deviation together with mean and expected mean. These can be used to test null hypothesis, whether the test sample is significant enough.

./target/release/mimcge diffusion mimcge 17 --exponent 5 --test-size 1000