CLT13

This is an Implementation of the CLT13 multilinear map specialized for obfuscation purposes.

General Intuition

Our CLT13 implementation provides the following functionality. One party can create a secret key that allows them to create encodings of messages and to create a public key. The public key allows another party to add and multiply encodings.

The public key also provides zero-testing of encodings who are at the top-level index. This "top-level index" means something specific: every encoded message has some index. The encoding that results from multiplying two messages will be at the union of the two multiplicands' indices. Two encodings can be added only if they share the same index. Zero-testing will fail unless an encoding is at some predefined top-level index.

Asymmetric Modification

This implementation has been modified to support asymmetric index sets. That is, where the original design operates over levels 1 through kappa, our design uses distinct index sets. In the original CLT13, there is a single z whose powers represent the encoding levels. In our modified version, we produce multiple zs, one for each distinct index.

The top-level index can be any combination of powers of indices. This top-level index must be given as the pows argument to clt_state_init. It is used to create the zero-testing parameter. Each slot i in the pows array represents the power of that z_i in the top-level index set.

Usage Overview

Use clt_state_init to create a secret key. Parameters here: kappa is the maximum multiplicative degree allowed (used to determine the size of the noise), lambda is the security parameter, nzs is the number of distinct indices, pows is the top-level index. Using a clt_state, one can create a clt_pp public key using clt_pp_init, or create encodings using clt_encode. In addition, there are a number of optimizations and options you can set using flags. These are documented in the code.

Example Usage

    unsigned long kappa = 2;
    unsigned long lambda = 40; 

    // initialize the rng
    aes_randstate_t rng;
    aes_randinit(rng);

    // create the top-level index
    int top_level [nzs];
    for (ulong i = 0; i < nzs; i++) 
        top_level[i] = 1;

    // initialize the secret key
    clt_state mmap;
    clt_state_init(&mmap, kappa, lambda, nzs, pows, NULL, rng);

    // create the public key from the secret key
    clt_pp pp;
    clt_pp_init(&pp, &mmap);

    // initialize the plaintexts
    mpz_t x [1];
    mpz_init_set_ui(x[0], 1);
    mpz_t y [1];
    mpz_init_set_ui(y[0], 1);

    // create encodings
    clt_elem x0, x1, xp;
    clt_elem_init(x0);
    clt_elem_init(x1)
    clt_elem_init(xp);
    clt_encode(x0, &mmap, 1, x, top_level, rng);
    clt_encode(x1, &mmap, 1, y, top_level, rng);

    // add the encodings
    clt_elem_add(xp, &pp, x0, x1);
    int ok = expect("is_zero(1 + 1)", 0, clt_is_zero(&pp, xp));

See test/test_clt.c for more examples.

License

Licenced under GPLv2.

Copyright 2016 Brent Carmer & Alex Malozemoff.