From 85ba70a9c598fee379720274c5ed430bdf8bce39 Mon Sep 17 00:00:00 2001 From: hasufell Date: Wed, 16 Apr 2014 23:23:41 +0200 Subject: [PATCH] POLY: first try of inverting polynomials --- src/poly.c | 134 +++++++++++++++++++++++++++++++++++++++++++++++++++++ src/poly.h | 10 ++++ 2 files changed, 144 insertions(+) diff --git a/src/poly.c b/src/poly.c index 56ad436..b1d98ec 100644 --- a/src/poly.c +++ b/src/poly.c @@ -21,11 +21,13 @@ #include "context.h" #include "err.h" +#include "poly.h" #include #include #include #include +#include /** * Initialize a mp_int and check if this was successful, the @@ -201,6 +203,138 @@ void pb_starmultiply(pb_poly *a, } /** + * c = a XOR b + * + * @param a polynom (is allowed to be the same as param c) + * @param b polynom + * @param c polynom [out] + * @param len max size of the polynoms, make sure all are + * properly allocated + */ +void pb_xor(pb_poly *a, + pb_poly *b, + pb_poly *c, + const size_t len) +{ + for (unsigned int i = 0; i < len; i++) + mp_xor(&(a->terms[i]), &(b->terms[i]), &(c->terms[i])); +} + +/** + * Invert the polynomial a modulo q. + * + * @param a polynomial to invert (is allowed to be the same as param Fq) + * @param Fq polynomial [out] + * @param ctx NTRU context + * @return true/false for success/failure + */ +bool pb_inverse_poly_q(pb_poly * const a, + pb_poly *Fq, + ntru_context *ctx) +{ + int k = 0, + j = 0, + v = 2; + int zero_poly_val = 1; + pb_poly *a_tmp, *b, *c, *f, *g, *degree_zero_poly; + + degree_zero_poly = build_polynom(&zero_poly_val, 1, ctx); + b = build_polynom(NULL, ctx->N, ctx); + mp_set(&(b->terms[0]), 1); + c = build_polynom(NULL, ctx->N, ctx); + f = build_polynom(NULL, ctx->N, ctx); + pb_copy(a, f); + a_tmp = build_polynom(NULL, ctx->N, ctx); + pb_copy(a, a_tmp); + g = build_polynom(NULL, ctx->N, ctx); + mp_set(&(g->terms[0]), 1); + g->terms[0].sign = 1; + mp_set(&(g->terms[ctx->N]), 1); + + while (1) { + while (mp_cmp_d(&(f->terms[0]), 0) == MP_EQ) { + for (unsigned int i = 1; i <= ctx->N; i++) { + mp_copy(&(f->terms[i]), &(f->terms[i - 1])); + mp_copy(&(c->terms[ctx->N - i]), &(c->terms[ctx->N + 1 - i])); + } + mp_set(&(f->terms[ctx->N]), 0); + mp_set(&(c->terms[0]), 0); + k++; + } + + /* hope this does not blow up in our face */ + pb_clamp(degree_zero_poly); + pb_clamp(f); + if (pb_cmp(f, degree_zero_poly) == PB_DEG_EQ) + goto OUT_OF_LOOP; + + pb_clamp(g); + if (pb_cmp(f, g) == PB_DEG_LT) { + pb_exch(f, g); + pb_exch(b, c); + } + + /* draw_polynom(f); */ + /* draw_polynom(b); */ + pb_xor(f, g, f, ctx->N); + pb_xor(b, c, b, ctx->N); + /* draw_polynom(f); */ + /* draw_polynom(b); */ + } + +OUT_OF_LOOP: + k = k % ctx->N; + + for (int i = ctx->N - 1; i >= 0; i--) { + j = i - k; + if (j < 0) + j = j + ctx->N; + mp_copy(&(b->terms[i]), &(Fq->terms[j])); + } + draw_polynom(Fq); + + while (v < (int)(ctx->q)) { + pb_poly *pb_tmp, + *pb_tmp_v, + *pb_tmp2; + pb_tmp = build_polynom(NULL, ctx->N, ctx); + v = v * 2; + pb_tmp_v = build_polynom(NULL, ctx->N, ctx); + mp_set_int(&(pb_tmp_v->terms[0]), v); + pb_tmp2 = build_polynom(NULL, ctx->N, ctx); + mp_set_int(&(pb_tmp2->terms[0]), 2); + + /* hope this does not blow up in our face */ + pb_starmultiply(a_tmp, Fq, pb_tmp, ctx, v); + pb_sub(pb_tmp2, pb_tmp, pb_tmp); + pb_mod(pb_tmp, pb_tmp_v, pb_tmp); + pb_starmultiply(Fq, pb_tmp, Fq, ctx, v); + + delete_polynom(pb_tmp); + delete_polynom(pb_tmp_v); + delete_polynom(pb_tmp2); + } + + for (int i = ctx->N - 1; i >= 0; i--) + if (mp_cmp_d(&(Fq->terms[i]), 0) == MP_LT) { + mp_int mp_tmp; + init_integer(&mp_tmp); + mp_set_int(&mp_tmp, ctx->q); + mp_add(&(Fq->terms[i]), &mp_tmp, &(Fq->terms[i])); + mp_clear(&mp_tmp); + } + + delete_polynom(a_tmp); + delete_polynom(b); + delete_polynom(c); + delete_polynom(f); + delete_polynom(g); + delete_polynom(degree_zero_poly); + + /* TODO: check if the f * Fq = 1 (mod p) condition holds true */ + + return true; +} * Print the polynomial in a human readable format to stdout. * * @param poly to draw diff --git a/src/poly.h b/src/poly.h index ef9700d..cdef091 100644 --- a/src/poly.h +++ b/src/poly.h @@ -27,6 +27,7 @@ #include #include +#include void init_integer(mp_int *new_int); @@ -47,6 +48,15 @@ void pb_starmultiply(pb_poly *a, ntru_context *ctx, unsigned int modulus); +void pb_xor(pb_poly *a, + pb_poly *b, + pb_poly *c, + const size_t len); + +bool pb_inverse_poly_q(pb_poly *a, + pb_poly *Fq, + ntru_context *ctx); + void draw_polynom(pb_poly * const poly); #endif /* NTRU_POLY_H */