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-rw-r--r--src/exhaustive/exhaustive.c4
-rw-r--r--src/exhaustive/supersingular.c44
-rw-r--r--src/exhaustive/supersingular.h28
-rw-r--r--src/io/cli.c89
-rw-r--r--src/misc/config.h3
5 files changed, 128 insertions, 40 deletions
diff --git a/src/exhaustive/exhaustive.c b/src/exhaustive/exhaustive.c
index dbc1125..5ecac24 100644
--- a/src/exhaustive/exhaustive.c
+++ b/src/exhaustive/exhaustive.c
@@ -20,6 +20,7 @@
#include "io/output.h"
#include "misc/config.h"
#include "obj/curve.h"
+#include "supersingular.h"
#include "util/memory.h"
#include "util/timeout.h"
@@ -124,6 +125,9 @@ static void exhaustive_ginit(gen_f *generators) {
if (cfg->method == METHOD_ANOMALOUS) {
generators[OFFSET_A] = &gen_skip;
generators[OFFSET_B] = &anomalous_gen_equation;
+ } else if (cfg->method == METHOD_SUPERSINGULAR) {
+ generators[OFFSET_A] = &gen_skip;
+ generators[OFFSET_B] = &supersingular_gen_equation;
} else if (cfg->koblitz) {
switch (cfg->koblitz_value) {
case 0:
diff --git a/src/exhaustive/supersingular.c b/src/exhaustive/supersingular.c
new file mode 100644
index 0000000..87e6786
--- /dev/null
+++ b/src/exhaustive/supersingular.c
@@ -0,0 +1,44 @@
+/*
+ * ecgen, tool for generating Elliptic curve domain parameters
+ * Copyright (C) 2017-2018 J08nY
+ */
+#include "supersingular.h"
+
+GENERATOR(supersingular_gen_equation) {
+ if (equalis(curve->field, 2)) {
+ return -2;
+ }
+ if (mod4(curve->field) == 3) {
+ curve->a = mkintmod(subis(curve->field, 1), curve->field);
+ curve->b = mkintmod(stoi(0), curve->field);
+ return 1;
+ }
+ GEN q = stoi(3);
+ while (mod4(q) != 3 && kronecker(curve->field, q) != -1) {
+ q = nextprime(q);
+ }
+
+ if (equalis(q, 3)) {
+ curve->a = mkintmod(stoi(0), curve->field);
+ curve->b = mkintmod(stoi(1), curve->field);
+ return 1;
+ } else {
+ GEN H = polclass(negi(q), 0, 0);
+ GEN r = FpX_roots(H, curve->field);
+ GEN root = gel(r, 1);
+ curve->a =
+ Fp_div(Fp_mul(stoi(27), root, curve->field),
+ Fp_mul(stoi(4), Fp_sub(stoi(1728), root, curve->field),
+ curve->field),
+ curve->field);
+ curve->b = negi(curve->a);
+ return 1;
+ }
+}
+
+GENERATOR(supersingular_gen_order) {
+ // copy field to order
+ curve->order = addis(curve->field, 1);
+ obj_insert(curve->curve, 1, curve->order);
+ return 1;
+}
diff --git a/src/exhaustive/supersingular.h b/src/exhaustive/supersingular.h
new file mode 100644
index 0000000..bf7f267
--- /dev/null
+++ b/src/exhaustive/supersingular.h
@@ -0,0 +1,28 @@
+/*
+ * ecgen, tool for generating Elliptic curve domain parameters
+ * Copyright (C) 2017-2018 J08nY
+ */
+#ifndef ECGEN_EXHAUSTIVE_SUPERSINGULAR_H
+#define ECGEN_EXHAUSTIVE_SUPERSINGULAR_H
+
+#include "misc/types.h"
+
+/**
+ * @brief
+ * @param curve
+ * @param args
+ * @param state
+ * @return
+ */
+GENERATOR(supersingular_gen_equation);
+
+/**
+ * @brief
+ * @param curve
+ * @param args
+ * @param state
+ * @return
+ */
+GENERATOR(supersingular_gen_order);
+
+#endif // ECGEN_EXHAUSTIVE_SUPERSINGULAR_H
diff --git a/src/io/cli.c b/src/io/cli.c
index 32888a8..aa9628a 100644
--- a/src/io/cli.c
+++ b/src/io/cli.c
@@ -40,50 +40,52 @@ enum opt_keys {
OPT_ANOMALOUS,
OPT_HEXCHECK,
OPT_METADATA,
+ OPT_SUPERSINGULAR,
OPT_BRAINPOOL_RFC,
OPT_TWIST,
};
// clang-format off
struct argp_option cli_options[] = {
- {0, 0, 0, 0, "Field specification:", 1},
- {"fp", OPT_FP, 0, 0, "Prime field.", 1},
- {"f2m", OPT_F2M, 0, 0, "Binary field.", 1},
+ {0, 0, 0, 0, "Field specification:", 1},
+ {"fp", OPT_FP, 0, 0, "Prime field.", 1},
+ {"f2m", OPT_F2M, 0, 0, "Binary field.", 1},
- {0, 0, 0, 0, "Generation methods:", 2},
- {"order", OPT_ORDER, "ORDER", 0, "Generate a curve with given order (using Complex Multiplication). **NOT IMPLEMENTED**", 2},
- {"anomalous", OPT_ANOMALOUS, 0, 0, "Generate an anomalous curve (of trace one, with field order equal to curve order).", 2},
- {"ansi", OPT_ANSI, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (ANSI X9.62 verifiable procedure).", 2},
- {"brainpool", OPT_BRAINPOOL, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (Brainpool procedure).", 2},
- {"brainpool-rfc", OPT_BRAINPOOL_RFC, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (Brainpool procedure, as per RFC 5639).", 2},
- {"invalid", OPT_INVALID, "RANGE",OPTION_ARG_OPTIONAL, "Generate a set of invalid curves, for a given curve (using Invalid curve algorithm).", 2},
- {"twist", OPT_TWIST, 0, 0, "Generate a twist of a given curve.", 2},
+ {0, 0, 0, 0, "Generation methods:", 2},
+ {"order", OPT_ORDER, "ORDER", 0, "Generate a curve with given order (using Complex Multiplication).", 2},
+ {"supersingular", OPT_SUPERSINGULAR, 0, 0, "Generate a supersingular curve.", 2},
+ {"anomalous", OPT_ANOMALOUS, 0, 0, "Generate an anomalous curve (of trace one, with field order equal to curve order).", 2},
+ {"ansi", OPT_ANSI, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (ANSI X9.62 verifiable procedure).", 2},
+ {"brainpool", OPT_BRAINPOOL, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (Brainpool procedure).", 2},
+ {"brainpool-rfc", OPT_BRAINPOOL_RFC, "SEED", OPTION_ARG_OPTIONAL, "Generate a curve from SEED (Brainpool procedure, as per RFC 5639).", 2},
+ {"invalid", OPT_INVALID, "RANGE", OPTION_ARG_OPTIONAL, "Generate a set of invalid curves, for a given curve (using Invalid curve algorithm).", 2},
+ {"twist", OPT_TWIST, 0, 0, "Generate a twist of a given curve.", 2},
- {0, 0, 0, 0, "Generation options:", 3},
- {"random", OPT_RANDOM, "WHAT", OPTION_ARG_OPTIONAL, "Generate a random curve (using Random approach). "
- "Optionally, only generate random parameters WHAT (seed,field,a,b,equation).", 3},
- {"prime", OPT_PRIME, 0, 0, "Generate a curve with prime order.", 3},
- {"cofactor", OPT_COFACTOR, "VALUE", 0, "Generate a curve with cofactor of VALUE.", 3},
- {"koblitz", OPT_KOBLITZ, "A", OPTION_ARG_OPTIONAL, "Generate a Koblitz curve (a in {0, 1}, b = 1).", 3},
- {"unique", OPT_UNIQUE, 0, 0, "Generate a curve with only one generator.", 3},
- {"hex-check", OPT_HEXCHECK, "HEX", 0, "Check a generated curve param hex expansion for the HEX string.", 3},
- {"points", OPT_POINTS, "TYPE", 0, "Generate points of given type (random/prime/all/nonprime/none).", 3},
- {"count", OPT_COUNT, "COUNT", 0, "Generate multiple curves.", 3},
- {"metadata", OPT_METADATA, 0, 0, "Compute curve metadata "
- "(j-invariant, discriminant, trace of Frobenius, embedding degree, CM discriminant).", 3},
+ {0, 0, 0, 0, "Generation options:", 3},
+ {"random", OPT_RANDOM, "WHAT", OPTION_ARG_OPTIONAL, "Generate a random curve (using Random approach). "
+ "Optionally, only generate random parameters WHAT (seed,field,a,b,equation).", 3},
+ {"prime", OPT_PRIME, 0, 0, "Generate a curve with prime order.", 3},
+ {"cofactor", OPT_COFACTOR, "VALUE", 0, "Generate a curve with cofactor of VALUE.", 3},
+ {"koblitz", OPT_KOBLITZ, "A", OPTION_ARG_OPTIONAL, "Generate a Koblitz curve (a in {0, 1}, b = 1).", 3},
+ {"unique", OPT_UNIQUE, 0, 0, "Generate a curve with only one generator.", 3},
+ {"hex-check", OPT_HEXCHECK, "HEX", 0, "Check a generated curve param hex expansion for the HEX string.", 3},
+ {"points", OPT_POINTS, "TYPE", 0, "Generate points of given type (random/prime/all/nonprime/none).", 3},
+ {"count", OPT_COUNT, "COUNT", 0, "Generate multiple curves.", 3},
+ {"metadata", OPT_METADATA, 0, 0, "Compute curve metadata "
+ "(j-invariant, discriminant, trace of Frobenius, embedding degree, CM discriminant).", 3},
- {0, 0, 0, 0, "Input/Output options:", 4},
- {"input", OPT_INPUT, "FILE", 0, "Input from file.", 4},
- {"output", OPT_OUTPUT, "FILE", 0, "Output into file. Overwrites any existing file!", 4},
- {"append", OPT_APPEND, 0, 0, "Append to output file (don't overwrite).", 4},
- {"verbose", OPT_VERBOSE, "FILE", OPTION_ARG_OPTIONAL, "Verbose logging (to stdout or file).", 4},
+ {0, 0, 0, 0, "Input/Output options:", 4},
+ {"input", OPT_INPUT, "FILE", 0, "Input from file.", 4},
+ {"output", OPT_OUTPUT, "FILE", 0, "Output into file. Overwrites any existing file!", 4},
+ {"append", OPT_APPEND, 0, 0, "Append to output file (don't overwrite).", 4},
+ {"verbose", OPT_VERBOSE, "FILE", OPTION_ARG_OPTIONAL, "Verbose logging (to stdout or file).", 4},
- {0, 0, 0, 0, "Other:", 5},
- {"data-dir", OPT_DATADIR, "DIR", 0, "Set PARI/GP data directory (containing seadata package).", 5},
- {"memory", OPT_MEMORY, "SIZE", 0, "Use PARI stack of SIZE (can have suffix k/m/g).", 5},
- {"threads", OPT_THREADS, "NUM", 0, "Use NUM threads.", 5},
- {"thread-stack", OPT_TSTACK, "SIZE", 0, "Use PARI stack of SIZE (per thread, can have suffix k/m/g).", 5},
- {"timeout", OPT_TIMEOUT, "TIME", 0, "Timeout computation of a curve parameter after TIME (can have suffix s/m/h/d).", 5},
+ {0, 0, 0, 0, "Other:", 5},
+ {"data-dir", OPT_DATADIR, "DIR", 0, "Set PARI/GP data directory (containing seadata package).", 5},
+ {"memory", OPT_MEMORY, "SIZE", 0, "Use PARI stack of SIZE (can have suffix k/m/g).", 5},
+ {"threads", OPT_THREADS, "NUM", 0, "Use NUM threads.", 5},
+ {"thread-stack", OPT_TSTACK, "SIZE", 0, "Use PARI stack of SIZE (per thread, can have suffix k/m/g).", 5},
+ {"timeout", OPT_TIMEOUT, "TIME", 0, "Timeout computation of a curve parameter after TIME (can have suffix s/m/h/d).", 5},
{0}
};
// clang-format on
@@ -141,6 +143,7 @@ static void cli_end(struct argp_state *state) {
case METHOD_SEED:
case METHOD_INVALID:
case METHOD_TWIST:
+ case METHOD_SUPERSINGULAR:
break;
default:
printf("%u\n", cfg->method);
@@ -158,6 +161,11 @@ static void cli_end(struct argp_state *state) {
argp_failure(state, 1, 0,
"Complex multiplication only creates prime field curves.");
}
+ if (cfg->method == METHOD_SUPERSINGULAR && cfg->field == FIELD_BINARY) {
+ argp_failure(state, 1, 0,
+ "Can only generate supersingular curves over prime fields "
+ "currently.");
+ }
// default values
if (!cfg->count) {
cfg->count = 1;
@@ -187,7 +195,7 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
cfg->field |= FIELD_BINARY;
break;
- /* Generation method */
+ /* Generation method */
case OPT_INVALID:
cfg->method |= METHOD_INVALID;
if (arg) {
@@ -207,6 +215,9 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
case OPT_ANOMALOUS:
cfg->method |= METHOD_ANOMALOUS;
break;
+ case OPT_SUPERSINGULAR:
+ cfg->method |= METHOD_SUPERSINGULAR;
+ break;
case OPT_ANSI:
cfg->method |= METHOD_SEED;
cfg->seed_algo = SEED_ANSI;
@@ -247,7 +258,7 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
cfg->method |= METHOD_TWIST;
break;
- /* Generation options */
+ /* Generation options */
case OPT_COUNT:
cfg->count = strtoul(arg, NULL, 10);
break;
@@ -336,7 +347,7 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
}
break;
}
- /* IO options */
+ /* IO options */
case OPT_INPUT:
cfg->input = arg;
break;
@@ -353,7 +364,7 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
}
break;
- /* Misc options */
+ /* Misc options */
case OPT_DATADIR:
cfg->datadir = arg;
break;
@@ -381,7 +392,7 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
}
break;
- /* Args */
+ /* Args */
case ARGP_KEY_ARG:
if (state->arg_num >= 1) {
argp_usage(state);
diff --git a/src/misc/config.h b/src/misc/config.h
index 55a3cdd..7db13de 100644
--- a/src/misc/config.h
+++ b/src/misc/config.h
@@ -47,7 +47,8 @@ typedef enum {
METHOD_ANOMALOUS = 1 << 1,
METHOD_SEED = 1 << 2,
METHOD_INVALID = 1 << 3,
- METHOD_TWIST = 1 << 4
+ METHOD_TWIST = 1 << 4,
+ METHOD_SUPERSINGULAR = 1 << 5
} method_e;
/**
generated by cgit v1.2.3-70-g09d2 (git 2.51.2) at 2025-11-08 22:07:45 +0000