Add KSS curve generation.

README.md

@@ -22,7 +22,7 @@ Tool for generating Elliptic curve domain parameters.
  - `-s / --ansi[=SEED]`		Generate a curve from `SEED` (ANSI X9.62 verifiable procedure).
  - `-b / --brainpool[=SEED]`Generate a curve using the Brainpool verifiably pseudorandom algorithm from the original paper.
  - `--brainpool-rfc[=SEED]` Generate a curve using the Brainpool verifiably pseudorandom algorithm as per RFC 5639.
- - `-F / --family=FAMILY`   Generate a pairing friendly curve from a curve family (e.g. "BN", "BLS12", "BLS24").
+ - `-F / --family=FAMILY`   Generate a pairing friendly curve from a curve family (e.g. "BN", "BLS12", "BLS24", "KSS16", "KSS18", "KSS36", "KSS40").
  - `--nums`                 Generate a curve using the NUMS procedure (as per draft-black-numscurves-02).
  - `--twist`                Generate a twist of a given curve.
 

src/exhaustive/exhaustive.c

@@ -148,7 +148,7 @@ static void exhaustive_ginit(gen_f *generators) {
 		}
 		generators[OFFSET_FIELD] = &family_gen_field;
 		generators[OFFSET_A] = &gen_skip;
-		if (cfg->family == FAMILY_KSS16) {
+		if (cfg->family == FAMILY_KSS16 || cfg->family == FAMILY_KSS40) {
 			generators[OFFSET_B] = &family_gen_equation_cm;
 		} else {
 			generators[OFFSET_B] = &family_gen_equation_iter;

src/exhaustive/family.c

@@ -7,7 +7,9 @@
 #include "cm/cm_any.h"
 #include "gen/seed.h"
 #include "misc/config.h"
+#include "util/bits.h"
 #include "util/random.h"
+#include "io/output.h"
 
 #define FAMILIES (FAMILY_KSS40 + 1)
 
@@ -17,49 +19,54 @@ static GEN rz_store[FAMILIES] = {0};
 static GEN tz_store[FAMILIES] = {0};
 static GEN D_store[FAMILIES] = {0};
 
+// clang-format off
 void family_init() {
 	pari_sp ltop = avma;
 	nz_store[FAMILY_BN] = gclone(closure_evalgen(compile_str("(z) -> z")));
-	pz_store[FAMILY_BN] = gclone(closure_evalgen(
-	    compile_str("(z) -> 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1")));
-	rz_store[FAMILY_BN] = gclone(closure_evalgen(
-	    compile_str("(z) -> 36*z^4 + 36*z^3 + 18*z^2 + 6*z + 1")));
-	tz_store[FAMILY_BN] =
-	    gclone(closure_evalgen(compile_str("(z) -> 6*z + 1")));
+	pz_store[FAMILY_BN] = gclone(closure_evalgen(compile_str("(z) -> 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1")));
+	rz_store[FAMILY_BN] = gclone(closure_evalgen(compile_str("(z) -> 36*z^4 + 36*z^3 + 18*z^2 + 6*z + 1")));
+	tz_store[FAMILY_BN] = gclone(closure_evalgen(compile_str("(z) -> 6*z + 1")));
 	D_store[FAMILY_BN] = gclone(stoi(-3));
 
 	nz_store[FAMILY_BLS12] = gclone(closure_evalgen(compile_str("(z) -> z")));
-	pz_store[FAMILY_BLS12] = gclone(closure_evalgen(
-	    compile_str("(z) -> (z - 1)^2 * (z^4 - z^2 + 1)/3 + z")));
-	rz_store[FAMILY_BLS12] =
-	    gclone(closure_evalgen(compile_str("(z) -> z^4 - z^2 + 1")));
-	tz_store[FAMILY_BLS12] =
-	    gclone(closure_evalgen(compile_str("(z) -> z + 1")));
+	pz_store[FAMILY_BLS12] = gclone(closure_evalgen(compile_str("(z) -> (z - 1)^2 * (z^4 - z^2 + 1)/3 + z")));
+	rz_store[FAMILY_BLS12] = gclone(closure_evalgen(compile_str("(z) -> z^4 - z^2 + 1")));
+	tz_store[FAMILY_BLS12] = gclone(closure_evalgen(compile_str("(z) -> z + 1")));
 	D_store[FAMILY_BLS12] = gclone(stoi(-3));
 
 	nz_store[FAMILY_BLS24] = gclone(closure_evalgen(compile_str("(z) -> z")));
-	pz_store[FAMILY_BLS24] = gclone(closure_evalgen(
-	    compile_str("(z) -> (z - 1)^2 * (z^8 - z^4 + 1)/3 + z")));
-	rz_store[FAMILY_BLS24] =
-	    gclone(closure_evalgen(compile_str("(z) -> z^8 - z^4 + 1")));
-	tz_store[FAMILY_BLS24] =
-	    gclone(closure_evalgen(compile_str("(z) -> z + 1")));
+	pz_store[FAMILY_BLS24] = gclone(closure_evalgen(compile_str("(z) -> (z - 1)^2 * (z^8 - z^4 + 1)/3 + z")));
+	rz_store[FAMILY_BLS24] = gclone(closure_evalgen(compile_str("(z) -> z^8 - z^4 + 1")));
+	tz_store[FAMILY_BLS24] = gclone(closure_evalgen(compile_str("(z) -> z + 1")));
 	D_store[FAMILY_BLS24] = gclone(stoi(-3));
 
-	//TODO: This does not work...
-	nz_store[FAMILY_KSS16] =
-	    gclone(closure_evalgen(compile_str("(z) -> 70*z + 25")));
-	pz_store[FAMILY_KSS16] = gclone(closure_evalgen(
-	    compile_str("(z) -> (z^10 + 2*z^9 + 5*z^8 + 48*z^6 + 152*z^5 + 240*z^4 "
-	                "+ 625*z^2 + 2398*z + 3125)/980")));
-	rz_store[FAMILY_KSS16] = gclone(
-	    closure_evalgen(compile_str("(z) -> (z^8 + 48*z^4 + 625)/61250")));
-	tz_store[FAMILY_KSS16] =
-	    gclone(closure_evalgen(compile_str("(z) -> (2*z^5 + 41*z + 35)/35")));
-	D_store[FAMILY_KSS16] = gclone(stoi(-1));
+	nz_store[FAMILY_KSS16] = gclone(closure_evalgen(compile_str("(z) -> 70*z + 25")));
+	pz_store[FAMILY_KSS16] = gclone(closure_evalgen(compile_str("(z) -> (z^10 + 2*z^9 + 5*z^8 + 48*z^6 + 152*z^5 + 240*z^4 + 625*z^2 + 2398*z + 3125)/980")));
+	rz_store[FAMILY_KSS16] = gclone(closure_evalgen(compile_str("(z) -> (z^8 + 48*z^4 + 625)/61250")));
+	tz_store[FAMILY_KSS16] = gclone(closure_evalgen(compile_str("(z) -> (2*z^5 + 41*z + 35)/35")));
+	D_store[FAMILY_KSS16] = gclone(stoi(-4));
+
+	nz_store[FAMILY_KSS18] = gclone(closure_evalgen(compile_str("(z) -> 42*z + 14")));
+	pz_store[FAMILY_KSS18] = gclone(closure_evalgen(compile_str("(z) -> (z^8 + 5*z^7 + 7*z^6 + 37*z^5 + 188*z^4 + 259*z^3 + 343*z^2 + 1763*z + 2401)/21")));
+	rz_store[FAMILY_KSS18] = gclone(closure_evalgen(compile_str("(z) -> (z^6 + 37*z^3 + 343)/343")));
+	tz_store[FAMILY_KSS18] = gclone(closure_evalgen(compile_str("(z) -> (z^4 + 16*z + 7)/7")));
+	D_store[FAMILY_KSS18] = gclone(stoi(-3));
+
+	nz_store[FAMILY_KSS36] = gclone(closure_evalgen(compile_str("(z) -> 777 * z + 287")));
+	pz_store[FAMILY_KSS36] = gclone(closure_evalgen(compile_str("(z) -> (z^14 - 4*z^13 + 7*z^12 + 683*z^8 - 2510*z^7 + 4781*z^6 + 117649*z^2 - 386569*z + 823543)/28749")));
+	rz_store[FAMILY_KSS36] = gclone(closure_evalgen(compile_str("(z) -> (z^12 + 683*z^6 + 117649)/161061481")));
+	tz_store[FAMILY_KSS36] = gclone(closure_evalgen(compile_str("(z) -> (2*z^7 + 757*z + 259)/259")));
+	D_store[FAMILY_KSS36] = gclone(stoi(-3));
+
+	nz_store[FAMILY_KSS40] = gclone(closure_evalgen(compile_str("(z) -> 2370*z + 1205")));
+	pz_store[FAMILY_KSS40] = gclone(closure_evalgen(compile_str("(z) -> (z^22 - 2*z^21 + 5*z^20 + 6232*z^12 - 10568*z^11 + 31160*z^10 + 9765625*z^2 - 13398638*z + 48828125)/1123380")));
+	rz_store[FAMILY_KSS40] = gclone(closure_evalgen(compile_str("(z) -> (z^16 + 8*z^14 + 39*z^12 + 112*z^10 - 79*z^8 + 2800*z^6 + 24375*z^4 + 125000*z^2 + 390625)/2437890625")));
+	tz_store[FAMILY_KSS40] = gclone(closure_evalgen(compile_str("(z) -> (2*z^11 + 6469*z + 1185)/1185")));
+	D_store[FAMILY_KSS40] = gclone(stoi(-4));
 
 	avma = ltop;
 }
+// clang-format on
 
 static seed_t *family_new_seed() {
 	seed_t *result = seed_new();
@@ -70,21 +77,18 @@ static seed_t *family_new_seed() {
 GENERATOR(family_gen_seed_random) {
 	curve->seed = family_new_seed();
 	curve->seed->family.z = random_int(cfg->bits);
+	if (random_bits(1)) {
+		togglesign(curve->seed->family.z);
+	}
+	curve->seed->seed = bits_from_i(curve->seed->family.z);
 	return 1;
 }
 
 GENERATOR(family_gen_seed_input) {
-	pari_sp ltop = avma;
 	GEN inp = input_int("z:", cfg->bits);
-	if (gequalm1(inp)) {
-		avma = ltop;
-		return 0;
-	} else if (equalii(inp, gen_m2)) {
-		avma = ltop;
-		return INT_MIN;
-	}
 	curve->seed = family_new_seed();
 	curve->seed->family.z = inp;
+	curve->seed->seed = bits_from_i(curve->seed->family.z);
 	return 1;
 }
 
@@ -96,13 +100,11 @@ GENERATOR(family_gen_field) {
 		avma = ltop;
 		return -1;
 	}
-	printf("p");
 	GEN rz = closure_callgen1(rz_store[cfg->family], n);
 	if (typ(rz) != t_INT || !isprime(rz)) {
 		avma = ltop;
 		return -1;
 	}
-	printf("r");
 	curve->field = gerepilecopy(ltop, pz);
 	return 1;
 }

src/io/cli.c

@@ -63,7 +63,7 @@ struct argp_option cli_options[] = {
 		{"nums",		   OPT_NUMS, 		   0,		0,				   "Generate a curve using the NUMS procedure.",											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},
-		{"family",			OPT_FAMILY,		"NAME", 0, "Generate a curve from a curve family (e.g. BN, BLS12, BLS24, KSS)."},
+		{"family",			OPT_FAMILY,		"NAME", 0, "Generate a curve from a curve family (e.g. BN, BLS12, BLS24, KSS16, KSS18, KSS36, KSS40).",  2},
 
 		{0,               0,                 0,       0,                   "Generation options:",                                                                  3},
 		{"random",        OPT_RANDOM,        "WHAT",  OPTION_ARG_OPTIONAL, "Generate a random curve (using Random approach). "
@@ -294,16 +294,12 @@ error_t cli_parse(int key, char *arg, struct argp_state *state) {
 			} else if (strcasecmp(arg, "BLS24") == 0) {
 				cfg->family = FAMILY_BLS24;
 			} else if (strcasecmp(arg, "KSS16") == 0) {
-				argp_failure(state, 1, 0, "Family not yet supported.");
 				cfg->family = FAMILY_KSS16;
 			} else if (strcasecmp(arg, "KSS18") == 0) {
-				argp_failure(state, 1, 0, "Family not yet supported.");
 				cfg->family = FAMILY_KSS18;
 			} else if (strcasecmp(arg, "KSS36") == 0) {
-				argp_failure(state, 1, 0, "Family not yet supported.");
 				cfg->family = FAMILY_KSS36;
 			} else if (strcasecmp(arg, "KSS40") == 0) {
-				argp_failure(state, 1, 0, "Family not yet supported.");
 				cfg->family = FAMILY_KSS40;
 			} else {
 				argp_failure(state, 1, 0, "Unknown curve family = %s", arg);

src/io/input.c

@@ -32,11 +32,13 @@ static GEN input_i(const char *prompt, unsigned long bits) {
 		free(line);
 		return gen_m1;
 	}
-	for (size_t i = 0, j = 0; (line[j] = line[i]); j += !isspace(line[i++]))
-		;
+	bool sign = line[0] == '-';
 
 	pari_sp ltop = avma;
-	GEN in = strtoi(line);
+	GEN in = strtoi(line + sign);
+	if (sign) {
+		togglesign(in);
+	}
 	free(line);
 
 	// check bitsize here

src/io/output.c

@@ -84,9 +84,17 @@ static JSON_Value *output_jjson(curve_t *curve) {
 	if (curve->seed && curve->seed->seed) {
 		char *hex_str = bits_to_hex(curve->seed->seed);
 		char *hex = try_calloc(strlen(hex_str) + 3);
-		hex[0] = '0';
-		hex[1] = 'x';
+		if (curve->seed->seed->sign) {
+			hex[0] = '-';
+			hex[1] = '0';
+		} else {
+			hex[0] = '0';
+			hex[1] = 'x';
+		}
 		strcat(hex, hex_str);
+		if (curve->seed->seed->sign) {
+			hex[2] = 'x';
+		}
 		json_object_set_string(root_object, "seed", hex);
 		try_free(hex_str);
 		try_free(hex);

src/misc/types.h

@@ -15,11 +15,13 @@
 /**
  * @brief
  * @param bits
+ * @param sign
  * @param bitlen
  * @param allocated
  */
 typedef struct {
 	unsigned char *bits;
+	bool sign;
 	size_t bitlen;
 	size_t allocated;
 } bits_t;

src/util/bits.c

@@ -44,10 +44,12 @@ void bits_cpy(bits_t *dest, const bits_t *src) {
 	memcpy(dest->bits, src->bits, src->allocated);
 	dest->allocated = src->allocated;
 	dest->bitlen = src->bitlen;
+	dest->sign = src->sign;
 }
 
 bits_t *bits_copy(const bits_t *bits) {
 	bits_t *result = try_calloc(sizeof(bits_t));
+	result->sign = bits->sign;
 	result->bitlen = bits->bitlen;
 	result->allocated = bits->allocated;
 	if (bits->allocated != 0)
@@ -70,6 +72,7 @@ bits_t *bits_from_i(GEN i) {
 	GEN bitvec = binary_zv(i);
 	size_t bit_len = (size_t)glength(bitvec);
 	bits_t *result = bits_new(bit_len);
+	result->sign = signe(i) == -1;
 	for (size_t j = 0; j < bit_len; ++j) {
 		if (gel(bitvec, j + 1) == (GEN)1) {
 			result->bits[j / 8] |= 1 << (7 - (j % 8));
@@ -84,6 +87,7 @@ bits_t *bits_from_i_len(GEN i, size_t bit_len) {
 	GEN bitvec = binary_zv(i);
 	size_t i_len = (size_t)glength(bitvec);
 	bits_t *result = bits_new(bit_len);
+	result->sign = signe(i) == -1;
 	size_t offset = 0;
 	if (i_len < bit_len) {
 		offset = bit_len - i_len;
@@ -150,22 +154,53 @@ GEN bits_to_i(const bits_t *bits) {
 		if (GET_BIT(bits->bits, i) != 0)
 			result = addii(result, int2n(bits->bitlen - i - 1));
 	}
+	if (bits->sign) {
+		setsigne(result, -1);
+	}
 	return gerepilecopy(ltop, result);
 }
 
 char *bits_to_hex(const bits_t *bits) {
-	char *result = try_calloc(BYTE_LEN(bits->bitlen) * 2 + 1);
-	// probably right pad with zeroes, as thats what is actually stored.
+	char *result =
+	    try_calloc(BYTE_LEN(bits->bitlen) * 2 + 1 + (bits->sign ? 1 : 0));
+	if (bits->sign) {
+		result[0] = '-';
+	}
+	size_t offset = bits->bitlen % 8;
+	// if offset == 0
+	// | a b | c d |
+	// ^-----^ first byte
+	//       ^-----^ second byte
+	// else
+	// 0 0 | a b | c d | e
+	//  ^-----^ (8-offset zero bits, offset bits from first byte)
+	//        ^-----^ (8-offset bits from first byte, offset bits from second byte)
+	//           ....
+	//              ^-----^ (8-offset bits from second to last byte, offset bits from last byte)
 	for (size_t i = 0; i < BYTE_LEN(bits->bitlen); ++i) {
-		sprintf(result + (i * 2), "%02x", bits->bits[i]);
+		size_t pos = (i * 2) + (bits->sign ? 1 : 0);
+		unsigned char value;
+		if (offset) {
+			value = bits->bits[i] >> (8 - offset);
+			if (i != 0) {
+				value |= (bits->bits[i-1] & ~(1 << (8 - offset))) << offset;
+			}
+		} else {
+			value = bits->bits[i];
+		}
+		sprintf(result + pos, "%02x", value);
 	}
 	return result;
 }
 
 char *bits_to_bin(const bits_t *bits) {
-	char *result = try_calloc(bits->bitlen + 1);
+	char *result = try_calloc(bits->bitlen + 1 + (bits->sign ? 1 : 0));
+	if (bits->sign) {
+		result[0] = '-';
+	}
 	for (size_t i = 0; i < bits->bitlen; ++i) {
-		sprintf(result + i, "%1u", GET_BIT(bits->bits, i));
+		sprintf(result + i + (bits->sign ? 1 : 0), "%1u",
+		        GET_BIT(bits->bits, i));
 	}
 	return result;
 }
@@ -459,6 +494,7 @@ void bits_sha1(const bits_t *bits, unsigned char hashout[20]) {
 }
 
 bool bits_eq(const bits_t *one, const bits_t *other) {
+	if (one->sign != other->sign) return false;
 	if (one->bitlen != other->bitlen) return false;
 	if (one->bitlen == 0) return true;
 	if (memcmp(one->bits, other->bits, one->bitlen / 8) != 0) return false;

test/ecgen.sh

@@ -128,9 +128,17 @@ function supersingular() {
 
 function family() {
     start_test
-    assert_raises "${ecgen} --fp -r --family=BN 32"
-    assert_raises "${ecgen} --fp -r --family=BLS12 32"
-    assert_raises "${ecgen} --fp -r --family=BLS24 32"
+    assert_raises "${ecgen} --fp -r --family=BN 16"
+    assert_raises "${ecgen} --fp -r --family=BLS12 16"
+    assert_raises "${ecgen} --fp -r --family=BLS24 16"
+
+    assert_raises "${ecgen} --fp --family=BN 16"    0 "0xe5a2"
+    assert_raises "${ecgen} --fp --family=BLS12 16" 0 "0xafa2"
+    assert_raises "${ecgen} --fp --family=BLS24 16" 0 "0x8278"
+    assert_raises "${ecgen} --fp --family=KSS16 16" 0 "0x8acc"
+    assert_raises "${ecgen} --fp --family=KSS18 16" 0 "0xd2ac"
+    assert_raises "${ecgen} --fp --family=KSS36 16" 0 "0xf07f"
+    assert_raises "${ecgen} --fp --family=KSS40 16" 0 "-0xb18f"
 }
 
 function invalid() {

test/src/util/test_bits.c

@@ -172,7 +172,7 @@ Test(bits, test_bits_to_hex) {
 
 	char *hex = bits_to_hex(bits);
 	cr_assert_not_null(hex, );
-	cr_assert_str_eq(hex, "abc0", );
+	cr_assert_str_eq(hex, "0abc", );
 	try_free(hex);
 	bits_free(&bits);
 }