second-round version of SQIsign

Co-authored-by: Marius A. Aardal <marius.andre.aardal@gmail.com>
Co-authored-by: Gora Adj <gora.adj@tii.ae>
Co-authored-by: Diego F. Aranha <dfaranha@cs.au.dk>
Co-authored-by: Andrea Basso <sqisign@andreabasso.com>
Co-authored-by: Isaac Andrés Canales Martínez <icanalesm0500@gmail.com>
Co-authored-by: Jorge Chávez-Saab <jorgechavezsaab@gmail.com>
Co-authored-by: Maria Corte-Real Santos <mariascrsantos98@gmail.com>
Co-authored-by: Luca De Feo <github@defeo.lu>
Co-authored-by: Max Duparc <max.duparc@epfl.ch>
Co-authored-by: Jonathan Komada Eriksen <jonathan.eriksen97@gmail.com>
Co-authored-by: Décio Luiz Gazzoni Filho <decio@decpp.net>
Co-authored-by: Basil Hess <bhe@zurich.ibm.com>
Co-authored-by: Antonin Leroux <antonin.leroux@polytechnique.org>
Co-authored-by: Patrick Longa <plonga@microsoft.com>
Co-authored-by: Luciano Maino <mainoluciano.96@gmail.com>
Co-authored-by: Michael Meyer <michael@random-oracles.org>
Co-authored-by: Hiroshi Onuki <onuki@mist.i.u-tokyo.ac.jp>
Co-authored-by: Lorenz Panny <lorenz@yx7.cc>
Co-authored-by: Giacomo Pope <giacomopope@gmail.com>
Co-authored-by: Krijn Reijnders <reijnderskrijn@gmail.com>
Co-authored-by: Damien Robert <damien.robert@inria.fr>
Co-authored-by: Francisco Rodríguez-Henriquez <francisco.rodriguez@tii.ae>
Co-authored-by: Sina Schaeffler <sschaeffle@student.ethz.ch>
Co-authored-by: Benjamin Wesolowski <benjamin.wesolowski@ens-lyon.fr>

scripts/precomp/precompute_torsion_constants.sage

@@ -0,0 +1,40 @@
+#!/usr/bin/env sage
+proof.all(False)  # faster
+
+################################################################
+
+from parameters import p
+
+################################################################
+
+tors2part = (p+1).p_primary_part(2)
+lambda_security = round(p.bit_length() / 128) * 64
+N_sec = next_prime(1 << 4*lambda_security)
+N_com = N_sec
+
+defs = {
+        'TORSION_2POWER_BYTES': (tors2part.bit_length() + 7) // 8,
+    }
+
+from cformat import Ibz, Object, ObjectFormatter
+
+objs = ObjectFormatter([
+        Object('ibz_t', 'TWO_TO_SECURITY_BITS', Ibz(1 << lambda_security)),  # lambda_security = SECURITY_BITS (128, 192, 256)
+        Object('ibz_t', 'TORSION_PLUS_2POWER', Ibz(tors2part)),
+        Object('ibz_t', 'SEC_DEGREE', Ibz(N_sec)),
+        Object('ibz_t', 'COM_DEGREE', Ibz(N_com)),
+    ])
+
+with open('include/torsion_constants.h','w') as hfile:
+    with open('torsion_constants.c','w') as cfile:
+        print(f'#include <quaternion.h>', file=hfile)
+        print(f'#include <stddef.h>', file=cfile)
+        print(f'#include <stdint.h>', file=cfile)
+        print(f'#include <torsion_constants.h>', file=cfile)
+
+        for k,v in defs.items():
+            print(f'#define {k} {v}', file=hfile)
+
+        objs.header(file=hfile)
+        objs.implementation(file=cfile)
+