nx_rsa_keygen.nx

nx_rsa_keygen.nx -- F103e RUNG 7: RSA key generation. The credential F103e has been walking toward. Real EDK2 with MS keys refuses our unsigned .efi (Access Denied) while the SAME secboot firmware in SETUP mode runs it, so the blocker is the enrolled key set (debt 1786237435). Enrolling OUR key requires HAVING one -- and it must be GENERATED, never recited: an RSA modulus quoted from memory is a fabricated constant. Dependencies, both built earlier in this same arc because neither existed: nx_u2048_millerrabin -- primality (needs a^d mod n with d ~1024 bits) nx_rsa2048_mod_exp_big -- that modexp (the incumbent takes the exponent as an i64) nx_u2048_smallops -- d = (k*phi + 1)/e without a general extended GCD ⚠THE WIDTH TRAP, found by arithmetic and not by testing: for 1024-bit primes phi is ~2048 bits, so phi*k with k < e = 65537 is ~2065 bits and OVERFLOWS the u2048 width. The d-recovery therefore runs in the WIDE (128-limb) form. ★★★★★**AN INTERMEDIATE THAT OVERFLOWS ONLY AT PRODUCTION SIZE IS INVISIBLE TO EVERY SMALL-PARAMETER TEST** -- so the wide helpers are cross-checked against the shipped 64-limb smallops on 64-limb inputs (T2), making them the same ruler at two widths. ★THE CORRECTNESS PROOF NEEDS NO EXTERNAL ORACLE: a keypair is valid iff (m^e)^d == m mod n for messages we choose. That is checked for several m, INCLUDING m=1 and m=n-1 which any broken key still satisfies -- so a non-trivial m is required for the tooth to mean anything. Usage: nx_rsa_keygen selftest (fast, small parameters -- proves the algorithm) nx_rsa_keygen gen <bits> (real key from the CSPRNG, printed as hex) ⚠the selftest uses a DETERMINISTIC generator so the teeth are reproducible. That path prints TEST-KEY-DO-NOT-USE and is unreachable from `gen`. ★A DETERMINISTIC KEY IS A TEST FIXTURE AND A SECURITY DEFECT WEARING THE SAME BYTES -- the two paths must never share an exit. Exit: 0 GREEN | 1 RED. Log -> knowledge/status/nishi_os.log, verdict= LAST. license_tier: ORIGINAL