nx_totp_extvec_gate.nx

nx_totp_extvec_gate.nx -- TOTP vs RFC 6238 Appendix B, all SIX published SHA-1 vectors. COMPLETES THE 2FA CHAIN. nx_hotp_extvec_gate proved HOTP (RFC 4226, 10/10). This proves TOTP, which adds the TIME-STEP DERIVATION T = floor(unix_time / X) on top of HOTP and uses EIGHT digits rather than six. ★Neither addition is implied by the other: an 8-digit dynamic truncation exercises a different modulus than 6, and T-derivation is integer division that nothing below it can validate. TWO INDEPENDENT CHECKS PER ROW, because the table publishes enough to separate them: 1. DERIVED T -- our own time/30 must equal the document's "Value of T (Hex)" column 2. TOTP CODE -- totp_sha1_value(seed, 20, time, 30, 8) must equal the document's TOTP column ★IF ONLY THE CODE WERE CHECKED, A WRONG T AND A COMPENSATING TRUNCATION BUG COULD CANCEL. Checking the intermediate the authority happened to publish makes that impossible -- USE EVERY COLUMN THE AUTHORITY GIVES YOU; THE INTERMEDIATE ONES ARE THERE TO LOCALISE FAILURES. ⚠SCOPE, STATED HONESTLY: RFC 6238 publishes EIGHTEEN rows -- 6 time points x {SHA1, SHA256, SHA512}. This gate grades the SIX SHA-1 rows only, because this tree has TOTP over SHA-1 and not over SHA-256 or SHA-512. The other twelve are NOT skipped-and-forgotten: they are counted and reported as UNIMPLEMENTED-MODE, which is a capability gap, not a pass. ★A ROW YOU CANNOT COMPUTE IS NOT A ROW YOU PASSED, AND CALLING IT "N/A" IN SILENCE IS HOW COVERAGE INFLATES. ⚠THE SEED IS READ FROM THE DOCUMENT (`String seed = "3132...3930";`) -- 20 bytes, never typed from recall. ★THE KEY IS AN ANSWER TOO. ⚠ROW SELECTION IS BY THE EXACT CELL "| SHA1 |" (two spaces). "SHA1" alone is NOT a safe discriminator here because SHA256/SHA512 rows exist; a substring test would grade all eighteen against a SHA-1 implementation. ★A SUBSTRING NEEDLE FLATTERS SILENTLY. license_tier: ORIGINAL expect_exit: 0