Add rsa.phi-not-coprime-e.2048.txt

rsa-phi-not-coprime-e/README.md

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+## RSA primes where `GCD(φ(n), e) != 1`
+
+The `rsa.phi-not-coprime-e.2048.txt` file contains two candidate primes for
+RSA 2048 key generation, one per line, in big endian hex.
+
+The second prime is congruent to 1 mod 65537, which means φ(n) = (p - 1)(q - 1)
+is not coprime with e = 65537.  Therefore, this prime cannot be used in a valid
+RSA key.
+
+The first prime is provided so the entire file forms a stand-alone input to
+RSA key generation (excluding primality testing input).  This means if you
+provide it as input to FIPS186-5 algorithm A.1.3, it fails the condition 5.6.
+If you swap the two candidates, it fails the condition 4.5.
+
+### Working
+
+```python
+>>> import sympy
+>>> p = 0xf68be4166c4bf00a01261d1d51e8a3da28da241cd07d2eb50696c14e7e02de7f83250b669842b0d3cb77e926408377b47b7ed01d54d8ad2ec57a453c3eca57b8faf1caf84c94e383351a0ad2ee179be14c9170b63e6328062689f5569e6cfe4524cd3bff0c2abb7de6d4a80827c1b2cd180e23a8b84a21cee5cd0a9be7306a9d
+>>> q = e58b13cc5ae5cf25e685f0c6b5c8eee7d2f3a2a54f3b7520d64d30c36e476f0a42c8183f84695537c94001633d560aa16c8edcc990ff0f30869d7ddab426500763aebf8d27ccfca872696872316e6a378323d9a9a8fa256d16f70601e7b519c22daf63126caf2642253de823ab3d575ee84445bc5bb9aa1df2ae9cb624d0b963
+>>> e = 0x10001
+>>> all(map(sympy.isprime, [p, q]))
+True
+>>> phi = (p - 1) * (q - 1)
+>>> sympy.gcd(phi, e)
+65537
+```
+
+The candidate q was found by brute force; one can be expected every 65537 primes.
+
+## License
+
+The vectors in this folder are available under the terms of the
+[Zero-Clause BSD](https://opensource.org/licenses/0BSD) license or (at your
+option) [CC0 1.0](https://creativecommons.org/publicdomain/zero/1.0/).
+
+> Copyright (c) 2024 The CCTV Authors
+>
+> Permission to use, copy, modify, and/or distribute this software for any purpose
+with or without fee is hereby granted.
+>
+> **The software is provided "as is" and the author disclaims all warranties with
+regard to this software including all implied warranties of merchantability and
+fitness. In no event shall the author be liable for any special, direct,
+indirect, or consequential damages or any damages whatsoever resulting from loss
+of use, data or profits, whether in an action of contract, negligence or other
+tortious action, arising out of or in connection with the use or performance of
+this software.**

rsa-phi-not-coprime-e/rsa.phi-not-coprime-e.2048.txt

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+f68be4166c4bf00a01261d1d51e8a3da28da241cd07d2eb50696c14e7e02de7f83250b669842b0d3cb77e926408377b47b7ed01d54d8ad2ec57a453c3eca57b8faf1caf84c94e383351a0ad2ee179be14c9170b63e6328062689f5569e6cfe4524cd3bff0c2abb7de6d4a80827c1b2cd180e23a8b84a21cee5cd0a9be7306a9d
+e58b13cc5ae5cf25e685f0c6b5c8eee7d2f3a2a54f3b7520d64d30c36e476f0a42c8183f84695537c94001633d560aa16c8edcc990ff0f30869d7ddab426500763aebf8d27ccfca872696872316e6a378323d9a9a8fa256d16f70601e7b519c22daf63126caf2642253de823ab3d575ee84445bc5bb9aa1df2ae9cb624d0b963