Deciphering a key from XOR encrypted cypher using boolean logic

following the white rabbit direct to cables i have this hotdog ..because xor is the base of all hardware encryption 

Elsa David of course i know we're talking about optic tronics

If K$K$ is random and you only know A$A$ or B$B$ (but not both) then, no, there is no way to infer anything about the key - this is the (in)famous one-time-pad.

If you know A$A$ and B$B$, then you can recover K$K$ very easily. Exclusive-or has those properties:

• ∀n$\mathrm{\forall }n$,     n⊕n=0$n\oplus n=0$
• ∀n$\mathrm{\forall }n$,     n⊕0=n$n\oplus 0=n$ (identity element)
• ∀a,b$\mathrm{\forall }a,b$,     a⊕b=b⊕a$a\oplus b=b\oplus a$ (commutativity)
• ∀a,b,c$\mathrm{\forall }a,b,c$,     a⊕b⊕c=(a⊕b)⊕c=a⊕(b⊕c)$a\oplus b\oplus c=(a\oplus b)\oplus c=a\oplus (b\oplus c)$ (associativity)

So we can do the following:

B=A⊕K   ⇒   A⊕B=A⊕(A⊕K)=(A⊕A)⊕K=0⊕K=K$B=A\oplus K\Rightarrow A\oplus B=A\oplus (A\oplus K)=(A\oplus A)\oplus K=0\oplus K=K$

So A⊕B=K$A\oplus B=K$

Viewed differently, the exclusive-or operator is invertible:

⊕01001110$\begin{array}{|ccc|}\hline \oplus & 0& 1\\ 0& 0& 1\\ 1& 1& 0\\ \hline\end{array}$

A0011B0101⊕0110$\begin{array}{|ccc|}\hline A& B& \oplus \\ 0& 0& 0\\ 0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\\ \hline\end{array}$

And since the truth table is symmetric, the exclusive-or operation just happens to be its own inverse, i.e. x⊕−1y=x⊕y$x{\oplus }^{-1}y=x\oplus y$. So if we take our original equation:

A⊕K=B$A\oplus K=B$

We can represent it as follows:

K⊕A=B$K\oplus A=B$

And we can then undo (invert) the exclusive-or by A:

K⊕A⊕−1A=B⊕−1A   ⇒   K=B⊕−1A$K\oplus A{\oplus }^{-1}A=B{\oplus }^{-1}A\Rightarrow K=B{\oplus }^{-1}A$

And as we found above, this is identical to:

K=B⊕A=A⊕B$K=B\oplus A=A\oplus B$

As found at the beginning.

However, this is assuming A, B and K are all the same length. If K is smaller than A and B, then it means that K will be used multiple times (repeated over the length of the plaintext, presumably). This repetition can be exploited to successfully recover K from only B provided there is enough repetition and there is enough ciphertext to work with - see Vigenere cipher.

DECRYPTING PKCS # 8 and OpenSSLPrivate Keys with Java

The code works with Java 1.3 (+JCE), 1.4, 5.0, 6.0, but not all of the ciphers and hashes are available until Java 5.0 (unless you use BouncyCastle). Fortunately the most common formats [OpenSSL MD5 with 3DES], [PKCS #8 V1.5 MD5 with DES], [PKCS #8 V2.0 HmacSHA1 with 3DES] work with all versions of Java, including Java 1.3.

pkcs8 example:

FileInputStream in = new FileInputStream( "/path/to/pkcs8_private_key.der" );

// If the provided InputStream is encrypted, we need a password to decrypt
// it. If the InputStream is not encrypted, then the password is ignored
// (can be null).  The InputStream can be DER (raw ASN.1) or PEM (base64).
PKCS8Key pkcs8 = new PKCS8Key( in, "changeit".toCharArray() );

// If an unencrypted PKCS8 key was provided, then this actually returns
// exactly what was originally passed in (with no changes).  If an OpenSSL
// key was provided, it gets reformatted as PKCS #8 first, and so these
// bytes will still be PKCS #8, not OpenSSL.
byte[] decrypted = pkcs8.getDecryptedBytes();
PKCS8EncodedKeySpec spec = new PKCS8EncodedKeySpec( decrypted );

// A Java PrivateKey object is born.
PrivateKey pk = null;
if ( pkcs8.isDSA() )
{
  pk = KeyFactory.getInstance( "DSA" ).generatePrivate( spec );
}
else if ( pkcs8.isRSA() )
{
  pk = KeyFactory.getInstance( "RSA" ).generatePrivate( spec );
}

// For lazier types:
pk = pkcs8.getPrivateKey();

Both RSA and DSA keys are supported. Here is a list of supported formats:

• OpenSSL "Traditional SSLeay Compatible Format"
  • Unencrypted PEM or DER
  • Encrypted PEM:
    • des
    • des2
    • des3
    • blowfish
    • aes128
    • aes192
    • aes256
    • rc2-40
    • rc2-64
    • rc2-128
    
    

    Note:

    OpenSSL "traditional SSLeay" format does not allow encrypted keys to be encoded in DER. Only unencrypted keys can be encoded in DER.

• PKCS #8 (Unencrypted)
  • PEM or DER
• PKCS #8 with PKCS #5 Version 1.5 Encryption
  • PEM or DER: 
    • MD2 with DES
    • MD2 with RC2-64
    • MD5 with DES
    • MD5 with RC2-64
    • SHA1 with DES
    • SHA1 with RC2-64
    
    
• PKCS #8 with PKCS #5 Version 1.5 Encryption and PKCS #12 Key Derivation
  • PEM or DER: 
    • SHA1 with 3DES
    • SHA1 with 2DES
    • SHA1 with RC2-128
    • SHA1 with RC2-40
    • SHA1 with RC4-128
    • SHA1 with RC4-40
    
    
• PKCS #8 with PKCS #5 Version 2.0 Encryption and HmacSHA1
  • PEM or DER: 
    • DES
    • 3DES
    • Blowfish
    • AES-128
    • AES-192
    • AES-256
    • RC2-40
    • RC2-64
    • RC2-128
    
    

---

Here are links to the raw samples and test results:

1. 2048 Bit RSA
2. 2048 Bit DSA

The samples were all generated using OpenSSL's rsa, genrsa, dsa, gendsa, dsaparam and pkcs8 commands. We're curious to know if PKCS #8 keys created by other programs will also work, but OpenSSL is all we have to play with at the moment.
The password to decrypt the samples is always "changeit", and they all have the same RSA or DSA key.

http://juliusdavies.ca/commons-ssl/pkcs8.html

following the "rabbit" on the "cables

Data encryption of optical fibre communication using pseudo-random spatial light modulation

https://www.degruyter.com/abstract/j/oere.2016.24.issue-2/oere-2016-0012/oere-2016-0012.xml

GALS System Design:
Side Channel Attack Secure Cryptographic Accelerators

https://iis-people.ee.ethz.ch/~kgf/acacia/c4.html

[3 pages, no date, no author]
Cylink Corporation has made encryption security products for networking, for over 16 years. Those products are built by foreign nationals and used by businesses, banks and governments around the world, including in the United States. Cylink has managed to export product without United States restriction, including to embargoed nations.
1. NASDAQ Ticker: CYLK
2. Pittway Corporation funded Cylink. The Harris family holds majority control in Pittway Corporation.
3. Cylink began as a partnership founded in 1984.
4. Cylink incorporated in 1989.
5. Cylink makes high grade encryption products and sold the products to organized crime.
6. Cylink was managed by Dr. Jimmy K. Omura, Louis Morris, Robert Fougner and Dr. Leo Guthart. Dr. Leo Guthart is the Vice-Chairman of the Board of Directors of Pittway Corporation.
7. Dr. Jimmy K. Omura has received several awards from the Director of the National Security Agency over the years.
8. Cylink enters into a number of contracts with the United States government to develop high grade encryption products.
9. Robert Fougner was Louis Morris's personal attorney, and manages Cylink's export licensing.
10. In the early 1990's, Dr. Jimmy K. Omura (Chief Technology Officer), Louis Morris (Chief Executive Officer) and Robert Fougner (Cylink attorney) created a joint venture with an engineering company based in Armenia named Hylink.
11. The senior Hylink executive is a ranking KGB officer named (General?) Gurgen Khchatrian.
12. The KGB trained field officer reporting to Khchatrian is named (Colonel?) Gaigic Evoyan. Evoyan travels to Cylink frequently. Evoyan travels with his own bodyguards. The FBI monitored Evoyan' s movements when he was traveling to Cylink.
13. The Russians travel into the United States under Armenian passports as Hylink engineers and wives.
14. The Hylink engineers enter the United States on business visas. Robert Fougner arranges to pay the engineers salary and all expenses in cash while the Hylink engineers are working at Cylink.
15. The Hylink engineers and their wives have unrestricted access to all Cylink facilities and encryption software source code and design information.
16. The Hylink engineers and Cylink develop and Cylink sells encryption products to various US Government departments including the United States Department of Defense and the Department of Justice.
17. Cylink sold their encryption products into United States banks and the United States Federal Reserve funds transfer system ("FedNet").
18. The Cylink engineering team and the Hylink engineers reported to the Cylink engineering Vice-president Leslie Nightingale. The engineers developed cryptography based networking product for the equivalent of the Federal Reserve funds transfer system in Europe, which is called S.W.I.F.T.
19. Cylink has exported high grade computers and encryption source code to Lebanon without being required to use United States export licenses arranged by Cylink.
20. Cylink has exported high grade encryption products to Iran, Iraq, Turkey and into several African nations.
21. Cylink has transferred high grade cryptography source code including its RSA source code to Hylink in Armenia. RSA encryption is the most secure cryptographic code available in the world at the time.
22. Some Hylink engineers brought into the United States to work in Cylink engineering are: Ashot Andreasyan, Nubarova Melik, Andre Melkoumian, Galina Melkoumian, Leonid Milenkiy, Mihran Mkrtchian, Elizabeth Mkrtchian, Karen Zelenko.
23. Cylink became a publicly traded company (CYLK) m 1996.
24. Pittway Corporation maintained sixty percent controlling stock in Cylink.
25 Founding CEO Louis Morris suffered a health problem and retired from Cylink.
26. Fernand Sarrat was recruited from IBM to replace Morris as CEO.
27. Fernand Sarrat and other select employees such as Dr. Jimmy K. Omura, John Kalb, and John Marchioni traveled to France, Belgium and Israel for a series of meetings.
28. Cylink purchased Algorithmic Research Limited, a small company in Israel selling encryption product outside of the United States.
29. The Director of the National Security Agency, federal prosecutors and several United States law enforcement agencies met in California to discuss Cylink. A two day meeting in 1997 took place in mid August.
30. Retired Secretary of Defense Perry joined the Cylink Board of Directors.
31. National Security Agency deputy director William Crowell joined Cylink in a marketing role.
32. High grade encryption products continued to be shipped outside of the United States by Cylink without export licenses.
33. Dr. Jimmy K. Omura left Cylink when Cylink sold its wireless products division to PCOM in Campbell, California.
34. A United States law enforcement agency seizes a multi-million dollar Cylink transshipment of high grade encryption products destined to the nation of Iran through the UAE. The criminal investigation against Cylink is put on hold.
35. Fernand Sarrat and the Cylink chief financial officer John Daws are implicated internally in a revenue accounting fraud with the vice president of sales, and terminated from Cylink employment.
36. William Crowell becomes CEO of Cylink.
37. President Clinton appoints Cylink CEO William Crowell to a special committee on encryption. William Crowell releases publicity statements on new recommendations about United States encryption policy and certain export regulations are relaxed, waiving Cylink's earlier export violations.
38. Honeywell purchased Pittway Corporation.
39. How is Cylink able to use foreign nationals to build security product for use within United States Government agencies and departments?
40. How is Cylink able to freely export security product, and other encryption companies were punished?
41. Which United States agency recruited Cylink to work with the KGB trained personnel in Armenia?
42. Which United States agency used Cylink product to listen to United States banking and funds transfers?
43. Which United States agency arranges for the legal protection of Cylink from investigation and prosecution?
44. What United States government agency provided Dr. Jimmy K. Omura and Louis Morris immunity from prosecution?
45. How is Robert Fougner able to stay at Cylink and avoid legal prosecution?
46. Is Cylink the National Security Agency's model business, or another Central Intelligence Agency business operating illegally inside United States borders?
CC
Congressman Dan Burton
Congressman John McCain
Congressman Orrin Hatch
Congressman Tom Campbell
Embassy of Switzerland
Embassy of the Russian Chancery
French Trade Commission
James Bidzos
John X. Miller
Rush Limbaugh
Steve Kroft

http://cryptome.org/cylinked.htm