1. 251959084756578934940271832400483985714 292821262040320277771378360436620207075 955562640185258807844069182906412495150 821892985591491761845028084891200728449 926873928072877767359714183472702618963 750149718246911650776133798590957000973 304597488084284017974291006424586918171 951187461215151726546322822168699875491 824224336372590851418654620435767984233 871847744479207399342365848238242811981 638150106748104516603773060562016196762 561338441436038339044149526344321901146 575444541784240209246165157233507787077 498171257724679629263863563732899121548 314381678998850404453640235273819513786 36564391212010397122822120720357 Breaking Cryptography Parallel Decryption Brad Heap May 2009

2. Encryption 101 Requires Code Breaking Sender Receiver Message Compromised Without Encryption

3. Types of Algorithms Symmetric Key – Both sender and receiver need the same key to encrypt and decrypt message. – Fast to encode and decode. – Some algorithms allow for multiple encoding passes.

4. Types of Algorithms Asymmetric Key (Public/Private Key) – Sender and receiver need different keys to encrypt and decrypt messages. – Public Key is a semi-prime calculated from two long prime numbers (the private key) – Sender encodes messages as blocks raised to nth power. – Slow to encode and decode. – Often Symmetric Key is encoded in Asymmetric at start of message and rest of message is Symmetric.

5. One Way Messages One Way – Primarily used as a check or where the plaintext is irrelevant... e.g.: EFTPOS Card Pin Numbers. Data Integrity... MD5 Checksum. – Vulnerable to collisions. e.g. Pin: 1234, Checksum: 1 + 2 + 3 + 4 = 9 Another pin was 2341, Checksum 2 + 3 + 4 +1 = 9. In this example a wrong pin number could still give out cash.

6. Breaking the Key Brute Force – E.g. 1 You know a key is a 16 digit number 10 Possible Numbers Per digit Permutations: 9,999,999,999,999,999 combinations to check. Checking Process is naturally parallel. Assume 256 node cluster at 100 checks per second. Maximum Time: 390,624,999,999 seconds (12,735 years)

7. Breaking the Key Brute Force – E.g. 2 You know a key is 8 alphanumeric characters. 90 Possible Characters Per character. Permutations: 4,304,672,100,000,000 combinations to check. Checking Process is naturally parallel. Assume 256 node cluster at 100 checks per second. Maximum Time: 168,151,253,906 seconds (131,573 years)

8. Breaking the Key With modern codes Brute Force is often not a viable solution. However knowledge is power, and the more we know about the design of the key and/or algorithm used for encoding the more that we can learn about its structure... Therefore we can dramatically reduce the number of keys to check.

9. Dictionary Attack E.g. 1 Assume we have learnt that the 16 digit number is a prime. There are 29,844,570,422,669 16 digit primes. Assuming same computing power as before it would now only take a maximum of 1,165,803,532 seconds (912 years) to break.

10. Dictionary Attack E.g. 2 Assume we have learnt that the 8 characters spell a word. There are around 100,000 words in English. Let us assume it can have a number and order of capital and lowercase letters, leaving us with 2,965,420,000 possible orders. Assuming same computing power as before it would now only take a maximum of 115,836 seconds (32 hours) to break.

11. Random Numbers A secure key or encryption algorithm routine is one that is relies completely random numbers and cannot be guessed or predicted. However generating true random numbers is very hard. Both humans and computers are vulnerable to creating “random” numbers through patterns or sequences which can be worked out.

12. Random Number Conjecture If it is possible to build a true random mechanical random number generator, would it be possible to generate a computer simulation of this number generator? If so is the mechanical simulator truly random?

13. Trapdoor Function Some encryption algorithms have special functions that can be applied to the encrypted data without a key to reveal the encoded messages. These functions are often deliberately encoded into an algorithm so that the government or other source of authority can still check/read the data. Without knowledge of a trapdoor breaching it is a very complex and time consuming task.

14. Breaking the Text - Pattern Matching Sometimes in it impractical to try and break the key. In this case trying to work out words contained in the encoded text can lead to a break through. E.g: Cipher Text: +83(88 Guessing that the ‘8’ is really a ‘e’: +e3(ee Plain Text: degree

15. Pattern Matching – Image Example Messages are not always hidden in text format. Data can be hidden in images. Guessing the algorithm or where the data is stored can be tricky. E.g. By removing all but the last 2 bits of each color component, an almost completely black image results. Making the resulting image 85 times brighter results in:

16. Permutations A curse of the brute force attack is the numbers of permutation of numbers that need to be checked. In permutations of a set alphabet there will be a huge number of permutations that are so similar to the original alphabet that they will never be used in code. For instance a 4 letter alphabet ABCD. There are 24 permutations. However 21 of the Permutations either transpose or reverse onto themselves.

17. Permutations For instance Permutation: DACB. Cannot be used because C will also transpose to C hence so will never been encoded. For instance Permutation: BADC Cannot be used because if you encode text a second time with the Permutation you will decode it. Only DCBA, CDAB, BADC are permutations that do not transpose onto themselves.

18. Permutations Having Permutations that transpose onto themselves is a weakness in a code because it can fail to encode some data. However limiting what permutations of a set alphabet that can be used can make the code weaker as there is less permutations to check. “Damned if you do, damned if you don’t.”

19. Summary Code cracking is a naturally Parallel exercise. Even with the most powerful systems a brute force attack is practically impossible. However, the more you can learn about how a code operates the more easy it becomes to crack.

20. Further Thoughts Other Ways to Keep a Secret: – CA Authority – Salting – One Time Pad – Quantum Encryption

21. Quantum Encryption

22. Further Reading Code Breaking. Rudolf Kippenhahn. 1999. The Code Book. Simon Singh. 2000. A good maths text-book. Particularly something on discrete mathematics. How Encryption Works. Jeff Tyson. http://computer.howstuffworks.com/encryption.htm How Quantum Cryptology Works. Josh Clark. http://science.howstuffworks.com/quantum- cryptology.htm Cryptanalysis. Wikipedia. http://en.wikipedia.org/wiki/Cryptanalysis