1. Cryptography and Code Breaking Cryptography is the study and practice of hiding messages.

2. Places Cryptography is Used

3. Austria in the 1990's A series of letter bombs were sent to various recipients. The list of recipients was encrypted by the terrorists. The terrorists wanted to demonstrate that the government was powerless to stop them.

4. Cryptographic Methods There are two common types of cryptography. Private Key Cryptography Public Key Cryptography

5. Private Key Cryptography Using Private Key Cryptography you have to exchange keys prior to communication. The Key must be kept private from third parties.

6. Public Key Cryptography Using Public Key Cryptography you don't have to exchange keys prior to communicating. Two keys are used with this method, a public key and a personal key.

7. Personal Key The personal key is two randomly chosen prime numbers. Example: P = 7, Q = 11 This key is not shared with anyone. It is used by the receiver to decrypt the message.

8. Public Key The public key is the product of the two chosen primes from the personal key. Example: N = P * Q = 7 * 11 = 77 This key is shared with everyone. It is used to encrypt messages to be sent to the person with the matching personal key.

9. Factorization The strength lies in the difficulty of factoring numbers. What are the factors of 77? 7 and 11 What are the factors of 70058167? 8867 and 7901

10. Example Keys Here is an example of a small public key that could be used to encrypt a message 27997833911221327870829467638722601621070446786 9554285375600099293261284001076093456710529553 6085606182235191095136578863710595448200657677 5098580557613579098734950144178863178946295187 237869221823983 Can you tell the factors?

11. Factors Using our method you would find that the factors are: 35324619344027701212726049781984643686711974001 9762502364930346877612125367942320005854795652 8088349 and 7925869954478333033347085841480059687737975857 3642199607343303414557678728181521353814093047 40185467

12. My Team Studied Factorization If you can factor the public key you can decipher the message. We devised what we thought was a new technique to factor numbers. We discovered that this technique already existed (fermat factorization).

13. Applications of Research The mail bombers accidently used a weak key. This allowed the encryption to be broken. The technique used to break the message was the same technique my team reinvented, fermat factorization.

14. Take Away Messages Cryptography is used everywhere! Cryptography is not always secure. More researchers are needed.