Kendall Rowe, Lauren Chandler, Anna Rose Robinson, Naomi Hardy-Njie, and Tiffany Pozo-Lin

Hello! Welcome to the Girls Talk Math Cryptology Blog. We are here to write about what we have learned in these past two weeks. We were given the task of completing a packet we learned about cryptography, which is the art of solving codes. We have also learned how to decrypt messages using modular arithmetic. We now know what a cipher is, and the different types of ciphers which are the Ceaser Cipher, Affine Cipher and the One Time Pad. We have been taught about the Euclidean Algorithm and the Diffie-Hellman Key Exchange. Last but not least, we have been introduced to some very important female cryptographer role models including Mavis Batey, Grace Hopper, Elizebeth Smith Friedman, Agnes Meyer Driscoll and Genevieve Young Hitt who almost all fought in World War II.

During this week we learned different forms of ciphers. But before you learn a cipher you need to know what a cipher is. A cipher is a system that converts a plaintext message into a cipher message using cryptographic algorithm and a secret key value. The first cipher example is a one-time pad cipher. The One-time Pad was the first and only mathematically unbreakable encryption in existence. The One-time Pad is very similar to the Caesar Cipher because they both involve shifting. The Caesar Cipher is a substitution cipher based on a “shift”. A plain text character is replaced by a cipher letter that is certain amounts of shifts away from that letter in the alphabet. To complete any type of cipher the Intermediate Plain and Cipher Conversion Table is always needed.

We learned how to do the Euclidean Algorithm, which is the most efficient way for finding the greatest common divisor. To do the Euclidean Algorithm you take two (2) numbers a and r, which will be 60 and 24 for now. 60 is the dividend 24 is the divisor. Then you would want to take the modulo of 24 to 60. Which would give you 12. Now we know that, b= 12. Repeat those steps with 12 using r=24 mod 12= 0. A= 12 and b= 0, b= 0. You will end up with a return a= 12 which basically means that 12 is your greatest common divisor for 60 and 24. Earlier we were speaking of this function called modulo. The modulo of a number is the remainder. For example, 24 mod 3 is equal to 0 because 3 goes into 24 evenly which means there is no remainder. When taking the mod, remember that it is the remainder of the quotient if there is one.

During the first week our grouped learned about Affine Ciphers. We first learned the formula used to create the code and would later help us to break it as well: C = m * a + b (mod 26). From the packet we figured out what each variable stands for; C is the entire coded message, m is the value of the original letter, a and b are for numbers of choice and the last step involves dividing the product by 26 (the number of letters in the English alphabet), taking the remainder, and ultimately multiplying it by 26. Next, we applied this knowledge by coming up with our own a and b values and putting the formula to the test with a 4-step process. We determined the number of each letter of the message, multiplied them individually by 5, added 9, completed mod 26, and determined the letter corresponding to the product we got. I chose to use 5 and 9 in my example but it can work with any number you choose. I enjoyed learning about Affine Ciphers because the process was very clear and easy to follow. It was cool to use math to create a code because it helped me to keep track of the way I change each letter and how to break a message that had been created already.