- Final
- Tuesday, December 20, Noon to 2:30
- This room
- Questions re cryptography we covered, fine-grained writing skills, etc. (like midterm)
- Rules and format similar to midterm, especially open references
- Designed for 1 1/2 to 2 hours, you have 2 1/2
- Donuts and cider
- SOFIs: 5 responses (25%) as of last night
- $1/SOFI added to printing balance
- Public keys
- Keys have 2 parts, one public for encrypting and one private for decrypting
- Keys have 2 parts, one public for encrypting and one private for decrypting
- RSA
- RSA = “Rivest, Shamir, Adelman”, the inventors
- Keys are triplets of numbers (n, e, d)
- Public key = (n, e)
- Private key = (n, d)
- Represents messages as numbers (computers do this internally anyhow) and uses modular arithmetic
- x mod n = remainder when dividing x by n
- e.g., 9 mod 4 = 1
- To encrypt plaintext M: Me mod n
- To decrypt ciphertext C: Cd mod n
- Relationship between n, e, d
- n is the product of 2 large prime numbers, p and q
- ed mod (p-1)(q-1) = 1
- Security relies on it being very hard to factor n into p and q (from p, q, and e it is easy to calculate d)
- e.g., factor 1517
- …and cryptographers think “large” numbers start at around 300 digits long
- Computer scientists generally believe factoring is hard, but no-one knows for sure
- e.g., factor 1517
- Try it
- Key calculator at https://www.cs.drexel.edu/~introcs/Fa12/notes/10.1_Cryptography/RSAWorksheetv4d.html
- Encrypt/decrypt at https://www.cs.drexel.edu/~introcs/Fa12/notes/10.1_Cryptography/RSA_Express_EncryptDecrypt.html
- Alyssa, Arisa, Kaitlyn
- 276 315 91 305
- N-391
- E-59
- 123 305 231 213 66 315 91 213 305 276 276 295 8 276 213 295 91 305 213 123 305 231 231 305 91 213 231 59 295 257 213 8 66 315 91 276
- 68 41 94 213 8 66 315 213 276 305 305 213 41 231 213 187 295 276 213 276 257 66 187 41 257 171 213 231 59 41 276 213 337 66 91 257 41 257 171
- Mike, Jeremy, Travis
- N=731
- E= 5
- 106 339 729 70 211 110 149 339 564 149 431 70 406 110 663 524 149 70 12 406 360 12 70 339 149 149 360 729 70 590 110 232 73 400 341 241
- 568 339 564 339 232 729 70 73 149 70 360 70 211 110 149 339 564
- 663 360 400 400 360 70 149 12 138 410 729 70 408 110 564 70 590 360 211 590 70 211 360 12 339 564 241
- 359 406 138 12 70 138 261 70 360 421 110 138 12 70 232 729 70 153 564 71 70 359 339 138 149 149 70 12 110 663 339 564
- Vaughn&Shenea -
- n= 65
- e= 5
- 46 2 20 51 2 34 23 2 20 20 2 11 7 2 51 39 56 2 55 2 36 2 2 15 55 2 51 39 56 4 56 2 2 4 56 2 8 2 39 2 53 56 2 15 11 2 34 23 2 20 20 56 20 2 51 11 44 11 4 4 11 19 11 2
- Adam, Tariq, Chris
- N = 323
- E = 17
- 155 173 280 29 193 115 117 29 114 16 117 280 16 35 48 117 289 16 16 141 12
- Tommy, Phillip
- N=437
- e=5
- 89 100 410 89 326 424 326 85 80 89 410 85 326 406 262 115 70 122 326 85 85 326 325 373 326 70 104 80 114 122 100 85 406 326 80 424 406 326 424 406 67 165 115
- 145 225 100 261 52 89 115 70 261 115 89 163 261 80 410 261 70 225 326 115 261 17 52 89 115 115 69 261 59 100 17 122 261 163 100 89 69