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Cryptography Esthers added slides (the rest are in the lecture slide deck) RSA- Rivest Shamir Adleman Uses modular arithmetic as its secret sauce. Generate large primes p and q . Calculate n = p*q . n is the modulus (public)

  1. Cryptography Esther’s added slides (the rest are in the lecture slide deck)

  2. RSA- Rivest Shamir Adleman Uses modular arithmetic as its secret sauce. • Generate large primes p and q . • Calculate n = p*q . n is the “modulus” (public) • Calculate the totient phi = (p-1)(q-1) , or lcm(p-1,q-1) in the new standard • Choose integer e between 1 and phi s.t. e and phi are coprime. • e is the “public key exponent” • Compute d such that d*e = 1 mod phi • d = (1 + k*phi)/e • d is private • Publish: (n, e) on key servers somewhere • Keep private: (n, d) (“Side channel attack” still possible where someone steals your private key on your comp)

  3. RSA- Rivest Shamir Adleman • You can encrypt a message m by raising to the e power and taking the mod n to get c. c = m e mod n • • Decrypt it to get m back by raising c to the d power and taking the mod n. m = c d mod n • Chinese remainder theorem: m ed ≡ m mod n . Since c is m e mod n, c d mod n is the desired m. • Why does this work? • You can’t compute d, p, or q from knowing n and e. • Prime factorization of large integers is hard, and if you pick one with a large number of digits (>=2048 bits) it’s very secure. The “RSA problem”: to take e th root of c, mod n. The RSA algo defines a one way • function .

  4. Digital Signatures In summary: • Allow you to verify that a file has not been tampered with (integrity) and it’s the right person who sent it (authenticity) • Compute a hash of the file, encrypt it, and attach it to the end of the file as a signature. • When the person receives the file, they hash it, decrypt the signature, and compare the hash with the decrypted signature.

  5. Checking a hash Checking debian checksum and signatures https://www.debian.org/CD/verify https://cdimage.debian.org/debian-cd/9.6.0-live/amd64/iso-hybrid/ https://linuxconfig.org/how-to-verify-an-authenticity-of-downloaded-debian-is o-images Checking ubuntu-mate distro checksum http://ubuntu-mate.org/download/

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