Cryptography Beyond Textbooks: RSA, OAEP & PSS

Find the full handbook here: https://www.freecodecamp.org/news/the-cryptography-handbook-rsa-algorithm/

Timestamp:

00:00 - The Goal
01:38 - RSA Cryptosystem
02:50 - OS2IP & IP2OS
06:08 - RSA Operations
14:15 - Issues with Euler's Totient Function
15:07 - The Carmichael function
20:11 - Why Textbook RSA is Insecure
21:16 - Determinism Exploit
24:36 - Malleability Exploit
28:53 - Low-Exponent Attacks
33:22 - Håstad’s Broadcast Attack
45:08 - Padding Schemes in RSA
46:46 - PKCS#1 v1.5
57:07 - The Bleichenbacher Attack
01:07:45 - Optimal Asymmetric Encryption Padding (OAEP)
01:19:06 - Why SHA-I or MD5 are safe OAEP
01:21:25 - Probabilistic Signature Scheme (PSS)
01:29:30 - Assessing RSA's Long-Term Viability
01:31:08 - References

References
[1] FIPS 186-5: Digital Signature Standard (DSS)
[2] RFC 8017 PKCS #1: RSA Cryptography Specifications
[3] Lagrange's theorem
[4] Ronald L. Rivest, Robert D. Silverman: Are Strong Primes Needed for RSA?
[5] pyca/cryptography
[6] OpenSSL Github: rsa_chk.c
[7] RFC 2313: PKCS #1: RSA Encryption
[8] Daniel Bleichenbacher: Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS #1
[9] RFC 8017: PKCS #1 RSA Cryptography Specifications Version 2.2
[10] RSA_public_encrypt: Warnings
[11] pyca/PKCS1v1
[12] Probabilistic signature scheme
[13] RFC 8017: RSASSA-PSS
[14] Algorithms for quantum computation: discrete logarithms and factoring