Overview. Recall Basic Idea. CSC 580 Cryptography and Computer Security. March 9, 2017
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1 CSC 580 Cryptography and Computer Security Public Key Cryptography - Ideas and RSA (Related to parts of Chapters 9 and 10) March 9, 2017 Overview Today: HW 7 quiz Public Key Algorithms - ideas, math, and RSA Next: Spring Break! Have fun! If you want to be productive: Work on project phase 3 Read Sections , 2.8, 10.1, 10.2 Recall Basic Idea Network Interface agxu4n<:1evxxyel4} 0h7dP6]%< Network Interface Keys the same or different? Encryption Function Different: Public-key crypto Some algorithms: RSA, ElGamal, ECC, Best feature: Simpler key management (can send to a stranger!) Decryption Function Pay with Worst feature: Slow (1-2 Mbps for 2048-bit RSA - others are a little faster ) Pay with
2 Public Key Crypto Where do the keys come from? Symmetric Ciphers Public Key Crypto Secret Key (SK) PubKey (PU) PrivKey (PR) Mathematical/Computational Properties KPG(R) (PU, PR) is efficiently computatable (polynomial time) For all messages M, D(PR, E(PU, M)) = M (decryption works) Computing PR from PU is computationally infeasible (we hope!) Generally: PR has some additional information that makes some function of PU easy to compute (which is hard without that info) - this is the trapdoor secret How can this be possible? How can this be possible? What if I told you the prime factorization of N is 5,407 * 6,011?
3 How can this be possible? What if I told you the prime factorization of N is 5,407 * 6,011? 5,406 multiples of 6,011 share the factor 6,011 with N 6,010 multiples of 5,407 share the factor 5,407 with N No numbers in common between these two sets (prime numbers!) So 5,406+6,010 = 11,416 numbers share a factor with 32,501,477 The factorization of N is a trapdoor that allows you to compute some functions of N faster Using Public Key Crypto in the JCA Generating a keypair: kp.getpublic() gives PublicKey (IS-A Key, so can be used to initialize a Cipher in ENCRYPT_MODE) kp.getprivate() gives PrivateKey (IS-A Key, so can be used to initialize a Cipher in DECRYPT_MODE) Otherwise works just like Cipher with a symmetric cipher algorithm! Related Notion - Key Agreement Original idea - before public key encryption Alice Bob PubKey (PU A ) PrivKey (PR A ) PubKey (PU B ) PrivKey (PR B )
4 Related Notion - Key Agreement Original idea - before public key encryption Alice Properties: PK KeyPair properties GS(PU A,PR B )=GS(PU B,PR A ) Bob Infeasible to compute S from only public keys (PU A and PU B ) Note: No message - so can send no information. PubKey (PU A ) PrivKey (PR A ) But two sides get a shared secret PubKey (PU B ) PrivKey (PR B ) Using Key Agreement in the JCA For algorithm DH (Diffie-Hellman) Generating a keypair requires first generating public parameters: But: Parameter generation can be slow so often done in advance and saved. Weakness recently found for this, however be cautious! Given parameters, Alice and Bob can do key agreement: Bob s public key (received) Key Sizes for Public Key Systems From NIST publication a Issue: PK algorithms based on mathematical relationships, and can be broken with algorithms that are faster than brute force. We spent time getting a feel for how big symmetric cipher\ keys needed to be How big do keys in a public key system need to be? From NIST pub a:
5 Weakness in long-term fixed DH parameters From 2015 ACM Conference on Computer and Communication Security:
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