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Bronson Jastrow. Public Key Encryption. Outline. What is cryptography? Symmetric Key Cryptography Public Key Cryptography How Public Key Cryptography Works Authenticating sources Hybrid Cryptosystems Perfect Forward Secrecy Attacks on Public Key Systems. What is Cryptography?.

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Public Key Encryption

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Bronson jastrow

Bronson Jastrow

Public Key Encryption



  • What is cryptography?

  • Symmetric Key Cryptography

  • Public Key Cryptography

  • How Public Key Cryptography Works

  • Authenticating sources

  • Hybrid Cryptosystems

  • Perfect Forward Secrecy

  • Attacks on Public Key Systems

What is cryptography

What is Cryptography?

  • The securing of communications between parties.

  • Many ways to implement cryptography

  • Four basic goals of cryptography:

    • Confidentiality

    • Integrity

    • Authentication

    • Non-repudiation

Goals of cryptography

Goals of Cryptography

  • Confidentiality:Ensure only intended recipients have the means to read data.

  • Integrity:Ensure intended recipients have received data unaltered by a third party.

Goals of cryptography1

Goals of Cryptography

  • Authentication:Ensure subsequent messages from a source can be verified as originating from that source.

  • Non-Repudiaton:Ensure messages are traceable back to only the originator for when disputes arise.

Symmetric key cryptography

Symmetric Key Cryptography

  • The same key is used for both encrypting and decrypting data.

  • Shared Secret (One key shared by all).

  • Known as Private Key Cryptography.

  • Not ideal for exchange over unsecured networks.

Public key cryptography

Public Key Cryptography

  • Different keys are used for encryption and decryption.

  • Encrypt with public key.

  • Decrypt with private key.

  • Known as Asymmetric Key Cryptography.

Public key cryptography1

Public Key Cryptography

  • Public keys may be shared.

  • Private keys must be kept secret.

  • Public keys may be exchanged over unsecured networks.

  • The keys are mathematically linked.

  • Computationally infeasible to compute the private key from the public key.

  • Disadvantage: Encryption and decryption are slow.

Trap door function

Trap Door Function

  • A function which is easy to compute in one direction, but difficult in the opposite direction.

    • Integer Factorization

    • Discrete Logarithm

    • Elliptic Curve

  • Used for implementation of public key cryptography.

  • Example: RSA is based on Integer Factorization

Integer factorization

Integer Factorization

  • Hard to decompose an integer into its prime factorized form.

  • Easy to compute an integer from its prime factorized form.

  • Ex: What is the prime factorization of 247? 13*19

Integer factorization1

Integer Factorization

  • No efficient way to determine prime factorization.

  • Even more difficult to determine a semiprime(a product of two primes).

Rsa 768 factorization

RSA-768 Factorization

  • 2009 – A 768 bit (232 decimal) semiprime generated by the RSA algorithm was factored.

  • Estimated 1,500 years of 2.2Ghz AMD Opteron processing.

  • RSA-1024 is considered 1,000 harder to crack

Rsa 768 perspective

RSA-768 Perspective

  • RSA-768 = 12301866845301177551304949583849627207728535695953347921973224521517264005 07263657518745202199786469389956474942774063845925192557326303453731548268 50791702612214291346167042921431160222124047927473779408066535141959745985 6902143413

  • RSA-768 = 33478071698956898786044169848212690817704794983713768568912431388982883793 878002287614711652531743087737814467999489 * 36746043666799590428244633799627952632279158164343087642676032283815739666 511279233373417143396810270092798736308917

Digital signatures

Digital Signatures

  • Messages may be signed with the sender’s private key.

  • Signatures can be verified by the matching public key.

  • Verification means the message is from the owner of the private key

  • Verification also means the message has not been tampered with.

  • Signer cannot deny having signed message.

Public key vs symmetric key cryptography

Public Key vs. Symmetric Key Cryptography

  • Public Key Cryptography

    • Keys can be exchanged safely over the internet.

    • Slow encryption and decryption times.

    • Signatures to verify identity.

  • Symmetric Key Cryptography

    • Key exchange over internet is insecure

    • Fast encryption and decryption compared to public key cryptography.

Hybrid cryptosystems

Hybrid Cryptosystems

  • Combining of Symmetric Key and Public Key algorithms.

  • Exchange public keys.

  • Encrypt symmetric key to use for session.

  • Send encrypted symmetric key.

  • Exchange messages using symmetric key.

Hybrid cryptosystems1

Hybrid Cryptosystems

  • SSL/TLS uses hybrid cryptosystems to secure internet transactions.Ex. Email, Banking

  • Problem: How to protect users from man-in-the-middle attacks

Key exchange

Key Exchange

  • How does a user know that the party they exchange keys with is legitimate?

  • Answer: Certificate Authorities.

  • Certificate Authority is a trusted third party.

  • Certificate from website is sent to user.

  • Certificate contains public key, and a copy signed by a certificate authority.

Key revocation

Key Revocation

  • Key Compromise

  • Affiliation Change

  • Key Superseded

Key revocation1

Key Revocation

  • What happens when a key is compromised?

  • Certificate Revocation List (CRL)

  • Keep a list of revoked public keys

  • When revoked, list a new public key

Key revocation2

Key Revocation

  • How to handle revocation requests?

  • Depends on setup

    • Owner of private key

    • Compound Principals

Notifying users

Notifying Users

  • Push from server to client

    • Susceptible to DOS attack

  • Download by user from centralized server.

  • Set a short expiration date on updated list

Perfect forward secrecy

Perfect Forward Secrecy

  • All past communication is safe even if a private key is compromised.

  • Session keys must not be derived if long term keys are lost.

  • Problem: Private keys decrypt symmetric keys and verify identity.

  • Solution: Use private keys only to verify identity.

Diffie hellman key exchange

Diffie-Hellman Key Exchange

  • D-H key exchange can be used to achieve perfect forward secrecy

  • Allows two hosts to create symmetric keys through an insecure network.

  • Works between hosts which have never communicated.

Diffie hellman key exchange1

Diffie-Hellman Key Exchange

  • p is prime

  • g is a primitive root mod p

Diffie hellman in practice

Diffie-Hellman In Practice

  • Typically uses elliptic curve instead of discrete logarithm

  • Browser support is lacking

    • Firefox

    • Chrome

  • Performance issues for TLS handshakes

Attacks on public key systems

Attacks on Public Key Systems

  • Easiest way is to break people, not break encryption.

  • Broken algorithm: Messages can be decrypted without private key.

  • Totally broken algorithm: Private key can be recovered from public key.

  • Current systems are considered secure if key length is long.

Public key cryptography conclusion

Public Key Cryptography Conclusion

  • Secures communication over unsecured networks.

  • Allows authentication, integrity checks, and non-repudiation.

  • Used in conjunction with symmetric key encryption in TLS/SSL.



  • [1] Bernat, V. (2011). SSL/TLS & Perfect Forward Secrecy. Retrieved 10 2, 2013, from Vincent Bernat Blog:

  • [2] Cooper, A. D. (1998). A closer Look at Revocation and Key Compromise in Public Key Infrastructures. Gaithersburg: National Institute of Standards and Technology.

  • [3] Dev-NJITWILL. Crypto.

  • [4] Diffie, W., & Hellman, M. E. (1976). New Directions in Cryptography. IEEE.

  • [5] Göthberg, D. Public Key Encryption. Sweden, Sweden.

  • [6] Kleinjung, T. (2010). Factorization of a 768-bit RSA modulus.

  • [7] Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (1996). Handbook of Applied Cryptography. CRC Press.

  • [8] Rescorla, E. (2006). Diffie-Hellman Key Exchange - A Non-Mathematician's Explanation. ISSA Journal , 7.

  • [9] Ristic, I. (2013, June 25). SSL Labs: Deploying Forward Secrecy. Retrieved 10 10, 2013, from Qualys Community:

  • [10] Vinck, A. H. (2012, May 12). Introduction to Public Key Cryptography. Duisburg-Essen, Germany. Retrieved from

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