Download presentation

Presentation is loading. Please wait.

Published byJamari Mann Modified over 2 years ago

1 RSA: More about attacks Need to take care with the implementation, e.g.: - Do not take p or q very small. - Difference of p and q should not be very small. More subtle, e.g.: Thm: If 3d < n^{ ¼ } and q

{ "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3546979/slides/slide_1.jpg", "name": "RSA: More about attacks Need to take care with the implementation, e.g.: - Do not take p or q very small.", "description": "- Difference of p and q should not be very small. More subtle, e.g.: Thm: If 3d < n^{ ¼ } and q

2
RSA: More about attacks Public-key cryptosystem: can it have perfect secrecy ? RSA is insecure against a chosen-ciphertext attack (we’ll do soon). Is RSA insecure against a known-plaintext attack ? Is RSA insecure against a chosen-plaintext attack ?

3
RSA: Protocol Failures Secure system can still be used in an insecure (careless) way. This is called a protocol failure. Examples: Exercises 16 and 17 (Chapter 6, page 194)

4
RSA: Insecurity against Chosen-Ciphertext Eve wants to decrypt y (a ciphertext). She can choose another ciphertext ŷ \neq y that she can use to decrypt y. Choose a random x_0 and compute y_0 = (x_0)^e mod n. Let ŷ = y_0y mod n. Eve gets the decryption of ŷ. How to find y ?

5
RSA: Timing Attacks In 1995, Paul Kocher (an undergraduate at Standford), discovered that it is possible to determine d (the decryption exponent) by carefully timing the computation times for a sequence of decryptions. Moral of the story: a new type of attack can break a system that is though to be secure… Good news for RSA: it is possible to thwart the timing attack.

6
Other Public-key Cryptosystems RSA is the “standard” but there are other public-key cryptosystems. E.g. one by Rabin and one by ElGamal. All three cryptosystems: - thought to be secure - can be used for digital signatures - slow Hence: used to encrypt a session key, then use a (secure) private key cryptosystem

7
Other Public-key Cryptosystems The Rabin cryptosystem: - based on the difficulty of finding square roots mod a composite number (problem equivalent to factoring) - provably secure (unlike RSA; assuming factoring is computationally infeasible, the Rabin cryptosystem is secure) - 4 possible plaintexts for each ciphertext [RSA: conjectured to be as secure as factoring.] The ElGamal cryptosystem: - based on the difficulty of computing discrete logarithms in a finite field - used in many cryptographic protocols

8
Public-key Cryptosystems Outline of a general public-key cryptosystem: - components: a set M of messages, a set K of keys, for each key k 2 K, an encryption function E k and a decryption function D k (usually functions from M to M) - requirements: - E k (D k (m)) = D k (E k (m)) for all m, k. - E k (m) and D k (m) are easy to compute for all m, k. - figuring out D k from E k is computationally infeasible for almost all k 2 K - given k 2 K, finding E k and D k is easy

Similar presentations

OK

Dan Boneh Public Key Encryption from trapdoor permutations The RSA trapdoor permutation Online Cryptography Course Dan Boneh.

Dan Boneh Public Key Encryption from trapdoor permutations The RSA trapdoor permutation Online Cryptography Course Dan Boneh.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Free download ppt on abortion Ppt on grease lubrication manifold Ppt on job interview skills Ppt on rainwater harvesting Ppt on 2nd green revolution Ppt on use of ms excel Download ppt on ohm's law for class 10 Ppt on power generation in india Ppt on swine flu free download Ppt on asymptotic notation of algorithms meaning