Unformatted text preview: PSyear)
techniques,
’01: 15 = 3 * 5 (4 bits; IBM quantum computer!)
Dec 2003: 576bit cracked
Nov. 2005: 640bit cracked
See http://www.rsasecurity.com/rsalabs/node.asp?id=2093 for
See http://www.rsasecurity.com/rsalabs/node.asp?id=2093
the remaining bounty !!
the Recommended Key Sizes for RSA Old Standard: Individual users: 512 bits (155 decimal digits) New Standard: Individual users: 768 bits (231 decimal digits) Organizations (short term): 1024bits (308 decimal digits) Organizations (long term): 2048bits (616 decimal digits) Ref: No. of operations required to crack 512bit RSA with best
Ref:
known attack = 1/50 * NDES
known
where NDES is the no. of operations required to crack 56bit DES by
DES
bruteforce keyenumeration
bruteforce Implementation Aspects of RSA How to find the big primes p and q ? Generate random numbers and test for their primality using
Generate
known testing algorithms
known How many times (numbers) one need to try before finding a
How
prime no. ? For a randomly chosen no. N, the probability of it being
For
prime ~= 1/ ln N ; => need to try ln N times on average
prime For a 100digit number, one 1 in 230 chance.
e can be fixed to some constant value without decreasing security ;
e is commonly set to 3 or 65537 = 216+1 in practice to speed up
+1 encryption: m e mod n ; one can compute m 65537 quickly as well
quickly
Once e is fixed, d can be found using the Euclid’s Algorithm
Once
fixed can Breaking News: (Feb 15, 2012): Implementation Flaws in RSA
Breaking
random key generations
random
http://www.nytimes.com/2012/02/15/technology/researchersfindflawin Some arcane Attacks on RSA Guessing plaintext attack: if the attackers know the candidate set of plaintexts to
Guessing
be sent (with exact wordings), the attacker can encrypt each of the possible
choice using the recipient’s public key and compare them to the actual ciphertext
sent ;
Chosen ciphertext attack: don’t sign arbitrary messages sent by others because
Chosen
signing is equivale...
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This note was uploaded on 12/05/2013 for the course IERG 4130 taught by Professor Chowszeming,sherman during the Fall '13 term at CUHK.
 Fall '13
 CHOWSzeMing,Sherman

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