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Attacks on RSA cryptosystem
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | 1 The attacker knows the modulus n and its to-tient value φ(n) There are several ways in which the value of φ(n) might be guessed by a clever attacker if one is not careful with implementing the RSA system – as will be seen below. The attacker knows that n is a product od two primes, say p and q, and that its totient value is φ(n) = (p − 1) * (q − 1), but does not a priori know the values of the prime numbers p and q. Now φ(n) = p * q − (p + q) + 1 = n − (p + q) + 1, and so q = (n − φ(n) + 1) − p. Substituting this into the equation of n we find n = p * ((n − φ(n) + 1) − p), and thus p 2 − p * (n − φ(n) + 1) + n = 0 The only unknown in this quadratic equation is p. Now using the quadratic formula, p's value can befound. Then from the value of p and n we can find the value of q. Defense: Guard φ(n) as carefully as p, q or the private key t. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://diamond.boisestate.edu/~liljanab/ISAS/course_materials/AttacksRSA.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
