The MIT/RSA Algorithm
In 1978,
Ron Rivest, Adi Shamir, and Leonard Adleman, all of MIT,
published the imaginatively named RSA algorithm for the
generation of encryption/decryption functions from number theory.
The difficulty arises when chosing the algorithms EA and
DA
such that they are inverses of one another and yet difficult to crack.
| Key length |
Factorization times |
With 107x1GHz machines |
| 429-bits (RSA-129) |
4,600 MIPS-years |
14.5 secs |
| 512-bits |
420,000 MIPS-years |
22 minutes |
| 700-bits |
4.2 x 109 MIPS-years |
153 days |
| 1024-bits |
2.8 x 1015 MIPS-years |
280,000 years |
- We choose two very large prime numbers, p and q,
each over 100 digits.
- We define EA to be the pair (e,n) where n = pxq
(for p, q being 100 digit primes,
n will typically at least 200 decimal digits).
- We define DA to be the pair (d,n)
where (e x d) mod ( (p-1) x (q-1) ) = 1
We then use:
- Encryption function : C := Pe mod n
- Decryption function : P := Cd mod n
CITS3002 Computer Networks, Lecture 12, Cryptography's role in networking, p14, 22nd May 2024.
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CITS3002