1 / 7

RSA Cryptosystem

RSA Cryptosystem. by Drs. Charles Tappert and Ron Frank The information presented here comes primarily from https ://en.wikipedia.org/wiki/RSA_(cryptosystem ) and http://www.math.uchicago.edu/~ may/VIGRE/VIGRE2007/ REUPapers /FINALAPP/Calderbank.pdf. RSA Cryptosystem.

azura
Télécharger la présentation

RSA Cryptosystem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. RSA Cryptosystem by Drs. Charles Tappert and Ron Frank The information presented here comes primarily from https://en.wikipedia.org/wiki/RSA_(cryptosystem) and http://www.math.uchicago.edu/~may/VIGRE/VIGRE2007/ REUPapers/FINALAPP/Calderbank.pdf

  2. RSA Cryptosystem • RSA is the most commonly used public-key cryptosystem • Named after its developers: Rivest, Shamir, Adleman • Developed when they were in their early 20s and researchers at the MIT Lab • Algorithm announced in Scientific American in 1977 • RSA is based on Euler’s number theoretic result • If p and q are prime numbers and a is an integer not divisible by either p or q, then • a(p-1)(q-1) = 1 mod pq • φ(pq) = φ(p) φ(q) = (p-1)(q-1)

  3. RSA Cryptosystem • The principle behind RSA is to find 3 very large positive integers n, e, and d such that • (me)d = m (mod n) where m = the message < n • e encodes, d (difficult to find unless provided) decodes • and n is the product of two very large integers p and q • The RSA algorithm involves four steps • Key generation • Key distribution • Encryption • Decryption

  4. RSA Cryptosystem Key generation • Choose two distinct large prime numbers p and q • n = pq is the modulus for both public & private keys • Compute l(n) = lcm(f(p),f(q)) = lcm(p-1,q-1) • Where l is Carmichael’s totient function • Choose an integer e such that 1 < e < l(n) and gcd(e,l(n)) = 1 (that is, e and l(n) are coprime) • Determine d as d = e-1 (mod l(n)) • That is, solve for d from de = (mod l(n)) • e = public key exponent, d = private key exponent • Public key = (n, e), Private key = (n, d)

  5. RSA Cryptosystem Key Distribution, Encryption, Decryption • Distribution: the public key (n, e) is distributed • Encryption: plaintext message is converted into an integer m, then encrypted into code c = me (mod n) • Decryption: m = cd (mod n)

  6. RSA Cryptosystem Example • Choose two distinct prime numbers p=61 & q= 53 • Compute n = pq = 61*53 = 3233 • Compute l(n) = lcm(p-1,q-1) = lcm(60,52) = 780 • Choose any integer e < 780 coprime to 780, let e=17 • Compute d from de = 1 mod l(n) to get d = 413 • Public key (n=3233, e=17) • Send plaintext message “A”, m = 65 (ASCII for “A”) • Encode c = 6517 mod 3233 = 2790 • Private key (n=3233, d=413) • Decode c=2790: m = 2790413 mod 3233 = 65

  7. RSA Cryptosystem Calculator • http://umaranis.com/rsa_calculator_demo.html • https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html

More Related