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| | '''Cohen's cryptosystem'''<ref> |
| | {{cite web |
| | |title=Simple Public Key Encryption |
| | |url=http://web.archive.org/web/20111007060226/http://bramcohen.com/simple_public_key.html |
| | |author=Bram Cohen |
| | }}</ref> is a [[public-key cryptosystem]] proposed in 1998 by [[Bram Cohen]]. |
| | |
| | ==Key generation== |
| | |
| | In Cohen's cryptosystem, private key is a positive integer <math>p</math>. |
| | |
| | The algorithm uses <math>k</math> public-keys <math>w_0,\ldots,w_{k-1}</math> defined as follows: |
| | |
| | Generate <math>k</math> random integers <math>u_0,\ldots,u_{k-1}</math> chosen randomly and uniformly between <math>-B</math> and <math>B</math>. Where <math>B</math> is some bound. |
| | |
| | Let <math>A=\lfloor\frac{p}{2k}\rfloor</math> and generate <math>k</math> random integers <math>v_0,\ldots,v_{k-1}</math> chosen randomly and uniformly between <math>0</math> and <math>A</math>. |
| | |
| | Define <math>w_i=(u_i p+v_i)</math>. |
| | |
| | ==Encrypting a bit== |
| | |
| | To encrypt a bit <math>m</math> Alice randomly adds adds <math>\frac{k}{2}</math> public keys and multiplies the result by either 1 (if she wishes to send a 0) or by −1 (if she wishes to send a 1) to obtain the ciphertext <math>c=(-1)^{m} \sum w_i </math>. |
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| | ==De-cryption== |
| | |
| | To de-crypt, Bob computes <math>h= c \mod p = (-1)^{m} \sum v_i</math> |
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| | It is easy to see that if <math>m=0</math> then <math>0<h<p/2</math>. However, if <math>m=0</math> then <math>p>h>p/2</math>. Hence Bob can read the bit sent by Alice on the most significant bit of h. |
| | |
| | ==References== |
| | <references/> |
| | |
| | [[Category:Cryptography]] |
Revision as of 21:22, 20 January 2014
Template:One source
Cohen's cryptosystem[1] is a public-key cryptosystem proposed in 1998 by Bram Cohen.
Key generation
In Cohen's cryptosystem, private key is a positive integer .
The algorithm uses public-keys defined as follows:
Generate random integers chosen randomly and uniformly between and . Where is some bound.
Let and generate random integers chosen randomly and uniformly between and .
Define .
Encrypting a bit
To encrypt a bit Alice randomly adds adds public keys and multiplies the result by either 1 (if she wishes to send a 0) or by −1 (if she wishes to send a 1) to obtain the ciphertext .
De-cryption
To de-crypt, Bob computes
It is easy to see that if then . However, if then . Hence Bob can read the bit sent by Alice on the most significant bit of h.
References