What is the problem with the symmetric cryptography ?

With the symmetric cryptography, a same password is used to encrypt and decrypt a message. The problem is how to safely exchange this password ? This password has to be exchanged in clear in internet and a third person will be able to intercept this password and then decrypt all the encrypted messages.

What is the asymmetric cryptography ?

The asymmetric cryptography solves the problem of exchange of the password of the symmetric cryptography.

With the asymmetric cryptography, a private/public key pair is generated. A message encrypted with the public key can be decrypted only by the corresponding private key of the pair. And a message encrypted with the private key can be decrypted only by the corresponding public key of the pair. Even if it seems useless to encrypt a message that everybody can decrypt with the public key of the pair, it is used to verify the digital signature of a message (cf the post related to the digital signature). Why this technology is widely used on the internet ?

The owner of a key pair can publish the public key on the internet. A message encrypted with this public key, can only be decrypted by the corresponding private key of the owner.

How to generate a private/public key pair ?

The following example is done with the RSA algorithm. Generate the private key

We generate first the private key in the file myprivatekey.pem:

openssl genrsa -out myprivatekey.pem

The private key generated is as following:

Generate the public key, from the private key

openssl rsa -in myprivatekey.pem -outform PEM -pubout -out mypubkey.pem

The public key generated is as following:

Encrypt a message with the public key

We create a file hello-world.txt with the text “Hello World !!!”.

openssl rsautl -encrypt -pubin -inkey mypubkey.pem -in hello-world.txt -out hello-world.enc

The file hello-world.enc is the following:

f>ÞB¢Uba·7Î^?s^Mâ7;O^U¯ãû0EÅ«|+\T^Oþ\^OÍT¢?1d°åü^]å6í^_4E! ¬HAå^?¯Nðs%ÄÖzÍ^K8Ý¶XÛ±æüf^Y^Lx36¹x3^Vb.DW®¯ÛÞÔ^Eú²H^\Á±µ^?^E.(°¼ë^LÅf^F^]'\ý¥l­gg^]­ì(ÿ»ç2^LÁ^H·%Ñ^PÆÁj0-Åú$ÖV¤2ò}G8b^L[{Â^W4^Hd¥Úþ°^YûEFø?©+:^Q^YJb§ÏæÂÞ7À¾£ ù<à¢Õ$ïFPM^]^E£2YQû:^Wõýì½^Eþµÿ+}

Decrypt the encrypted message with the private key

openssl rsautl -decrypt -inkey myprivatekey.pem -in hello-world.enc -out hello-world.dec

We get the initial text “Hello World !!!” in the file hello-world.dec.

Menu

Asymmetric cryptography

What is the problem with the symmetric cryptography ?

What is the asymmetric cryptography ?

How to generate a private/public key pair ?

Encrypt a message with the public key