crypting system: Triple DES
IV ="XXXXXXXXXX/XXXXX" (Lenght=16)
Mode: CBC
Publickey "XXXXXXXXXXXX....." (Lenght = 50 for crypting )
Private key "XXXXXXX......" (Lenght = 50 for decrypting)
As I said before TripleDes is symmetric so uses the same key for both encrypting and decrypting. I suspect that "Public key" and "Private key" have a different meaning to those used in crytography. From a look at your document, my French is not brilliant, it looks like the public key is used to encrypt your request to the web site, and you decrypt the response from the web site using the private key. You need to get a good translation of that document.
Also the format of the keys "Cle privee" and "Cle publique" look odd for DES keys. I suspect they are formatted for use by the phpseclib library that the document mentions. You need more information on this.
EDIT: I've looked at your translation. It is as I thought
All these exchanges are encrypted. At each webservice call, your website must encrypt the parameters with your public key. Each response sent by the VANILLA PAY platform must be decrypted with your private key.The decryption uses the functions of the phpseclib library.
