Integrated Encryption Scheme
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Integrated Encryption Scheme (IES) is a publickey encryption scheme which provides semantic security against an adversary who is allowed to use chosenplaintext and chosenciphertext attacks. The scheme is based on Diffie–Hellman problem. Two incarnations of the IES are standardized: Discrete Logarithm Integrated Encryption Scheme (DLIES) and Elliptic Curve Integrated Encryption Scheme (ECIES), which is also known as the Elliptic Curve Augmented Encryption Scheme or simply the Elliptic Curve Encryption Scheme. These two incarnations are identical up to the change of an underlying group and so to be concrete we concentrate on the latter.
To send an encrypted message to Bob using ECIES Alice needs the following information:
 cryptographic suite to be used:
 KDF, e.g., ANSIX9.63KDF with SHA1 option;
 MAC, e.g., HMACSHA1160 with 160bit keys or HMACSHA180 with 80bit keys;
 symmetric encryption scheme , e.g., TDEA in CBC mode or XOR encryption scheme;
 EC domain parameters: for a curve over prime field or for a curve over binary field;
 Bob's public key: (Bob generates it as follows: , where is the private key he chooses at random: );
 optional shared information: and .
To encrypt a message Alice does the following:
 generates a random number and calculates ;
 derives a shared secret: , where (and );
 uses KDF to derive a symmetric encryption and a MAC keys: ;
 encrypts the message: ;
 computes the tag of encrypted message and : ;
 outputs .
To decrypt the ciphertext Bob does the following:
 derives the shared secret: , where (it is the same as the one Alice derived because ), or outputs failed if ;
 derives keys the same way as Alice did: ;
 uses MAC to check the tag and outputs failed if ;
 uses symmetric encryption scheme to decrypt the message .
ReferencesEdit
 Victor Shoup, A proposal for an ISO standard for public key encryption, Version 2.1, December 20, 2001.
 Certicom Research, Standards for efficient cryptography, SEC 1: Elliptic Curve Cryptography, Version 1.0, September 20, 2000.
