# Integrated Encryption Scheme

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**Integrated Encryption Scheme** (**IES**) is a hybrid encryption scheme which provides semantic security against an adversary who is allowed to use chosen-plaintext and chosen-ciphertext attacks. The security of the scheme is based on the computational 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.

## Contents

## Informal description[edit]

As a *brief and informal* description and overview of how IES works, we use a Discrete Logarithm Integrated Encryption Scheme (DLIES) based example, focusing on illuminating the reader's understanding, rather than precise technical details.

- Alice learns Bob's public key, through a public key infrastructure or other pre-distributed method. We assume Bob knows his own private key .
- Alice generates a fresh, ephemeral value , and its associated public value, .
- Alice then computes a symmetric key using this information and a KDF as follows: .
- Alice computes her ciphertext from her actual message , i.e. the symmetric encryption of , encrypted under key (using an authenticated encryption scheme) as follows: .
- Alice transmits (in a single message) both the public ephemeral , and the ciphertext .
- Bob, knowing and , can now compute and decrypt from .

## Formal description[edit]

### Information required[edit]

To send an encrypted message to Bob using ECIES, Alice needs the following information:

- cryptographic suite to be used, including a key derivation function (e.g.,
*ANSI-X9.63-KDF with SHA-1 option*), a message authentication code (e.g.,*HMAC-SHA-1-160 with 160-bit keys*or*HMAC-SHA-1-80 with 80-bit keys*) and a symmetric encryption scheme (e.g.,*TDEA in CBC mode*or*XOR encryption scheme*)—noted ; - elliptic curve domain parameters: for a curve over a prime field or for a curve over a binary field;
- Bob's public key: (Bob generates it as follows: , where is the private key he chooses at random: );
- optional shared information: and .
- denotes the point at infinity

### Encryption[edit]

To encrypt a message Alice does the following:

- generates a random number and calculates ;
- derives a shared secret: , where (and );
- uses a KDF to derive symmetric encryption keys and MAC keys: ;
- encrypts the message: ;
- computes the tag of encrypted message and : ;
- outputs .

### Decryption[edit]

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 .

## References[edit]

- 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 2.0, May 21, 2009.
- Gayoso Martínez, Hernández Encinas, Sánchez Ávila:
*A Survey of the Elliptic Curve Integrated Encryption Scheme*, Journal of Computer Science and Engineering, 2, 2 (2010), 7–13. - Ladar Levison: Code for using ECIES to protect data (ECC + AES + SHA), openssl-devel mailing list, August 6, 2010.
- Abdalla, Michel and Bellare, Mihir and Rogaway, Phillip: DHIES: An Encryption Scheme Based on the Diffie–Hellman Problem, IACR Cryptology ePrint Archive, 1999.