EPOC is a probabilistic

Probabilistic encryption

Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts...

 public-key

Public-key cryptography

Public-key cryptography refers to a cryptographic system requiring two separate keys, one to lock or encrypt the plaintext, and one to unlock or decrypt the cyphertext. Neither key will do both functions. One of these keys is published or public and the other is kept private...

 encryption

Encryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

 scheme.

EPOC was developed in 1999 by T. Okamoto, S. Uchiyama and E. Fujisaki of NTT

Nippon Telegraph and Telephone

, commonly known as NTT, is a Japanese telecommunications company headquartered in Tokyo, Japan. Ranked the 31st in Fortune Global 500, NTT is the largest telecommunications company in Asia, and the second-largest in the world in terms of revenue....

 Labs in Japan. It is based on the random oracle

Random oracle

In cryptography, a random oracle is an oracle that responds to every query with a random response chosen uniformly from its output domain, except that for any specific query, it responds the same way every time it receives that query...

 model, in which a primitive public-key encryption function is converted to a secure encryption scheme by use of a truly random hash function; the resulting scheme is designed to be semantically secure

Semantic security

Semantic security is a widely used definition for security in an asymmetric key encryption algorithm. For a cryptosystem to be semantically secure, it must be infeasible for a computationally bounded adversary to derive significant information about a message when given only its ciphertext and...

 against a chosen ciphertext attack.

EPOC's primitive encryption function is the OU (Okamoto-Uchiyama) function, in which to invert the OU function is proven to be as hard as factoring

Factoring

Factoring can refer to the following:* A form of commercial finance - see factoring ; structured settlement factoring transaction* Factorization, a mathematical concept* Factoring a design, as in code refactoring...

 a composite integer public-key. There are three versions of EPOC:

• EPOC-1 uses a one-way trapdoor function
  Trapdoor function
  A trapdoor function is a function that is easy to compute in one direction, yet believed to be difficult to compute in the opposite direction without special information, called the "trapdoor"...
  
   and a random function (hash function);

• EPOC-2 uses a one-way trapdoor function, two random functions (hash functions) and a symmetric-key encryption (e.g., one-time padding and block-ciphers);

• EPOC-3 uses the Okamoto-Uchiyama one-way trapdoor function and two random functions (hash functions) as well as any symmetric encryption scheme such as the one-time pad, or any classical block-cipher.

EPOC-1 is designed for key-distribution; EPOC-2 and EPOC-3 are designed for both key-distribution and encrypted data transfer.

See also

• Cryptography
  Cryptography
  Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
  
  
• Computational complexity theory
  Computational complexity theory
  Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...
  
  
• Okamoto-Uchiyama cryptosystem
  Okamoto-Uchiyama cryptosystem
  The Okamoto–Uchiyama cryptosystem was discovered in 1998 by T. Okamoto and S. Uchiyama. The system works in the group ^*, where n is of the form p2q and p and q are large primes.-Scheme definition:...