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Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC requires smaller keys compared to non-ECC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization. == Rationale == Public-key cryptography is based on the intractability of certain mathematical problems. Early public-key systems are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors. For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible: this is the "elliptic curve discrete logarithm problem" or ECDLP. The security of ECC depends on the ability to compute a point multiplication and the inability to compute the multiplicand given the original and product points. The size of the elliptic curve determines the difficulty of the problem. The primary benefit promised by ECC is a smaller key size, reducing storage and transmission requirements, i.e. that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key: for example, a 256-bit ECC public key should provide comparable security to a 3072-bit RSA public key. The U.S. National Institute of Standards and Technology (NIST) has endorsed ECC in its Suite B set of recommended algorithms, specifically Elliptic Curve Diffie–Hellman (ECDH) for key exchange and Elliptic Curve Digital Signature Algorithm (ECDSA) for digital signature. The U.S. National Security Agency (NSA) allows their use for protecting information classified up to top secret with 384-bit keys.〔(【引用サイトリンク】title=Fact Sheet NSA Suite B Cryptography )〕 However in August 2015, the NSA announced it plans to replace Suite B with a new cipher suite due to concerns about quantum computing attacks on ECC.〔 While the RSA patent expired in 2000, there may be patents in force covering certain aspects of ECC technology, though some (including RSA Laboratories〔(【引用サイトリンク】 url = http://www.emc.com/emc-plus/rsa-labs/standards-initiatives/are-elliptic-curve-cryptosystems-patented.htm )〕 and Daniel J. Bernstein〔(【引用サイトリンク】last=Bernstein )〕) argue that the Federal elliptic curve digital signature standard (ECDSA; NIST FIPS 186-3) and certain practical ECC-based key exchange schemes (including ECDH) can be implemented without infringing them. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elliptic curve cryptography」の詳細全文を読む スポンサード リンク
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