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EdDSA
In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. It is designed to be faster than existing digital signature schemes without sacrificing security. It was developed by a team including Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang. The reference implementation is public domain software. Summary The following is a simplified description of EdDSA, ignoring details of encoding integers and curve points as bit strings; the full details are in the papers and RFC. An EdDSA signature scheme is a choice: * of finite field \mathbb_q over odd prime power q; * of elliptic curve E over \mathbb_q whose group E(\mathbb_q) of \mathbb_q-rational points has order \#E(\mathbb_q) = 2^c \ell, where \ell is a large prime and 2^c is called the cofactor; * of base point B \in E(\mathbb_q) with order \ell; and * of cryptographic hash functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic-curve Cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.Commercial National Security Algorithm Suite and Quantum Computing FAQ U.S. National Security Agency, January 2016. Elliptic curves are applicable for , s, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twisted Edwards Curve
In algebraic geometry, the twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Daniel J. Bernstein, Bernstein, Birkner, Joye, Tanja Lange, Lange and Peters in 2008. The curve set is named after mathematician Harold Edwards (mathematician), Harold M. Edwards. Elliptic curves are important in public key cryptography and twisted Edwards curves are at the heart of an electronic signature scheme called EdDSA that offers high performance while avoiding security problems that have surfaced in other digital signature schemes. Definition Each twists of curves, twisted Edwards curve is a Twists of curves, twist of an Edwards curve. A twisted Edwards curve E_ over a field (mathematics), field \mathbb with \operatorname(\mathbb) \neq 2 is an wikt:affine, affine plane curve defined by the equation: : E_: a x^2+y^2= 1+dx^2y^2 where a, d are distinct non-zero elements of \mathbb. The special case a = 1 is ''untwisted'', because the curve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signature Algorithm
The Digital Signature Algorithm (DSA) is a Public-key cryptography, public-key cryptosystem and Federal Information Processing Standards, Federal Information Processing Standard for digital signatures, based on the mathematical concept of modular exponentiation and the Discrete logarithm, discrete logarithm problem. DSA is a variant of the Schnorr signature, Schnorr and ElGamal signature scheme, ElGamal signature schemes. The National Institute of Standards and Technology (NIST) proposed DSA for use in their Digital Signature Standard (DSS) in 1991, and adopted it as FIPS 186 in 1994. Four revisions to the initial specification have been released. The newest specification isFIPS 186-4 from July 2013. DSA is patented but NIST has made this patent available worldwide royalty-free. A draft version of the specificatioFIPS 186-5indicates DSA will no longer be approved for digital signature generation, but may be used to verify signatures generated prior to the implementation date of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-key Cryptography
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created by a known sender (authenticity), and that the message was not altered in transit (integrity). Digital signatures are a standard element of most cryptographic protocol suites, and are commonly used for software distribution, financial transactions, contract management software, and in other cases where it is important to detect forgery or tampering. Digital signatures are often used to implement electronic signatures, which includes any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schnorr Signature
In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr. It is a digital signature scheme known for its simplicity, among the first whose security is based on the intractability of certain discrete logarithm problems. It is efficient and generates short signatures. It was covered by which expired in February 2008. Algorithm Choosing parameters *All users of the signature scheme agree on a group, G, of prime order, q, with generator, g, in which the discrete log problem is assumed to be hard. Typically a Schnorr group is used. *All users agree on a cryptographic hash function H: \^* \rightarrow \mathbb_q. Notation In the following, *Exponentiation stands for repeated application of the group operation *Juxtaposition stands for multiplication on the set of congruence classes or application of the group operation (as applicable) *Subtraction stands for subtraction on the set of congruence classe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ECDSA
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. Key and signature-size As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about 2^ operations to find the private key—the size of an ECDSA private key would be 160 bits. On the other hand, the signature size is the same for both DSA and ECDSA: approximately 4 t bits, where t is the security level measured in bits, that is, about 320 bits for a security level of 80 bits. Signature generation algorithm Suppose Alice wants to send a signed message to Bob. Initially, they must agree on the curve parameters (\textrm, G, n). In addition to the field and equation of the curve, we need G, a base point of pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve25519
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed for use with the elliptic curve Diffie–Hellman (ECDH) key agreement scheme. It is one of the fastest curves in ECC, and is not covered by any known patents. The reference implementation is public domain software. The original Curve25519 paper defined it as a Diffie–Hellman (DH) function. Daniel J. Bernstein has since proposed that the name Curve25519 be used for the underlying curve, and the name X25519 for the DH function. Mathematical properties The curve used is y^2 = x^3 + 486662x^2 + x, a Montgomery curve, over the prime field defined by the prime number 2^ - 19, and it uses the base point x = 9. This point generates a cyclic subgroup whose order is the prime 2^ + 27742317777372353535851937790883648493, this subgroup has a co-factor of 8, meaning the number of elements in the subgroup is 1/8 that of the elliptic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Westmere (microarchitecture)
Westmere (formerly Nehalem-C) is the code name given to the 32 nm die shrink of '' Nehalem''. While sharing the same CPU sockets, Westmere included Intel HD Graphics, while Nehalem did not. The first ''Westmere''-based processors were launched on January 7, 2010, by Intel Corporation. The Westmere architecture has been available under the Intel brands of Core i3, Core i5, Core i7, Pentium, Celeron and Xeon. Technology Westmere's feature improvements from Nehalem, as reported: * Native six-core (Gulftown) and ten-core (Westmere-EX) processors. * A new set of instructions that gives over 3x the encryption and decryption rate of Advanced Encryption Standard (AES) processes compared to before. ** Delivers seven new instructions (AES instruction set or AES-NI), out of which six implement the AES algorithm, and PCLMULQDQ (see CLMUL instruction set) implements carry-less multiplication for use in cryptography and data compression. * Integrated graphics, added into the processor p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montgomery Curve
In mathematics the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain computations, and in particular in different cryptography applications. Definition A Montgomery curve over a field is defined by the equation :M_: By^2 = x^3 + Ax^2 + x for certain and with . Generally this curve is considered over a finite field ''K'' (for example, over a finite field of elements, ) with characteristic different from 2 and with and , but they are also considered over the rationals with the same restrictions for and . Montgomery arithmetic It is possible to do some "operations" between the points of an elliptic curve: "adding" two points P, Q consists of finding a third one R such that R=P+Q; "doubling" a point consists of computing =P+P (For more information about operations see The group law) and below. A point P=(x,y) on the elliptic curve in the Montgomery form By^2 = x^3 + A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X86-64
x86-64 (also known as x64, x86_64, AMD64, and Intel 64) is a 64-bit version of the x86 instruction set, first released in 1999. It introduced two new modes of operation, 64-bit mode and compatibility mode, along with a new 4-level paging mode. With 64-bit mode and the new paging mode, it supports vastly larger amounts of virtual memory and physical memory than was possible on its 32-bit predecessors, allowing programs to store larger amounts of data in memory. x86-64 also expands general-purpose registers to 64-bit, and expands the number of them from 8 (some of which had limited or fixed functionality, e.g. for stack management) to 16 (fully general), and provides numerous other enhancements. Floating-point arithmetic is supported via mandatory SSE2-like instructions, and x87/ MMX style registers are generally not used (but still available even in 64-bit mode); instead, a set of 16 vector registers, 128 bits each, is used. (Each register can store one or two double-preci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nehalem (microarchitecture)
Nehalem is the codename for Intel's 45 nm microarchitecture released in November 2008. It was used in the first-generation of the Intel Core i5 and i7 processors, and succeeds the older Core microarchitecture used on Core 2 processors. The term "Nehalem" comes from the Nehalem River. Nehalem is built on the 45 nm process, is able to run at higher clock speeds, and is more energy-efficient than Penryn microprocessors. Hyper-threading is reintroduced, along with a reduction in L2 cache size, as well as an enlarged L3 cache that is shared among all cores. Nehalem is an architecture that differs radically from Netburst, while retaining some of the latter's minor features. Nehalem later received a die-shrink to 32 nm with Westmere, and was fully succeeded by "second-generation" Sandy Bridge in January 2011. Technology * Cache line block on L2/L3 cache was reduced from 128 bytes in Netburst & Conroe/Penryn to 64 bytes per line in this generation (same size as Yonah and Pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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