Guide to Elliptic Curve Cryptography (Springer Professional - download pdf or read online

By Darrel Hankerson, Alfred J. Menezes, Scott Vanstone

ISBN-10: 038795273X

ISBN-13: 9780387952734

After 20 years of analysis and improvement, elliptic curve cryptography now has frequent publicity and popularity. undefined, banking, and executive criteria are in position to facilitate huge deployment of this effective public-key mechanism.

Anchored through a accomplished remedy of the sensible features of elliptic curve cryptography (ECC), this consultant explains the fundamental arithmetic, describes cutting-edge implementation tools, and provides standardized protocols for public-key encryption, electronic signatures, and key institution. furthermore, the booklet addresses a few matters that come up in software program and implementation, in addition to side-channel assaults and countermeasures. Readers obtain the theoretical basics as an underpinning for a wealth of functional and available wisdom approximately effective application.

Features & Benefits:

  • Breadth of assurance and unified, built-in method of elliptic curve cryptosystems
  • Describes vital and govt protocols, corresponding to the FIPS 186-2 regular from the U.S. nationwide Institute for criteria and Technology
  • Provides complete exposition on ideas for successfully enforcing finite-field and elliptic curve arithmetic
  • Distills complicated arithmetic and algorithms for simple understanding
  • Includes worthwhile literature references, an inventory of algorithms, and appendices on pattern parameters, ECC criteria, and software program tools

This complete, hugely targeted reference is an invaluable and essential source for practitioners, execs, or researchers in desktop technological know-how, desktop engineering, community layout, and community facts safety.

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Darrel Hankerson, Alfred J. Menezes, Scott Vanstone's Guide to Elliptic Curve Cryptography (Springer Professional PDF

After twenty years of analysis and improvement, elliptic curve cryptography now has frequent publicity and recognition. undefined, banking, and executive criteria are in position to facilitate wide deployment of this effective public-key mechanism.

Anchored by way of a accomplished therapy of the sensible features of elliptic curve cryptography (ECC), this consultant explains the elemental arithmetic, describes state of the art implementation equipment, and offers standardized protocols for public-key encryption, electronic signatures, and key institution. furthermore, the ebook addresses a few matters that come up in software program and implementation, in addition to side-channel assaults and countermeasures. Readers obtain the theoretical basics as an underpinning for a wealth of sensible and obtainable wisdom approximately effective application.

Features & Benefits:

Breadth of insurance and unified, built-in method of elliptic curve cryptosystems
Describes very important and govt protocols, equivalent to the FIPS 186-2 normal from the U. S. nationwide Institute for criteria and Technology
Provides complete exposition on innovations for successfully enforcing finite-field and elliptic curve arithmetic
Distills complicated arithmetic and algorithms for simple understanding
Includes beneficial literature references, an inventory of algorithms, and appendices on pattern parameters, ECC criteria, and software program tools

This accomplished, hugely targeted reference is an invaluable and crucial source for practitioners, execs, or researchers in laptop technology, machine engineering, community layout, and community facts safety.

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Extra resources for Guide to Elliptic Curve Cryptography (Springer Professional Computing)

Sample text

If the running time of A is of the form L n [α, c] = O e(c+o(1))(logn) α (log log n)1−α where c is a positive constant and α is a constant satisfying 0 < α < 1, then A is a subexponential-time algorithm. Observe that if α = 0 then L n [0, c] is a polynomial expression in log2 n (so A is a polynomial-time algorithm), while if α = 1 then L n [1, c] is fully-exponential expression in log2 n (so A is a fully-exponential-time algorithm). Thus the parameter α is a good benchmark of how close a subexponential-time algorithm is to being efficient (polynomial-time) or inefficient (fully-exponential-time).

3. Return(Mont(A, 1)). As a rough comparison, Montgomery reduction requires t (t + 1) single-precision multiplications, while Barrett (with b = 2W ) uses t (t + 4) + 1, and hence Montgomery methods are expected to be superior in calculations such as general modular exponentiation. 6 for moduli of special form. 2. Prime field arithmetic 39 Montgomery arithmetic can be used to accelerate modular inversion methods that use repeated multiplication, where a −1 is obtained as a p−2 mod p (since a p−1 ≡ 1 (mod p) if gcd(a, p) = 1).

A’s signature on m is the pair (r, s). 2). Since the verifier knows neither A’s private key x nor k, this equation cannot be directly verified. 2) is equivalent to k ≡ s −1 (h + xr ) (mod q). 3) yields the equivalent congruence −1 T ≡ ghs yrs −1 (mod p). The verifier can therefore compute T and then check that r = T mod q. 2. 10 DSA signature generation I NPUT: DL domain parameters ( p, q, g), private key x, message m. O UTPUT: Signature (r, s). 1. Select k ∈ R [1, q − 1]. 2. Compute T = gk mod p.

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Guide to Elliptic Curve Cryptography (Springer Professional Computing) by Darrel Hankerson, Alfred J. Menezes, Scott Vanstone


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