Logarithm Problem Solving

Logarithm Problem Solving-74
For example, consider (Z ≡ 1 (mod 17), these are the only solutions.

For example, consider (Z ≡ 1 (mod 17), these are the only solutions.

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The kth power of one of the numbers in this group may be computed by finding its kth power as an integer and then finding the remainder after division by p.More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization.These algorithms run faster than the naïve algorithm, some of them linear in the square root of the size of the group, and thus exponential in half the number of digits in the size of the group..pass_color_to_child_links a.u-inline.u-margin-left--xs.u-margin-right--sm.u-padding-left--xs.u-padding-right--xs.u-relative.u-absolute.u-absolute--center.u-width--100.u-flex-inline.u-flex-align-self--center.u-flex-justify--between.u-serif-font-main--regular.js-wf-loaded .u-serif-font-main--regular.amp-page .u-serif-font-main--regular.u-border-radius--ellipse.u-hover-bg--black-transparent.web_page .u-hover-bg--black-transparent:hover. Content Header .feed_item_answer_user.js-wf-loaded . El Gamal encryption, Diffie–Hellman key exchange, and the Digital Signature Algorithm) and cyclic subgroups of elliptic curves over finite fields (see Elliptic curve cryptography).While there is no publicly known algorithm for solving the discrete logarithm problem in general, the first three steps of the number field sieve algorithm only depend on the group G, not on the specific elements of G whose finite log is desired.cyclic groups with order of the Oakley primes specified in RFC 2409.The Logjam attack used this vulnerability to compromise a variety of Internet services that allowed the use of groups whose order was a 512-bit prime number, so called export grade. The Logjam authors speculate that precomputation against widely reused 1024 DH primes is behind claims in leaked NSA documents that NSA is able to break much of current cryptography.A general algorithm for computing log a in finite groups G is to raise b to larger and larger powers k until the desired a is found.This algorithm is sometimes called trial multiplication.


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