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- Elliptic_curve_only_hash abstract "The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in the beginning of the competition since a second pre-image attack was found. The ECOH is based on the MuHASH hash algorithm, that has not yet been successfully attacked. However, MuHASH is too inefficient for practical use and changes had to be made. The main difference is that where MuHASH applies a random oracle , ECOH applies a padding function. Assuming random oracles, finding a collision in MuHASH implies solving the discrete logarithm problem. MuHASH is thus a provably secure hash, i.e. we know that finding a collision is at least as hard as some hard known mathematical problem. ECOH does not use random oracles and its security is not strictly directly related to the discrete logarithm problem, yet it is still based on mathematical functions. ECOH is related to the Semaev's problem of finding low degree solutions to the summation polynomial equations over binary field, called the Summation Polynomial Problem. An efficient algorithm to solve this problem has not been given so far. Although the problem was not proven to be NP-hard, it is assumed that such an algorithm does not exist. Under certain assumptions, finding a collision in ECOH may be also viewed as an instance of the subset sum problem. Besides solving the Summation Polynomial Problem, there exists another way how to find second pre-images and thus collisions, Wagner's generalized birthday attack. ECOH is a nice example of hash function that is based on mathematical functions (with the provable security approach) rather than on classical ad hoc mixing of bits to obtain the hash.".
- Elliptic_curve_only_hash wikiPageExternalLink ECOH_Comments.pdf.
- Elliptic_curve_only_hash wikiPageExternalLink Ecoh.pdf.
- Elliptic_curve_only_hash wikiPageExternalLink 168.pdf.
- Elliptic_curve_only_hash wikiPageID "25693976".
- Elliptic_curve_only_hash wikiPageLength "11006".
- Elliptic_curve_only_hash wikiPageOutDegree "35".
- Elliptic_curve_only_hash wikiPageRevisionID "651174747".
- Elliptic_curve_only_hash wikiPageWikiLink Birthday_attack.
- Elliptic_curve_only_hash wikiPageWikiLink CLMUL_instruction_set.
- Elliptic_curve_only_hash wikiPageWikiLink Category:Cryptographic_hash_functions.
- Elliptic_curve_only_hash wikiPageWikiLink Collision.
- Elliptic_curve_only_hash wikiPageWikiLink Collision_resistance.
- Elliptic_curve_only_hash wikiPageWikiLink Complexity_class.
- Elliptic_curve_only_hash wikiPageWikiLink Cryptanalysis.
- Elliptic_curve_only_hash wikiPageWikiLink Discrete_logarithm.
- Elliptic_curve_only_hash wikiPageWikiLink Elliptic_curve.
- Elliptic_curve_only_hash wikiPageWikiLink Hash_function.
- Elliptic_curve_only_hash wikiPageWikiLink MuHASH.
- Elliptic_curve_only_hash wikiPageWikiLink NIST_hash_function_competition.
- Elliptic_curve_only_hash wikiPageWikiLink NP-hardness.
- Elliptic_curve_only_hash wikiPageWikiLink Padding_(cryptography).
- Elliptic_curve_only_hash wikiPageWikiLink Parallel_computing.
- Elliptic_curve_only_hash wikiPageWikiLink Polynomial-time_reduction.
- Elliptic_curve_only_hash wikiPageWikiLink Preimage_attack.
- Elliptic_curve_only_hash wikiPageWikiLink Random_oracle.
- Elliptic_curve_only_hash wikiPageWikiLink SHA-1.
- Elliptic_curve_only_hash wikiPageWikiLink Security_of_cryptographic_hash_functions.
- Elliptic_curve_only_hash wikiPageWikiLink Subset_sum_problem.
- Elliptic_curve_only_hash wikiPageWikiLink Time_complexity.
- Elliptic_curve_only_hash wikiPageWikiLink Truncation_(disambiguation).
- Elliptic_curve_only_hash wikiPageWikiLink Weierstrasss_elliptic_functions.
- Elliptic_curve_only_hash wikiPageWikiLinkText "ECOH - Elliptic Curve Only hash function".
- Elliptic_curve_only_hash wikiPageWikiLinkText "ECOH".
- Elliptic_curve_only_hash wikiPageWikiLinkText "Elliptic curve only hash".
- Elliptic_curve_only_hash cryptanalysis "Second Pre-Image".
- Elliptic_curve_only_hash derivedFrom MuHASH.
- Elliptic_curve_only_hash designers "Daniel R. L. Brown, Matt Campagna, Rene Struik".
- Elliptic_curve_only_hash digestSize "224256384".
- Elliptic_curve_only_hash name "Elliptic curve only hash".
- Elliptic_curve_only_hash publishDate "2008".
- Elliptic_curve_only_hash wikiPageUsesTemplate Template:Clarify.
- Elliptic_curve_only_hash wikiPageUsesTemplate Template:Cryptography_navbox.
- Elliptic_curve_only_hash wikiPageUsesTemplate Template:Dn.
- Elliptic_curve_only_hash wikiPageUsesTemplate Template:Infobox_cryptographic_hash_function.
- Elliptic_curve_only_hash subject Category:Cryptographic_hash_functions.
- Elliptic_curve_only_hash type Algorithm.
- Elliptic_curve_only_hash type Function.
- Elliptic_curve_only_hash comment "The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in the beginning of the competition since a second pre-image attack was found. The ECOH is based on the MuHASH hash algorithm, that has not yet been successfully attacked. However, MuHASH is too inefficient for practical use and changes had to be made.".
- Elliptic_curve_only_hash label "Elliptic curve only hash".
- Elliptic_curve_only_hash sameAs Q5365792.
- Elliptic_curve_only_hash sameAs m.0b6d0gt.
- Elliptic_curve_only_hash sameAs Q5365792.
- Elliptic_curve_only_hash wasDerivedFrom Elliptic_curve_only_hash?oldid=651174747.
- Elliptic_curve_only_hash isPrimaryTopicOf Elliptic_curve_only_hash.