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...ecurity proof of Sakai-Kasahara's identity-based encryption scheme|journal=Cryptography ePrint Archive|volume=2005/226|url=http://eprint.iacr.org/2005/226.pdf}}</r ...nyone to encrypt a message to a user when the sender only knows the public identity (e.g. email address) of the user. In this way, this scheme removes the requ ...

...ryptography, as [[key exchange]] protocols, [[ID-based encryption|identity-based encryption]], and [[broadcast encryption]]. There exist constructions of cr ...rstand than GGH13 multilinear map; and GGH15,<ref name="ggh15" /> which is based on graphs. ...

.../math> to be equal to <math>x</math> when <math>k</math> corresponds to an identity that is allowed to decrypt, and <math>\perp</math> otherwise. Similarly, in ...<ref>{{cite web|last=Sahai|first=Amit|author2=Brent Waters|title=Attribute-Based Encryption for Circuits from Multilinear Maps|year=2012 |arxiv=1210.5287 |u ...

...], [[Diffie–Hellman key exchange]] and [[elliptic curve cryptography]] are based on number theory and hence depend on commutative algebraic structures. #Bob checks if ''w'' ' ' = ''t''^''r''. If this true, then the identity of Alice is established. ...

...[[computational number theory]] and have been applied in [[elliptic-curve cryptography]]. Their vertices represent [[supersingular elliptic curve]]s over [[finite ...h|expansion properties]] for their degree.{{r|clg|fjp|p1|p2}} The proof is based on [[Pierre Deligne]]'s proof of the [[Ramanujan–Petersson conjecture]].{{r ...

...Technical-White-Paper-06-with-Appendix-A-B.pdf |title=Algebraic methods in cryptography |publisher=American Mathematical Society |location=Contemp. Math. |volume=4 ...</math>, that is, the result of E-Multiplication of the private matrix and identity-permutation with the private braid. ...

{{Short description|Family of elliptic curves used in cryptography}} ...ed in [[elliptic curve cryptography]]. Applications of Edwards curves to [[cryptography]] were developed by [[Daniel J. Bernstein]] and [[Tanja Lange]]: they point ...

...phy|cryptographic]] weakness that allows the private key of a [[Public-key cryptography|key pair]] to be recovered from the public key in keys generated by devices ...lnerable RSA generation (CVE-2017-15361) |publisher=Centre for Research on Cryptography and Security, Faculty of Informatics, [[Masaryk University]] |location=Czec ...

...by the [[elliptic curve|Weierstrass equation]]. Sometimes it is used in [[cryptography]] instead of the Weierstrass form because it can provide a defence against ...elliptic curve: this operation is considered the most in [[elliptic curve cryptography]]. ...

...-(Here is a description of these problems: given a word w representing the identity in a finitely presented group, find a ...2.3734 Generic Complexity and One-Way Functions]'', Groups, Complexity and Cryptography, 1, (2009), 13–31.</ref> which yields the same class of functions but allow ...

...]]. It assumes that the quantum memory device of an attacker ([[Adversary (cryptography)|adversary]]) trying to break the protocol is imperfect (noisy). ...curity then holds as long as these assumptions are satisfied. In classical cryptography, i.e., without the use of quantum tools, most of these are [[Computational ...

...rmore, we can prove that the signature scheme is secure under well known [[Cryptography|cryptographic]] assumptions of the hardness of the [[discrete logarithm]] p ===Elliptic curves cryptography over a finite field=== ...

...onal sender and recipient untraceability. Anonymous communication networks based on this problem are often referred to as '''DC-nets''' (where DC stands for ...have paid the bill). Otherwise, one of the cryptographers paid, but their identity remains unknown to the other cryptographers. ...

In [[cryptography]], an '''accumulator''' is a [[one way function|one way]] membership [[hash ...ss=free}}</ref> Benaloh and de Mare proposed an alternative scheme in 1991 based on discretizing time into rounds.<ref name=":0" /><ref>{{Cite web |last1=Be ...

.../www.kaspersky.co.uk/blog/cybersecurity-case-study/8067/}}</ref> A browser-based prototype of the system was used in a Durga Puja online voting trial among ...ent in <math>G_q</math> as <math>g_1</math> and computing <math>g_2</math> based on applying a one-way hash function with the inclusion of election specific ...

...n [[elliptic curve]] to itself repeatedly. It is used in [[elliptic curve cryptography]] (ECC). Point at infinity {{tmath|\mathcal{O} }} is the [[identity element]] of elliptic curve arithmetic. Adding it to any point results in t ...

...h|''S''}}. [[Threshold cryptosystem|Threshold]] [[secret sharing]] schemes based on the CRT are due to Mignotte and Asmuth–Bloom, they use special sequences By [[Bézout's identity]], since <math>(m_i,M/m_i) = 1</math>, there exist positive integers {{math ...

...information, i.e., break the [[RSA (algorithm)|RSA]] system. This break is based on Wiener's theorem, which holds for small values of ''d''. Wiener has prov By using simple [[algebra]]ic manipulations and [[identity (mathematics)|identities]], a guess can be checked for [[accuracy]].<ref na ...

...and Bob) in order to allow reliable [[quantum teleportation]] or [[quantum cryptography]]. | title = Quantum privacy amplification and the security of quantum cryptography over noisy channels ...

...hould not forget about fields of characteristic 2 as [[hyperelliptic curve cryptography]] makes extensive use of such fields. ...et of points of a hyperelliptic curve. The group law on elliptic curves is based on the fact that a straight line through two points lying on an elliptic cu ...