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...|exhaustive key-search]] attack. But modern ciphers often have a key space of size <math>2^{128}</math> or greater, making such attacks infeasible with c .../cseweb.ucsd.edu/~mihir/papers/gb.html|date=2012-04-21}}. Summer course on cryptography, MIT, 1996-2001</ref> An extremely low KR advantage is essential for an enc ...

In [[computational complexity theory]] and [[cryptography]], '''averaging argument''' is a standard argument for proving theorems. It ...of the books in a library, then the library has a book, which at least 1/3 of people like. ...

...to solve using [[Gaussian elimination]] provided that a sufficient number of samples (from a distribution which is not too skewed) are provided to the a ...rning Parity with Noise (LPN), the samples may contain some error. Instead of samples (''x'',&nbsp;''ƒ''(''x'')), the algorithm is provided with (''x'',& ...

{{Short description|Study of the tropical semiring}} ...iscipline of [[idempotent analysis]], '''tropical analysis''' is the study of the [[tropical semiring]]. ...

...Computer Science, 1982.</ref> against pseudo-random sequences. A sequence of words passes Yao's test if an attacker with reasonable computational power ...collection <math>C=\{C_k\}</math> is a collection of [[boolean circuits]] of size less than <math>P_C(k)</math>. Let <math>p_{k,S}^C</math> be the proba ...

...air (''x'', ''y'') is then called a ''claw''. Some problems, especially in cryptography, are best solved when viewed as a claw finding problem, hence any algorithm .../math>. So if <math>|A| \cdot |B| \geq |C|</math>, the [[expected number]] of claws is at least 1. ...

...athematician at the [[University of Maryland]] who specializes in [[number theory]]. ...[University of Perugia]], [[Nankai University]] and the [[State University of Campinas]]. In 1979–1981 he was a [[Sloan Fellowship|Sloan Fellow]].{{cn|da ...

*[[Number theory]] *[[Cryptography]] ...

{{Short description|Proposed design of bank notes}} A '''quantum money''' scheme is a [[Quantum Cryptography|quantum cryptographic]] protocol that creates and verifies banknotes that a ...

...eems much more difficult<ref name="bonehMultilinear" /> and the security of the proposed candidates is still unclear.<ref name="AlbrechtSite" /> ...s of prime order <math>q</math>, and <math>G_T</math> another cyclic group of order <math>q</math> written multiplicatively. A pairing is a map: <math> e ...

...ithm]] or [[RSA (algorithm)|RSA]]. [[NIST]] has approved specific variants of the Merkle signature scheme in 2020.<ref>{{cite web | url=https://csrc.nist ...isdom.weizmann.ac.il/~naor/PAPERS/uowhf.pdf |journal=[[Symposium on Theory of Computing]] |pages=33–43}}</ref> ...

...ple) as subclasses. These complexity classes are of particular interest in cryptography because they are strongly related to cryptographic primitives such as [[One PPP is the set of all function computation problems that admit a [[polynomial-time reduction] ...

In [[cryptography]], the '''Niederreiter cryptosystem''' is a variation of the [[McEliece cryptosystem]] developed in 1986 by [[Harald Niederreiter]]. |title=Knapsack-type cryptosystems and algebraic coding theory ...

| known_for = Number Theory, Cryptography, Analysis | employer = Sambalpur University, Sambalpur, Odisha (Former Professor of Mathematics) ...

...fields generated by torsion points. They play a central role in the study of [[counting points on elliptic curves]] in [[Schoof's algorithm]]. The set of division polynomials is a sequence of [[polynomials]] in <math>\mathbb{Z}[x,y,A,B]</math> with <math>x, y, A, B</ ...

{{Short description|Overview of method used to digitally encrypt data}} ...up addition and certain related operations that are used in elliptic curve cryptography algorithms. ...

...man key exchange]] and [[elliptic curve cryptography]] are based on number theory and hence depend on commutative algebraic structures. ...a [[non-abelian group|non-abelian]] group. If ''w'' and ''a'' are elements of ''G'' the notation ''w''^''a'' would indicate the element ''a<sup ...

{{Short description|Theory of cryptography}} ...|The sponge construction for hash functions. ''P_i'' are blocks of the input string, ''Z_i'' are hashed output blocks.]] ...

...hich search memory much more efficiently than simply testing each sequence of bytes to determine if it provides the correct answer. They are often used i .... The former relies on detecting differences in the statistical properties of the data that make up cryptographic keys while the latter relies on determi ...

...hematical cryptography]], a '''Kleinian integer''' is a [[complex number]] of the form <math>m+n\frac{1+\sqrt{-7}}{2}</math>, with ''m'' and ''n'' [[Inte ...g (mathematics)|ring]] called the '''Kleinian ring''', which is the [[ring of integers]] in the imaginary [[quadratic field]] <math>\mathbb{Q}(\sqrt{-7}) ...