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Fast generation of prime numbers and secure public-key cryptographic parameters

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/0-387-34805-0_22openalex-snapshot
Efficient Identification and Signatures for Smart Cards
inferredcites →https://doi.org/10.1007/10722028openalex-snapshot
Algorithmic Number Theory
inferredcites →https://doi.org/10.1007/3-540-45961-8_11openalex-snapshot
A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory
inferredcites →https://doi.org/10.1007/3-540-46416-6_43openalex-snapshot
Non-interactive Public-Key Cryptography
inferredcites →https://doi.org/10.1007/3-540-46766-1_20openalex-snapshot
New Public-Key Schemes Based on Elliptic Curves over the Ring Zn
inferredcites →https://doi.org/10.1007/3-540-46877-3_10openalex-snapshot
Distributed Primality Proving and the Primality of (23539 + 1)/3
inferredcites →https://doi.org/10.1007/3-540-46877-3_7openalex-snapshot
Factoring with two large primes
inferredcites →https://doi.org/10.1007/3-540-46885-4_60openalex-snapshot
Fast Generation of Secure RSA-Moduli with Almost Maximal Diversity
inferredcites →https://doi.org/10.1007/3-540-46885-4_68openalex-snapshot
Efficient Identification and Signatures for Smart Cards
inferredcites →https://doi.org/10.1007/3-540-47555-9_16openalex-snapshot
Massively parallel elliptic curve factoring
inferredcites →https://doi.org/10.1007/3-540-47721-7_12openalex-snapshot
How To Prove Yourself: Practical Solutions to Identification and Signature Problems
inferredcites →https://doi.org/10.1007/3-540-48329-2_1openalex-snapshot
Efficient Signature Schemes Based on Birational Permutations
inferredcites →https://doi.org/10.1007/3-540-48658-5_26openalex-snapshot
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms
inferredcites →https://doi.org/10.1007/3-540-48658-5_27openalex-snapshot
Fast Generation of Provable Primes Using Search in Arithmetic Progressions
inferredcites →https://doi.org/10.1007/978-1-4612-4544-5openalex-snapshot
Factorization and Primality Testing
inferredcites →https://doi.org/10.1007/978-1-4615-3198-2openalex-snapshot
Elliptic Curve Public Key Cryptosystems
inferredcites →https://doi.org/10.1007/978-1-4684-0310-7openalex-snapshot
A Course in Number Theory and Cryptography
inferredcites →https://doi.org/10.1007/978-1-4757-1089-2openalex-snapshot
Prime Numbers and Computer Methods for Factorization
inferredcites →https://doi.org/10.1007/978-3-322-96647-6openalex-snapshot
Primality and Cryptography
inferredcites →https://doi.org/10.1007/bf00206325openalex-snapshot
The generation of random numbers that are probably prime
inferredcites →https://doi.org/10.1007/bf00967188openalex-snapshot
Mathematics of computation
inferredcites →https://doi.org/10.1007/bf01228507openalex-snapshot
Sieve algorithms for perfect power testing
inferredcites →https://doi.org/10.1007/bf01302992openalex-snapshot
�ber die Anzahl der Teiler einer nat�rlichen Zahl, welche die Formp?1 haben
inferredcites →https://doi.org/10.1007/bf01840433openalex-snapshot
Discrete logarithms inGF(p)
inferredcites →https://doi.org/10.1007/bf01931269openalex-snapshot
Some remarks concerning the M.I.T. public-key cryptosystem
inferredcites →https://doi.org/10.1007/bf02242355openalex-snapshot
Schnelle Multiplikation großer Zahlen
inferredcites →https://doi.org/10.1007/bf02403921openalex-snapshot
Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes
inferredcites →https://doi.org/10.1007/bfb0000440openalex-snapshot
The magic words are squeamish ossifrage
inferredcites →https://doi.org/10.1007/bfb0090185openalex-snapshot
Primality Testing and Abelian Varieties Over Finite Fields
inferredcites →https://doi.org/10.1016/0022-0000(84)90070-9openalex-snapshot
Probabilistic encryption
inferredcites →https://doi.org/10.1016/0022-314x(80)90084-0openalex-snapshot
Probabilistic algorithm for testing primality
inferredcites →https://doi.org/10.1016/0304-3975(76)90050-5openalex-snapshot
Analysis of a simple factorization algorithm
inferredcites →https://doi.org/10.1016/0304-3975(79)90002-1openalex-snapshot
Fast verification, testing, and generation of large primes
inferredcites →https://doi.org/10.1016/0304-3975(80)90007-9openalex-snapshot
Evaluation and comparison of two efficient probabilistic primality testing algorithms
inferredcites →https://doi.org/10.1016/0898-1221(93)90154-nopenalex-snapshot
Cryptography and coding II
inferredcites →https://doi.org/10.1016/b978-0-444-88071-0.50017-5openalex-snapshot
Algorithms in Number Theory
inferredcites →https://doi.org/10.1016/s0022-0000(76)80043-8openalex-snapshot
Riemann's hypothesis and tests for primality
inferredcites →https://doi.org/10.1017/s0305004100049252openalex-snapshot
Theorems on factorization and primality testing
inferredcites →https://doi.org/10.1049/el:19840357openalex-snapshot
Strong RSA keys
inferredcites →https://doi.org/10.1049/el:19860598openalex-snapshot
Generating strong primes
inferredcites →https://doi.org/10.1080/00029890.1912.11997658openalex-snapshot
On Composite Numbers P Which Satisfy The Fermat Congruence aP-1≡1 Mod P
inferredcites →https://doi.org/10.1080/0161-117791833219openalex-snapshot
PRELIMINARY COMMENTS ON THE M.I.T. PUBLIC-KEY CRYPTOSYSTEM
inferredcites →https://doi.org/10.1080/0161-117891852785openalex-snapshot
REMARKS ON A PROPOSED CRYPTANALYTIC ATTACK ON THE M.I.T. PUBLIC-KEY CRYPTOSYSTEM
inferredcites →https://doi.org/10.1080/0161-117891853162openalex-snapshot
SECURITY OF NUMBER THEORETIC PUBLIC KEY CRYPTOSYSTEMS AGAINST RANDOM ATTACK, I
inferredcites →https://doi.org/10.1090/notiopenalex-snapshot
Notices of the American Mathematical Society
inferredcites →https://doi.org/10.1090/procopenalex-snapshot
Proceedings of the American Mathematical Society
inferredcites →https://doi.org/10.1090/s0002-9939-1979-0537079-1openalex-snapshot
Values Taken Many Times by Euler's Phi-Function
inferredcites →https://doi.org/10.1090/s0025-5718-1969-0247789-3openalex-snapshot
On the numerical solution of a differential-difference equation arising in analytic number theory
inferredcites →https://doi.org/10.1090/s0025-5718-1975-0384673-1openalex-snapshot
New primality criteria and factorizations of 2^{𝑚}±1
inferredcites →https://doi.org/10.1090/s0025-5718-1982-0658227-7openalex-snapshot
A 𝑝+1 method of factoring
inferredcites →https://doi.org/10.1090/s0025-5718-1987-0866102-2openalex-snapshot
Implementation of a New Primality Test
inferredcites →https://doi.org/10.1090/s0025-5718-1989-0947467-1openalex-snapshot
Factoring with cyclotomic polynomials
inferredcites →https://doi.org/10.1090/s0025-5718-1989-0982368-4openalex-snapshot
The Probability that a Random Probable Prime is Composite
inferredcites →https://doi.org/10.1090/s0025-5718-1993-1189518-9openalex-snapshot
Average case error estimates for the strong probable prime test
inferredcites →https://doi.org/10.1090/s0025-5718-1993-1192971-8openalex-snapshot
On Strong Pseudoprimes to Several Bases
inferredcites →https://doi.org/10.1090/s0025-5718-60-99239-5openalex-snapshot
Mathematics of Computation
inferredcites →https://doi.org/10.1090/s0273-0979-1982-15057-1openalex-snapshot
Elementary methods in the study of the distribution of prime numbers
inferredcites →https://doi.org/10.1093/qmath/os-6.1.205openalex-snapshot
ON THE NORMAL NUMBER OF PRIME FACTORS OF p-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION
inferredcites →https://doi.org/10.1108/ir.1999.04926fae.001openalex-snapshot
Lecture Notes in Computer Science 1205
inferredcites →https://doi.org/10.1109/swat.1966.30openalex-snapshot
The recognition problem for the set of perfect squares
inferredcites →https://doi.org/10.1109/tit.1976.1055638openalex-snapshot
New directions in cryptography
inferredcites →https://doi.org/10.1109/tit.1978.1055817openalex-snapshot
An improved algorithm for computing logarithms overGF(p)and its cryptographic significance (Corresp.)
inferredcites →https://doi.org/10.1109/tit.1985.1057074openalex-snapshot
A public key cryptosystem and a signature scheme based on discrete logarithms
inferredcites →https://doi.org/10.1112/s0025579300004575openalex-snapshot
On the number of primes p for which p+a has a large prime factor
inferredcites →https://doi.org/10.1112/s002557930000471xopenalex-snapshot
On the largest prime factor of p + a
inferredcites →https://doi.org/10.1112/s0025579300009967openalex-snapshot
Popular values of Euler's function
inferredcites →https://doi.org/10.1137/0204018openalex-snapshot
Every Prime Has a Succinct Certificate
inferredcites →https://doi.org/10.1137/0206006openalex-snapshot
A Fast Monte-Carlo Test for Primality
inferredcites →https://doi.org/10.1137/0213053openalex-snapshot
How to Generate Cryptographically Strong Sequences of Pseudorandom Bits
inferredcites →https://doi.org/10.1137/0217012openalex-snapshot
How to Generate Factored Random Numbers
inferredcites →https://doi.org/10.1137/sicompopenalex-snapshot
SIAM Journal on Computing
inferredcites →https://doi.org/10.1145/100216.100295openalex-snapshot
The number field sieve
inferredcites →https://doi.org/10.1145/12130.12162openalex-snapshot
Almost all primes can be quickly certified
inferredcites →https://doi.org/10.1145/357980.358017openalex-snapshot
A method for obtaining digital signatures and public-key cryptosystems
inferredcites →https://doi.org/10.1145/359340.359342openalex-snapshot
A method for obtaining digital signatures and public-key cryptosystems
inferredcites →https://doi.org/10.2140/pjm.1988.131.157openalex-snapshot
Primality of the number of points on an elliptic curve over a finite field
inferredcites →https://doi.org/10.2307/1971363openalex-snapshot
Factoring Integers with Elliptic Curves
inferredcites →https://doi.org/10.2307/2002914openalex-snapshot
Proceedings of Symposia in Applied Mathematics.
inferredcites →https://doi.org/10.2307/2006975openalex-snapshot
On Distinguishing Prime Numbers from Composite Numbers
inferredcites →https://doi.org/10.2307/2007943openalex-snapshot
Primality and Cryptography.
inferredcites →https://doi.org/10.3929/ethz-a-000923053openalex-snapshot
On the power of pseudo-primality tests
inferredcites →https://doi.org/10.4169/000298910x484726openalex-snapshot
American Mathematical Monthly
inferredcites →https://doi.org/10.5555/314464.314478openalex-snapshot
Exact analysis of a priority queue algorithm for random variate generation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/9781394351930.ch7openalex-snapshot
Prime Number Generation and RSA Keys
inferred← citeshttps://doi.org/10.1007/11894063_13openalex-snapshot
Fast Generation of Prime Numbers on Portable Devices: An Update
inferred← citeshttps://doi.org/10.1007/3-540-36288-6_9openalex-snapshot
The Cramer-Shoup Strong-RSA Signature Scheme Revisited
inferred← citeshttps://doi.org/10.1007/3-540-44598-6_26openalex-snapshot
Efficient Non-malleable Commitment Schemes
inferred← citeshttps://doi.org/10.1007/3-540-48658-5_27openalex-snapshot
Fast Generation of Provable Primes Using Search in Arithmetic Progressions
inferred← citeshttps://doi.org/10.1007/3-540-48970-3_13openalex-snapshot
Generalised Cycling Attacks on RSA and Strong RSA Primes
inferred← citeshttps://doi.org/10.1007/3-540-68339-9_29openalex-snapshot
On Diffie-Hellman Key Agreement with Short Exponents
inferred← citeshttps://doi.org/10.1007/978-1-4419-5906-5_460openalex-snapshot
Maurer’s Method
inferred← citeshttps://doi.org/10.1007/978-1-4419-5906-5_471openalex-snapshot
Prime Number
inferred← citeshttps://doi.org/10.1007/978-3-030-34339-2_22openalex-snapshot
Using Freivalds’ Algorithm to Accelerate Lattice-Based Signature Verifications
inferred← citeshttps://doi.org/10.1007/978-3-030-71522-9_460openalex-snapshot
Maurer’s Method
inferred← citeshttps://doi.org/10.1007/978-3-030-71522-9_471openalex-snapshot
Prime Number
inferred← citeshttps://doi.org/10.1007/978-3-031-37238-4_3openalex-snapshot
Applications
inferred← citeshttps://doi.org/10.1007/978-3-0348-8295-8_10openalex-snapshot
Algorithms for Generating, Testing and Proving Primes: A Survey
inferred← citeshttps://doi.org/10.1007/978-3-0348-8295-8_21openalex-snapshot
Security of Biased Sources for Cryptographic Keys
inferred← citeshttps://doi.org/10.1007/978-3-0348-8295-8_4openalex-snapshot
Small Values of the Carmichael Function and Cryptographic Applications
inferred← citeshttps://doi.org/10.1007/978-3-319-32085-4_7openalex-snapshot
Special Primes: Properties and Applications
inferred← citeshttps://doi.org/10.1007/978-3-319-59879-6_18openalex-snapshot
Post-quantum RSA
inferred← citeshttps://doi.org/10.1007/978-3-540-24582-7_17openalex-snapshot
Prime Numbers of Diffie-Hellman Groups for IKE-MODP
inferred← citeshttps://doi.org/10.1007/978-3-540-24676-3_29openalex-snapshot
Finding Small Roots of Bivariate Integer Polynomial Equations Revisited
inferred← citeshttps://doi.org/10.1007/978-3-540-28628-8_14openalex-snapshot
Multi-trapdoor Commitments and Their Applications to Proofs of Knowledge Secure Under Concurrent Man-in-the-Middle Attacks
inferred← citeshttps://doi.org/10.1007/978-3-642-01001-9_2openalex-snapshot
Breaking RSA Generically Is Equivalent to Factoring
inferred← citeshttps://doi.org/10.1007/978-3-642-21969-6_16openalex-snapshot
Analyzing Standards for RSA Integers
inferred← citeshttps://doi.org/10.1007/978-3-642-30057-8_22openalex-snapshot
Generating Provable Primes Efficiently on Embedded Devices
inferred← citeshttps://doi.org/10.1007/978-3-662-43948-7_82openalex-snapshot
Close to Uniform Prime Number Generation with Fewer Random Bits
inferred← citeshttps://doi.org/10.1007/978-981-16-8664-1_17openalex-snapshot
An Empirical Study of Secure and Complex Variants of RSA Scheme
inferred← citeshttps://doi.org/10.1007/bf00129771openalex-snapshot
A Non-interactive Public-Key Distribution System
inferred← citeshttps://doi.org/10.1007/bf00190758openalex-snapshot
Short RSA keys and their generation
inferred← citeshttps://doi.org/10.1007/bfb0000440openalex-snapshot
The magic words are squeamish ossifrage
inferred← citeshttps://doi.org/10.1007/bfb0028487openalex-snapshot
On weak RSA-keys produced from pretty good privacy
inferred← citeshttps://doi.org/10.1007/bfb0055738openalex-snapshot
Fast RSA-type cryptosystem modulo p k q
inferred← citeshttps://doi.org/10.1007/s00145-009-9043-4openalex-snapshot
Efficient Non-Malleable Commitment Schemes
inferred← citeshttps://doi.org/10.1007/s00145-009-9045-2openalex-snapshot
Efficient Non-malleable Commitment Schemes
inferred← citeshttps://doi.org/10.1007/s10586-017-0992-3openalex-snapshot
Fast prime number generation algorithms on smart mobile devices
inferred← citeshttps://doi.org/10.1007/s10796-005-4808-2openalex-snapshot
Improving Customer Retention in E-Commerce through a Secure and Privacy-Enhanced Loyalty System
inferred← citeshttps://doi.org/10.1016/j.asoc.2026.115415openalex-snapshot
A sieve-driven genetic algorithm for RSA cryptosystem: Exploiting digit distribution and algebraic regularities
inferred← citeshttps://doi.org/10.1016/s0020-0255(99)00086-9openalex-snapshot
A novel ID-based group signature
inferred← citeshttps://doi.org/10.1016/s0022-314x(02)00029-xopenalex-snapshot
Short effective intervals containing primes
inferred← citeshttps://doi.org/10.1017/s0004972700019547openalex-snapshot
Polynomial representations of the Diffie-Hellman mapping
inferred← citeshttps://doi.org/10.1023/a:1008289605486openalex-snapshot
Analysis of Iterated Modular Exponentiation: The Orbits of xα mod N
inferred← citeshttps://doi.org/10.1023/a:1011219027181openalex-snapshot
How to choose secret parameters for RSA-type cryptosystems over elliptic curves
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Reviews
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Period of the power generator and small values of Carmichael’s function
inferred← citeshttps://doi.org/10.1093/ietfec/e90-a.12.2903openalex-snapshot
The Vanstone-Zuccherato Schemes Revisited
inferred← citeshttps://doi.org/10.1109/bigcomp.2014.6741451openalex-snapshot
Performance analysis and improvement of JPV primality test for smart IC cards
inferred← citeshttps://doi.org/10.1109/bigcomp.2016.7425951openalex-snapshot
Fast prime generation algorithms using proposed GCD test on mobile smart devices
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Parallel generation of RSA keys — A review
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ID-based cryptographic schemes using a non-interactive public-key distribution system
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A privacy-friendly loyalty system for electronic marketplaces
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Enhancing efficiency of enterprise digital rights management
inferred← citeshttps://doi.org/10.1109/icnc64010.2025.10993904openalex-snapshot
Advanced Techniques for Prime Number Generation in RSA Encryption: A Path Toward Greater Efficiency
inferred← citeshttps://doi.org/10.1109/ieeestd.2000.92292openalex-snapshot
IEEE Standard Specifications for Public-Key Cryptography
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A Novel Architecture for Fast RSA Key Generation Based on RNS
inferred← citeshttps://doi.org/10.1109/tit.2016.2594197openalex-snapshot
Breaking RSA Generically Is Equivalent to Factoring
inferred← citeshttps://doi.org/10.1109/tit.2018.2859045openalex-snapshot
Close to Uniform Prime Number Generation With Fewer Random Bits
inferred← citeshttps://doi.org/10.1109/ubmk67458.2025.11206992openalex-snapshot
High-Speed Prime Number Generation for Cryptographic Applications
inferred← citeshttps://doi.org/10.1142/9789812388841_0005openalex-snapshot
COMPUTATIONAL METHODS IN PUBLIC KEY CRYPTOLOGY
inferred← citeshttps://doi.org/10.1145/1854099.1854134openalex-snapshot
Elgamal public key cryptosystem and signature scheme in GU(m,p,n)
inferred← citeshttps://doi.org/10.1145/3011784.3011799openalex-snapshot
A collection of patterns for prime generation
inferred← citeshttps://doi.org/10.1145/319709.319716openalex-snapshot
Signature schemes based on the strong RSA assumption
inferred← citeshttps://doi.org/10.1145/3372297.3417264openalex-snapshot
A Performant, Misuse-Resistant API for Primality Testing
inferred← citeshttps://doi.org/10.1145/3476446.3536191openalex-snapshot
Random Primes without Primality Testing
inferred← citeshttps://doi.org/10.1145/357830.357847openalex-snapshot
Signature schemes based on the strong RSA assumption
inferred← citeshttps://doi.org/10.1145/501963.501965openalex-snapshot
Secure password-based cipher suite for TLS
inferred← citeshttps://doi.org/10.1155/2020/1480890openalex-snapshot
A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
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A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
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Probabilistic Analysis on JPV Algorithm and Improving It using GCD Function
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Notions for RSA integers
inferred← citeshttps://doi.org/10.1515/jmc-2024-0033openalex-snapshot
On integer sequences in cryptography
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Probabilistic Analysis on the Optimal Combination of Trial Division and Probabilistic Primality Tests for Safe Prime Generation
inferred← citeshttps://doi.org/10.17223/20710410/29/3openalex-snapshot
A SEMANTICALLY SECURE PUBLIC-KEY CRYPTOSYSTEM BASED ON RSA
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Números primos especiales y sus aplicaciones criptográficas
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New public-key cryptosystems with fast decryption
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Methods to Improve Privacy and Loyalty in Online Commerce
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A Study on the Development and Application of Number Theory in Engineering Field
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A Study on the Development and Application of Number Theory in Engineering Field
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Higher Arithmetic Applications in Engineering
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A TTA-like Processor for Fast RSA Key Generation Using RNS
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IMPLEMENTATION OF RSA KEY GENERATION BASED ON RNS USING VERILOG
inferred← citeshttps://doi.org/10.48550/arxiv.1104.4356openalex-snapshot
Notions for RSA integers
inferred← citeshttps://doi.org/10.48550/arxiv.1408.1888openalex-snapshot
On a Deterministic Property of the Category of $k$-almost Primes: A Deterministic Structure Based on a Linear Function for Redefining the $k$-almost Primes ($\exists n\in {\rm N} $, $1{\le} k {\le}n$) in Certain Intervals
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Studies of entropy measures concerning the gaps of prime numbers
inferred← citeshttps://doi.org/10.5120/ijca2016912384openalex-snapshot
A Flexible and Efficient Algorithm for Generating Prime Numbers using Biometric Identity (Bio-PNGA)
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Design and Analysis of Efficient Parallel Hardware Prime Generators
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