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Improved parallel approximation of a class of integer programming problems [chapter]

Noga Alon, Aravind Srinivasan
1996 Lecture Notes in Computer Science  
Using it, we show how to approximate a class of N P -hard integer programming problems in N C, to within factors better than the current-best N C algorithms (of Berger & Rompel and Motwani, Naor & Naor  ...  ); in some cases, the approximation factors are as good as the best-known sequential algorithms, due to Raghavan.  ...  We thank Prabhakar Raghavan for clarifying an issue about randomized rounding, and David Zuckerman for pointing out the work of [8] . We also thank the referee for his/her helpful comments.  ... 
doi:10.1007/3-540-61440-0_159 fatcat:shqy2jxdkrgprkelpnanpxkmni

Improved parallel approximation of a class of integer programming problems

N. Alon, A. Srinivasan
1997 Algorithmica  
Using it, we show how to approximate a class of N P -hard integer programming problems in N C, to within factors better than the current-best N C algorithms (of Berger & Rompel and Motwani, Naor & Naor  ...  ); in some cases, the approximation factors are as good as the best-known sequential algorithms, due to Raghavan.  ...  We thank Prabhakar Raghavan for clarifying an issue about randomized rounding, and David Zuckerman for pointing out the work of [8] . We also thank the referee for his/her helpful comments.  ... 
doi:10.1007/bf02523683 fatcat:7mmkyhnnbrbafldjieg5r55hxa

Factoring Primes to Factor Moduli: Backdooring and Distributed Generation of Semiprimes [article]

Giuseppe Vitto
2021 IACR Cryptology ePrint Archive  
We show how our prime generation procedure can be used to efficiently produce semiprimality certificates, ultimately allowing us to sketch a multi-party distributed protocol to generate semiprimes with  ...  We then formalize semiprimality certificates that, based on a result by Goldwasser and Kilian, allow to prove semiprimality of an integer with no need to reveal any of its factors.  ...  The fastest known general-purpose factoring algorithm is the General Number Field Sieve (GNFS) [26] which allows to factor an integer N with complexity exp 3 64 9 + o(1) (ln n) 1 3 (ln ln n) 2 3 A semiprimality  ... 
dblp:journals/iacr/Vitto21 fatcat:v6errb3xjzcgfndrhru7srupgi

Generating Random Factored Ideals in Number Fields [article]

Zachary Charles
2017 arXiv   pre-print
We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the  ...  Using this algorithm, we can produce a random ideal in the ring of algebraic integers uniformly at random among ideals with norm up to N, in polynomial time.  ...  Since there are currently no known polyonmial time factorization algorithms, we cannot simply generate an integer and factor it. Instead, we can generate the prime factorization uniformly at random.  ... 
arXiv:1612.06260v2 fatcat:7a2l2c6ubvbhnnvcg7fk3ql2ce

Generating random factored ideals in number fields

Zachary Charles
2017 Mathematics of Computation  
Using this randomly generated norm, we can produce a random factored ideal in the ring of algebraic integers uniformly at random among ideals with norm up to N , in randomized polynomial time.  ...  We do this by generating a random integer and its factorization according to the distribution of norms of ideals at most N in the given number field.  ...  Since there are currently no known polyonmial time factorization algorithms, we cannot simply generate an integer and factor it. Instead, we can generate the prime factorization uniformly at random.  ... 
doi:10.1090/mcom/3283 fatcat:iojw34votvejjnmjybtbyazd2m

On the Possibility of Constructing Meaningful Hash Collisions for Public Keys [chapter]

Arjen Lenstra, Benne de Weger
2005 Lecture Notes in Computer Science  
For instance, we show how to use hash collisions to construct two X.509 certificates that contain identical signatures and that differ only in the public keys.  ...  or share other characteristics with the hash collisions as quickly constructed in [14] .  ...  Acknowledgments are due to Hendrik W. Lenstra, Berry Schoenmakers, and Mike Wiener for helpful remarks and fruitful discussions.  ... 
doi:10.1007/11506157_23 fatcat:5dereqkvjvfhdewvfuglzrue5i

The Insecurity of Esign in Practical Implementations [chapter]

Pierre-Alain Fouque, Nick Howgrave-Graham, Gwenaëlle Martinet, Guillaume Poupard
2003 Lecture Notes in Computer Science  
Using a 1152-bit modulus, the generation of an Esign signature requires to draw at random a 768-bit integer.  ...  However, our results show that random data used to generate signatures must be very carefully produced and protected against any kind of exposure, even partial.  ...  Then, we detail how to use lattice reduction in order to factor modulus such as N under some assumptions on the random data used in Esign. Lattice Reduction Notations.  ... 
doi:10.1007/978-3-540-40061-5_31 fatcat:uqvwollwgjejlf64dp3yqglu24

How to generate cryptographically strong sequences of pseudo random bits

Manuel Blum, Silvio Micali
1982 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)  
We are grateful to Shafi Goldwasser for numerous valuable discussions. to Richard Karp for his precious gift of setting the context and making vague ideas precise. and to Andy Yao for having brought to  ...  Acknowledgements We are proud to thank many friends.  ...  However we do not know how to pick at random a prime p so that the factorization of p-l is known.  ... 
doi:10.1109/sfcs.1982.72 dblp:conf/focs/BlumM82 fatcat:wrehgywqbjf35khgqsho3v5gvq

What should computer science students learn from mathematics?

Y. C. Tay
2005 ACM SIGACT News  
To do so, it brings together some examples that illustrate the current state of computer science and information technology.  ...  Acknowledgment Many thanks to Helmer Aslaksen, Y.K. Leong, Peter Pang, Wei-Lung Wang and Hoeteck Wee for their helpful comments on the draft.  ...  Since no formula is known to generate primes, we need to be able to quickly generate large integers and verify whether they are in fact primes; i.e. we need an efficient algorithm for computing @ A @ !  ... 
doi:10.1145/1067309.1067311 fatcat:7bdoru6mrnaknet7hbzp4efwfi

How to Generate Cryptographically Strong Sequences of Pseudorandom Bits

Manuel Blum, Silvio Micali
1984 SIAM journal on computing (Print)  
We are grateful to Shafi Goldwasser for numerous valuable discussions. to Richard Karp for his precious gift of setting the context and making vague ideas precise. and to Andy Yao for having brought to  ...  Acknowledgements We are proud to thank many friends.  ...  However we do not know how to pick at random a prime p so that the factorization of p-l is known.  ... 
doi:10.1137/0213053 fatcat:czbi5oymxzbibnt3hkxbcwbobq

Mathematical Models in Public-Key Cryptology [chapter]

Joel Brawley, Shuhong Gao
1999 Discrete Mathematics and Its Applications  
In all of the private-key systems, two users who wish to correspond must have a common key before the communication starts, and in practice, establishing a common secret key can be expensive, difficult  ...  general information about the system and how it operates is known.  ...  To improve security, one can use a cryptographically strong pseudo-random bit generator to expand k r to a much longer string and then XOR it with m.  ... 
doi:10.1201/9781420050042.ch6 fatcat:cynowdu6wndsroli3gsy7tzhqm

Efficient generation of shared RSA keys

Dan Boneh, Matthew Franklin
2001 Journal of the ACM  
We describe efficient techniques for three (or more) parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known.  ...  None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption.  ...  A possible approach for solving this is to generate N as N = PaPb(qa -I-qb) where Pa,Pb are primes known to Alice, Bob respectively and qa, qb are random n bit integers.  ... 
doi:10.1145/502090.502094 fatcat:4n33cvishrghxoapigq663wppu

Efficient generation of shared RSA keys [chapter]

Dan Boneh, Matthew Franklin
1997 Lecture Notes in Computer Science  
We describe efficient techniques for three (or more) parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known.  ...  None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption.  ...  A possible approach for solving this is to generate N as N = PaPb(qa -I-qb) where Pa,Pb are primes known to Alice, Bob respectively and qa, qb are random n bit integers.  ... 
doi:10.1007/bfb0052253 fatcat:yh76lhcge5flvgsg3ksy2pfxce

Encryption and Decryption through RSA Cryptosystem using Two Public Keys and Chinese Remainder Theorem

Aarushi Rai, Shitanshu Jain
2017 International Journal of Computer Applications  
Instead of sending public key directly, two positive integers are used, on which some mathematical calculation is done. And by using those integers two public keys would be sent to the user.  ...  Network security refers to an activity which is designed to protect the usability and integrity of the network and data.  ...  Known plaintext attack deals with some known plaintext corresponding to the cipher text. It is applicable in the original RSA algorithm.  ... 
doi:10.5120/ijca2017914674 fatcat:alcmjnuwvnfjnmpqex7oepvlqu

Designer Primes [article]

Anna M. Johnston
2020 IACR Cryptology ePrint Archive  
Prime integers are the backbone of most public key cryptosystems. Attacks often go after the primes themselves, as in the case of all factoring and index calculus algorithms.  ...  Unfortunately many systems use fixed primes for a variety of reasons, including the difficulty of generating trusted, random, cryptographically secure primes.  ...  R A divisor of (P − 1), with known factorization R = ∏ t j=1 r mj j where r j are distinct primes and m are positive integers. r j Known prime divisors of R m j Exponents of known prime divisors of R,  ... 
dblp:journals/iacr/Johnston20 fatcat:62nyeoi3pzhenftpyabpxnfflm
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