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

1996
*
Lecture Notes in Computer Science
*

Using it, we show

doi:10.1007/3-540-61440-0_159
fatcat:shqy2jxdkrgprkelpnanpxkmni
*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. ...##
###
Improved parallel approximation of a class of integer programming problems

1997
*
Algorithmica
*

Using it, we show

doi:10.1007/bf02523683
fatcat:7mmkyhnnbrbafldjieg5r55hxa
*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. ...##
###
Factoring Primes to Factor Moduli: Backdooring and Distributed Generation of Semiprimes
[article]

2021
*
IACR Cryptology ePrint Archive
*

We show

dblp:journals/iacr/Vitto21
fatcat:v6errb3xjzcgfndrhru7srupgi
*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 ...##
###
Generating Random Factored Ideals in Number Fields
[article]

2017
*
arXiv
*
pre-print

We present a

arXiv:1612.06260v2
fatcat:7a2l2c6ubvbhnnvcg7fk3ql2ce
*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*. ...##
###
Generating random factored ideals in number fields

2017
*
Mathematics of Computation
*

Using this randomly

doi:10.1090/mcom/3283
fatcat:iojw34votvejjnmjybtbyazd2m
*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*. ...##
###
On the Possibility of Constructing Meaningful Hash Collisions for Public Keys
[chapter]

2005
*
Lecture Notes in Computer Science
*

For instance, we show

doi:10.1007/11506157_23
fatcat:5dereqkvjvfhdewvfuglzrue5i
*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. ...##
###
The Insecurity of Esign in Practical Implementations
[chapter]

2003
*
Lecture Notes in Computer Science
*

Using a 1152-bit modulus, the

doi:10.1007/978-3-540-40061-5_31
fatcat:uqvwollwgjejlf64dp3yqglu24
*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. ...##
###
How to generate cryptographically strong sequences of pseudo random bits

1982
*
23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
*

We are grateful

doi:10.1109/sfcs.1982.72
dblp:conf/focs/BlumM82
fatcat:wrehgywqbjf35khgqsho3v5gvq
*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*. ...##
###
What should computer science students learn from mathematics?

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 @ ! ...

##
###
How to Generate Cryptographically Strong Sequences of Pseudorandom Bits

1984
*
SIAM journal on computing (Print)
*

We are grateful

doi:10.1137/0213053
fatcat:czbi5oymxzbibnt3hkxbcwbobq
*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*. ...##
###
Mathematical Models in Public-Key Cryptology
[chapter]

1999
*
Discrete Mathematics and Its Applications
*

In all of the private-key systems, two users who wish

doi:10.1201/9781420050042.ch6
fatcat:cynowdu6wndsroli3gsy7tzhqm
*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. ...##
###
Efficient generation of shared RSA keys

2001
*
Journal of the ACM
*

We describe efficient techniques for three (or more) parties

doi:10.1145/502090.502094
fatcat:4n33cvishrghxoapigq663wppu
*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*. ...##
###
Efficient generation of shared RSA keys
[chapter]

1997
*
Lecture Notes in Computer Science
*

We describe efficient techniques for three (or more) parties

doi:10.1007/bfb0052253
fatcat:yh76lhcge5flvgsg3ksy2pfxce
*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*. ...##
###
Encryption and Decryption through RSA Cryptosystem using Two Public Keys and Chinese Remainder Theorem

2017
*
International Journal of Computer Applications
*

Instead of sending public key directly, two positive

doi:10.5120/ijca2017914674
fatcat:alcmjnuwvnfjnmpqex7oepvlqu
*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. ...##
###
Designer Primes
[article]

2020
*
IACR Cryptology ePrint Archive
*

Prime

dblp:journals/iacr/Johnston20
fatcat:62nyeoi3pzhenftpyabpxnfflm
*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, ...
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