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Faster Integer Multiplication
 STOC'07
, 2007
"... For more than 35 years, the fastest known method for integer multiplication has been the SchönhageStrassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding Ω(n log n) lower bound. The prevailing conjecture has always been that the complex ..."
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For more than 35 years, the fastest known method for integer multiplication has been the SchönhageStrassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding Ω(n log n) lower bound. The prevailing conjecture has always been
The Graph Of Integer Multiplication Is Hard For
, 1995
"... . We prove that the graph of integer multiplication requires nondeterministic readktimes branching programs of exponential size. On the other hand we show that one can add polynomially many integers by small deterministic readonceonly branching programs. This shows that the reason for the hardn ..."
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. We prove that the graph of integer multiplication requires nondeterministic readktimes branching programs of exponential size. On the other hand we show that one can add polynomially many integers by small deterministic readonceonly branching programs. This shows that the reason
Large Integer Multiplication on Hypercubes
"... Previous work has reported on the use of polynomial transforms to compute exact convolution and to perform multiplication of large integers on a massively parallel processor. We now present results of an improved technique, using the Fermat Number Transform. When the Fermat Number Transform was firs ..."
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Cited by 2 (0 self)
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Previous work has reported on the use of polynomial transforms to compute exact convolution and to perform multiplication of large integers on a massively parallel processor. We now present results of an improved technique, using the Fermat Number Transform. When the Fermat Number Transform
Even faster integer multiplication
, 2015
"... We give a new proof of Fürer’s bound for the cost of multiplying nbit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coefficient rings with “fast” roots of unity. Moreover, we establish the improved boundO(n lognKlog n) with K = 8. We show that ..."
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We give a new proof of Fürer’s bound for the cost of multiplying nbit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coefficient rings with “fast” roots of unity. Moreover, we establish the improved boundO(n lognKlog n) with K = 8. We show
Hardware Speedups in Long Integer Multiplication
 Computer Architecture News
, 1990
"... We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see [BR ..."
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Cited by 24 (5 self)
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We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see
Ultra Long Integer Multiplication on GDPS
"... Many Internet applications require intensive cryptographic calculation such as publickey encryptions and digital signatures. These schemes require a computation of large integer multiplications. Those cryptographic schemes are vulnerable to a bruteforce attack, and the large key is the countermeas ..."
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Many Internet applications require intensive cryptographic calculation such as publickey encryptions and digital signatures. These schemes require a computation of large integer multiplications. Those cryptographic schemes are vulnerable to a bruteforce attack, and the large key
Fast OnLine Integer Multiplication
 PROC. 5TH ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1974
"... A Turing machine multiplies binary integers onZine if it receives its inputs loworder digits first and produces the jth digit of the product before reading in the (j+l)st digits of the two inputs. We present a general method for converting any offline multiplication algorithm which forms the prod ..."
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Cited by 12 (1 self)
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A Turing machine multiplies binary integers onZine if it receives its inputs loworder digits first and produces the jth digit of the product before reading in the (j+l)st digits of the two inputs. We present a general method for converting any offline multiplication algorithm which forms
NonInteractive Proofs for Integer Multiplication
"... 1 Introduction Applications such as auctions, elections or benchmarking analysis all involve computing on confidential data from several parties who do not trust each other a priori. This means that solutions involving a single trusted party are typically unsatisfactory. In principle, all such probl ..."
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1 Introduction Applications such as auctions, elections or benchmarking analysis all involve computing on confidential data from several parties who do not trust each other a priori. This means that solutions involving a single trusted party are typically unsatisfactory. In principle, all such problems can be solved using general secure multiparty computation [18, 2, 8], where all parties take part in computing the desired results. But in practice, this is often not realistic: in auctions or elections, for instance, the number of parties holding inputs can be very large, they cannot be assumed to be expert users nor can their machines be assumed to be online at particular times. Hence assuming that all such parties can reliably take part in a multiround protocol is unrealistic. It is therefore often suggested that a smaller number of servers are assigned to do the computation, acting effectively as representatives for the clients supplying inputs. Of course, this makes sense only if the complexity of supplying inputs is much smaller than the complexity of taking part in the actual computation. In particular, we would want that supplying inputs is noninteractive. This problem can be solved using a noninteractive verifiable secret sharing (VSS) scheme. Having done the VSS's, the servers hold shares of all inputs and can do the computation using any of the (numerous) known multiparty computation techniques. Several noninteractive VSS protocols are known see, e.g., [22].
Efficient Integer Multiplication Overflow Detection Circuits
"... Multiplication of two nbit integers produces a 2nbit product. To allow the result to be stored in the same format as the inputs, many processors return the n least significant bits of the product and an overflow flag. This paper describes methods for integer multiplication with overflow detection ..."
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Multiplication of two nbit integers produces a 2nbit product. To allow the result to be stored in the same format as the inputs, many processors return the n least significant bits of the product and an overflow flag. This paper describes methods for integer multiplication with overflow detection
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