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Shamir's (*k*,*n*)-threshold secret sharing scheme (threshold scheme) has two problems: a heavy computational cost is required to make shares and recover the secret, and a large storage capacity is needed to retain all the shares. As a solution to the heavy computational cost problem, several fast threshold schemes have been proposed. On the other hand, threshold *ramp* secret sharing schemes (*ramp* scheme) have been proposed in order to reduce each bit-size of shares in Shamir's scheme. However, there is no fast *ramp* scheme which has both low computational cost and low storage requirements. This paper proposes a new (*k*,*L*,*n*)-threshold *ramp* secret sharing scheme which uses just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret at a low computational cost. Moreover, by proving that the fast (*k*,*n*)-threshold scheme in conjunction with a method to reduce the number of random numbers is an *ideal* secret sharing scheme, we show that our fast *ramp* scheme is able to reduce each bit-size of shares by allowing some degradation of security similar to the existing *ramp* schemes based on Shamir's threshold scheme.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.8 pp.1808-1821

- Publication Date
- 2009/08/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E92.A.1808

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category
- Theory

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Jun KURIHARA, Shinsaku KIYOMOTO, Kazuhide FUKUSHIMA, Toshiaki TANAKA, "A Fast (k,L,n)-Threshold Ramp Secret Sharing Scheme" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 8, pp. 1808-1821, August 2009, doi: 10.1587/transfun.E92.A.1808.

Abstract: Shamir's (*k*,*n*)-threshold secret sharing scheme (threshold scheme) has two problems: a heavy computational cost is required to make shares and recover the secret, and a large storage capacity is needed to retain all the shares. As a solution to the heavy computational cost problem, several fast threshold schemes have been proposed. On the other hand, threshold *ramp* secret sharing schemes (*ramp* scheme) have been proposed in order to reduce each bit-size of shares in Shamir's scheme. However, there is no fast *ramp* scheme which has both low computational cost and low storage requirements. This paper proposes a new (*k*,*L*,*n*)-threshold *ramp* secret sharing scheme which uses just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret at a low computational cost. Moreover, by proving that the fast (*k*,*n*)-threshold scheme in conjunction with a method to reduce the number of random numbers is an *ideal* secret sharing scheme, we show that our fast *ramp* scheme is able to reduce each bit-size of shares by allowing some degradation of security similar to the existing *ramp* schemes based on Shamir's threshold scheme.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.1808/_p

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@ARTICLE{e92-a_8_1808,

author={Jun KURIHARA, Shinsaku KIYOMOTO, Kazuhide FUKUSHIMA, Toshiaki TANAKA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A Fast (k,L,n)-Threshold Ramp Secret Sharing Scheme},

year={2009},

volume={E92-A},

number={8},

pages={1808-1821},

abstract={Shamir's (*k*,*n*)-threshold secret sharing scheme (threshold scheme) has two problems: a heavy computational cost is required to make shares and recover the secret, and a large storage capacity is needed to retain all the shares. As a solution to the heavy computational cost problem, several fast threshold schemes have been proposed. On the other hand, threshold *ramp* secret sharing schemes (*ramp* scheme) have been proposed in order to reduce each bit-size of shares in Shamir's scheme. However, there is no fast *ramp* scheme which has both low computational cost and low storage requirements. This paper proposes a new (*k*,*L*,*n*)-threshold *ramp* secret sharing scheme which uses just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret at a low computational cost. Moreover, by proving that the fast (*k*,*n*)-threshold scheme in conjunction with a method to reduce the number of random numbers is an *ideal* secret sharing scheme, we show that our fast *ramp* scheme is able to reduce each bit-size of shares by allowing some degradation of security similar to the existing *ramp* schemes based on Shamir's threshold scheme.},

keywords={},

doi={10.1587/transfun.E92.A.1808},

ISSN={1745-1337},

month={August},}

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TY - JOUR

TI - A Fast (k,L,n)-Threshold Ramp Secret Sharing Scheme

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1808

EP - 1821

AU - Jun KURIHARA

AU - Shinsaku KIYOMOTO

AU - Kazuhide FUKUSHIMA

AU - Toshiaki TANAKA

PY - 2009

DO - 10.1587/transfun.E92.A.1808

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E92-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2009

AB - Shamir's (*k*,*n*)-threshold secret sharing scheme (threshold scheme) has two problems: a heavy computational cost is required to make shares and recover the secret, and a large storage capacity is needed to retain all the shares. As a solution to the heavy computational cost problem, several fast threshold schemes have been proposed. On the other hand, threshold *ramp* secret sharing schemes (*ramp* scheme) have been proposed in order to reduce each bit-size of shares in Shamir's scheme. However, there is no fast *ramp* scheme which has both low computational cost and low storage requirements. This paper proposes a new (*k*,*L*,*n*)-threshold *ramp* secret sharing scheme which uses just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret at a low computational cost. Moreover, by proving that the fast (*k*,*n*)-threshold scheme in conjunction with a method to reduce the number of random numbers is an *ideal* secret sharing scheme, we show that our fast *ramp* scheme is able to reduce each bit-size of shares by allowing some degradation of security similar to the existing *ramp* schemes based on Shamir's threshold scheme.

ER -