Abstract
The present principles provide a threshold signature scheme. Considering n players, given asymmetric bilinear groups (G, Ĝ, G T ) with generators g, h, g̃, h̃, X, Y ∈R G and g̃z, g̃r ∈R Ĝ, each player chooses a set of random tdegree polynomials, and generate a set of partial homomorphic signature on several linearly independent vectors. The public key PK may be obtained based on the set of polynomials and the partial homomorphic signatures of n players. The private key share and verification key for a player can be defined based on the set of polynomials. The signature for the message can be obtained from t partial signatures, wherein each partial signature can be generated based on the player's private key share and some random variables. Whether a partial signature is valid can be determined based on the public key PK and the verification key. Whether the signature for the message is valid can be determined based on the public key PK.
Claims
 A method for signing a message using threshold signatures, comprising:
 accessing a plurality of linearly independent vectors, each vector including one or more of generators
 determining a partial homomorphic signature on one of the plurality of linearly independent vectors, wherein the partial homomorphic signature is suitable for use in determining a public key;
 determining a private key share responsive to a set of random polynomials; and determining a partial signature for the message responsive to the private key share, the partial signature, in combination with other partial signatures, suitable for generating a signature of the message, and the signature suitable for verification using the public key.
 The method of claim 1, wherein the plurality of linearly independent vectors are
 The method of claim 1, wherein the partial homomorphic signature is one of
 The method of claim 1, wherein the partial signature is determined by a first signer, and wherein each of the other partial signatures is determined by a respective one of other signers, further comprising:
 sending the partial signature and the partial homomorphic signature to the other signers.
 The method of claim 1, further comprising:
 determining a verification key responsive to the generators g, h and the set of random polynomials.
 The method of claim 5, further comprising:
 verifying the partial signature responsive to the verification key and the public key.
 A method for verifying a signature of a message, comprising:
 accessing the message, the signature, a public key and a verification key,
 wherein the signature is generated from a plurality of partial signatures, each one of the plurality of partial signatures being generated responsive to a private key share, wherein the private key share is determined responsive to a set of random polynomials, and
 wherein the public key is generated responsive to a partial homomorphic signature, the partial homomorphic signature being determined responsive to one of a plurality of linearly independent vectors, each vector including one or more of generators
 verifying whether the signature is valid.
 The method of claim 7, wherein the plurality of linearly independent vectors are
 The method of claim 7, wherein the partial homomorphic signature for signer i is one of
 The method of claim 7, wherein the verification key is generated responsive to the generators g, h and the set of random polynomials.
 An apparatus for signing a message using threshold signatures, comprising: a signer (130, 140, 150) configured to
 access a plurality of linearly independent vectors, each vector including one or more of generators
 determine a partial homomorphic signature on one of the plurality of linearly independent vectors, wherein the partial homomorphic signature is suitable for use in determining a public key;
 determine a private key share responsive to a set of random polynomials; and determine a partial signature for the message responsive to the private key share, the partial signature, in combination with other partial signatures, suitable for generating a signature of the message, and the signature suitable for verification using the public key.
 The apparatus of claim 11, wherein the plurality of linearly independent vectors
 The apparatus of claim 11, wherein the partial homomorphic signature is one of
 The apparatus of claim 11, wherein the partial signature is determined by a first signer, and wherein each of the other partial signatures is determined by a respective one of other signers, and wherein the first signer is further configured to send the partial signature and the partial homomorphic signature to the other signers.
 The apparatus of claim 11, wherein the signer is further configured to determine a verification key responsive to the generators g, h and the set of random polynomials.
 The apparatus of claim 15, wherein the signer is further configured to verify the partial signature responsive to the verification key and the public key.
 A apparatus for verifying a signature of a message, comprising: a verifier (170) configured to access the message, the signature, a public key and a verification key, wherein the signature is generated from a plurality of partial signatures, each one of the plurality of partial signatures being generated responsive to a private key share, wherein the private key share is determined responsive to a set of random polynomials, and wherein the public key is generated responsive to a partial homomorphic signature, the partial homomorphic signature being determined responsive to one of a plurality of linearly independent vectors, each vector including one or more of generators
 verify whether the signature is valid. 18. The apparatus of claim 17, wherein the plurality of linearly independent vectors
 The apparatus of claim 17, wherein the partial homomorphic signature for signer i is one of
 The apparatus of claim 17, wherein the verification key is generated responsive to the generators g, h and the set of random polynomials.
Applicants

Technicolor Usa Inc
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Inventors

Joye Marc
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Libert Benoit
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CPC Classifications

H04L9/3255
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IPC Classifications

H04L9/32
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Document Preview
 Publication: Mar 31, 2016

Application:
Sep 25, 2015
US 2015/0052129 W

Priority:
Sep 26, 2014
US 201462055804 P