An entity that desires to engage in anonymous transactions first generates a transaction identification that does not uniquely identify the entity. Additionally, the entity splits an entity identification uniquely associated with the entity into a plurality of secret shares and thereafter sends the transaction identification and the plurality of secret shares to a plurality of shareholders. Subsequently, anonymous transactions on behalf of the entity may be directly conducted by the shareholders based in part upon the plurality of secret shares. In one embodiment of the present invention, the entity identification comprises a public key uniquely assigned to the entity.

 
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> Mark forming apparatus, method of forming laser mark on optical disk, reproducing apparatus, optical disk and method of producing optical disk

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