Secure digital signature schemes

A computer program product (CPP), comprising:

• a set of one or more non-transitory computer-readable storage media;
• and
• program instructions, collectively stored in the set of one or more non-transitory computer readable storage media, or causing a processor set to perform the following computer operations:
• in response to receiving a session request from a user, compute a first cryptographic term;
• split the first cryptographic term into an initial portion and a remainder portion, the remainder portion including at least one bit;
• send the initial portion of the first cryptographic term to the user;
• receive two or more different potential second cryptographic terms from the user;
• use the at least one bit in the remainder portion to determine a correct one of the potential second cryptographic terms;
• use the correct one of the potentials second cryptographic terms to compute a third cryptographic term;
• and
• send the third cryptographic term to the user.

A computer system (CS), comprising:

• a processor set;
• a set of one or more non-transitory computer-readable storage media;
• program instructions, collectively stored in the set of one or more non-transitory computer readable storage media, for causing the processor set to perform the following computer operations:
• in response to receiving a session request from a user, compute a first cryptographic term;
• split the first cryptographic term into an initial portion and a remainder portion, the remainder portion including at least one bit;
• send the initial portion of the first cryptographic term to the user;
• receive two or more different potentials second cryptographic terms from the user;
• use the at least one bit in the remainder portion to determine a correct one of the potentials second cryptographic terms;
• use the correct one of the potentials second cryptographic terms to compute a third cryptographic term;
• and
• send the third cryptographic term to the user.

A computer-implemented method (CIM), comprising:

• receiving, from a server, an initial portion of a first cryptographic term;
• identifying a remainder portion of the first cryptographic term that is missing;
• enumerating potential values for the missing remainder portion of the first cryptographic term;
• developing potential second cryptographic terms for the respective potential values enumerated for the missing remainder portion;
• sending the potential second cryptographic terms to the server;
• receiving a third cryptographic term from the server;
• receiving the missing remainder portion of the first cryptographic term;
• and
• producing the first cryptographic term by combining the remainder portion of the first cryptographic term and the initial portion of the first cryptographic term.

A computer program product (CPP), comprising:

• a set of one or more non-transitory computer-readable storage media;
• and
• program instructions, collectively stored in the set of one or more non-transitory computer readable storage media, for causing a processor set to perform the following computer operations:
• receive, from a server, an initial portion of a first cryptographic term;
• identify a remainder portion of the first cryptographic term that is missing;
• enumerate potential values for the missing remainder portion of the first cryptographic term;
• develop potential second cryptographic terms for the respective potential values enumerated for the missing remainder portion;
• send the potential second cryptographic terms to the server;
• receive a third cryptographic term from the server;
• receive the missing remainder portion of the first cryptographic term;
• and
• produce the first cryptographic term by combining the remainder portion of the first cryptographic term and the initial portion of the first cryptographic term.