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LibTMCG provides several data structures for cards, stacks, and cryptographic keys.

There exist two different encoding schemes that can be used for the digital representation of playing cards. In the scheme of Schindelhauer [Sc98] the type of a card is shared among the players through bit-wise representation by quadratic (non-)residues. Thus the security relies on the well-known QRA (Quadratic Residuosity Assumption). Unfortunately, the size of a card grows linearly in the number of players and logarithmically in the number of card types. Recently the much more efficient solution of Barnett and Smart [BS03] has been implemented. This encoding works on a cyclic group of prime order and requires that the DDH (Decisional Diffie-Hellman Assumption) holds there.

For both schemes LibTMCG provides a structure whose name contains the
suffix `Card`

. This data type is used to represent an open
or even a masked card. Further, there is a corresponding structure whose
name contains the suffix `CardSecret`

. This data type is
used to represent the secret values involved in a card masking operation.

Because of the reduced computational and communication complexity
(see [St05] for more details) the usage of the second card
encoding scheme, i.e. `VTMF_Card`

and `VTMF_CardSecret`

, is
highly recommended.

- Data type:
**TMCG_Card** This

`struct`

represents a card in the encoding scheme of Schindelhauer [Sc98]. The type of the card is shared among the players by quadratic residues and non-residues, respectively. Thus the security relies on the Quadratic Residuosity Assumption.- Member of TMCG_Card:
*std::vector< std::vector<MP_INT> >***z** This

*k\times w*-matrix encodes the type of the corresponding card in a shared way. For each of the*k*players there is a separate row and for each of the*w*bits in the binary representation of the type there is a column. The elements are numbers from the group*{\bf Z}^{\circ}_{m_i}*where*m_i*is the public modulus of the*i*th player.

- Constructor on TMCG_Card:
**TMCG_Card***()* This default constructor initializes the card with an empty

*1\times 1*-matrix. Later the method`TMCG_Card::resize`

can be used to enlarge the card representation.

- Constructor on TMCG_Card:
**TMCG_Card***(*`size_t`

k,`size_t`

w) This constructor initializes the card with an empty

*k\times w*-matrix. The parameter`k`is the number of players and`w`is the maximum number of bits used by the binary representation of the card type.

- Constructor on TMCG_Card:
**TMCG_Card***(*`const TMCG_Card&`

that) This is a simple copy-constructor and

`that`is the card to be copied.

- Operator on TMCG_Card:
*TMCG_Card&***=***(*`const TMCG_Card&`

that) This is a simple assignment-operator and

`that`is the card to be assigned.

- Operator on TMCG_Card:
*bool***==***(*`const TMCG_Card&`

that) This operator tests two card representations for equality.

- Operator on TMCG_Card:
*bool***!=***(*`const TMCG_Card&`

that) This operator tests two card representations for inequality.

- Method on TMCG_Card:
*void***resize***(*`size_t`

k,`size_t`

w) This method resizes the representation of the card. The current content of the member

`z`

will be released and a new*k\times w*-matrix is created. The parameter`k`is the number of players and`w`is the maximum number of bits used by the binary representation of the card type.

- Method on TMCG_Card:
*bool***import***(*`std::string`

s) This method imports the content of the member

`z`

from the correctly formatted input string`s`. It returns`true`

, if the import was successful.

- Destructor on TMCG_Card:
**~TMCG_Card***()* This destructor releases all occupied resources.

- Member of TMCG_Card:

- Operator on TMCG_Card:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_Card&`

card) This operator exports the content of the member

`z`

(of the given`TMCG_Card`

`card`) to the output stream`out`.

- Operator on TMCG_Card:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_Card&`

card) This operator imports the content of the member

`z`

(of the given`TMCG_Card`

`card`) from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

- Data type:
**TMCG_CardSecret** This

`struct`

represents the secret used for a card masking operation in the original encoding scheme of Schindelhauer [Sc98].- Member of TMCG_CardSecret:
*std::vector< std::vector<MP_INT> >***r** This

*k\times w*-matrix encodes the first part of the secret. For each of the*k*players there is a separate row and for each of the*w*bits in the binary representation of the corresponding card type there is a column. The elements are numbers from the group*{\bf Z}^{\circ}_{m_i}*where*m_i*is the public modulus of the*i*th player.

- Member of TMCG_CardSecret:
*std::vector< std::vector<MP_INT> >***b** This

*k\times w*-matrix encodes the second part of the secret. For each of the*k*players there is a separate row and for each of the*w*bits in the binary representation of the corresponding card type there is a column. The elements are simply numbers from*\{0, 1\}*.

- Constructor on TMCG_CardSecret:
**TMCG_CardSecret***()* This default constructor initializes both members with an empty

*1\times 1*-matrix. Later the method`TMCG_CardSecret::resize`

can be used to enlarge the card representation.

- Constructor on TMCG_CardSecret:
**TMCG_CardSecret***(*`size_t`

k,`size_t`

w) This constructor initializes both members with an empty

*k\times w*-matrix. The parameter`k`is the number of players and`w`is the maximum number of bits used by the binary representation of the corresponding card type.

- Constructor on TMCG_CardSecret:
**TMCG_CardSecret***(*`const TMCG_CardSecret&`

that) This is a simple copy-constructor and

`that`is the secret to be copied.

- Operator on TMCG_CardSecret:
*TMCG_CardSecret&***=***(*`const TMCG_CardSecret&`

that) This is a simple assignment-operator and

`that`is the secret to be assigned.

- Method on TMCG_CardSecret:
*void***resize***(*`size_t`

k,`size_t`

w) This method resizes the representation of the secret. The current content of the members

`r`

and`b`

will be released and new*k\times w*-matrices are created. The parameter`k`is the number of players and`w`is the maximum number of bits used by the binary representation of the corresponding card type.

- Method on TMCG_CardSecret:
*bool***import***(*`std::string`

s) This method imports the content of the members

`r`

and`b`

from the correctly formatted input string`s`. It returns`true`

, if the import was successful.

- Destructor on TMCG_CardSecret:
**~TMCG_CardSecret***()* This destructor releases all occupied resources.

- Member of TMCG_CardSecret:

- Operator on TMCG_CardSecret:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_CardSecret&`

cardsecret) This operator exports the content of the members

`r`

and`b`

(of the given`TMCG_CardSecret`

`cardsecret`) to the output stream`out`.

- Operator on TMCG_CardSecret:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_CardSecret&`

cardsecret) This operator imports the content of the members

`r`

and`b`

(of the given`TMCG_CardSecret`

`cardsecret`) from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

- Data type:
**VTMF_Card** This

`struct`

represents a card in the encoding scheme of Barnett and Smart [BS03]. Here we use the discrete logarithm based instantiation of their general cryptographic primitive VTMF (Verifiable`k`-out-of-`k`Threshold Masking Function). The security relies on the DDH assumption in the underlying abelian group*G*.- Member of VTMF_Card:
*mpz_t***c_1** This is the first part of the encrypted card type. It is an element from the underlying group

*G*.

- Member of VTMF_Card:
*mpz_t***c_2** This is the second part of the encrypted card type. It is also an element from the underlying group

*G*.

- Constructor on VTMF_Card:
**VTMF_Card***()* This default constructor initializes an empty card where the members

`c_1`

and`c_2`

are set to zero.

- Constructor on VTMF_Card:
**VTMF_Card***(*`const VTMF_Card&`

that) This is a simple copy-constructor and

`that`is the card to be copied.

- Operator on VTMF_Card:
*VTMF_Card&***=***(*`const VTMF_Card&`

that) This is a simple assignment-operator and

`that`is the card to be assigned.

- Operator on VTMF_Card:
*bool***==***(*`const VTMF_Card&`

that) This operator tests two card representations for equality.

- Operator on VTMF_Card:
*bool***!=***(*`const VTMF_Card&`

that) This operator tests two card representations for inequality.

- Method on VTMF_Card:
*bool***import***(*`std::string`

s) This method imports the content of the members

`c_1`

and`c_2`

from a correctly formatted input string`s`. It returns`true`

, if the import was successful.

- Destructor on VTMF_Card:
**~VTMF_Card***()* This destructor releases all occupied resources.

- Member of VTMF_Card:

- Operator on VTMF_Card:
*std::ostream&***<<***(*`std::ostream&`

out,`const VTMF_Card&`

card) This operator exports the content of the members

`c_1`

and`c_2`

(of the given`VTMF_Card`

`card`) to the output stream`out`.

- Operator on VTMF_Card:
*std::istream&***>>***(*`std::istream&`

in,`VTMF_Card&`

card) This operator imports the content of the members

`c_1`

and`c_2`

(of the given`VTMF_Card`

`card`) from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

- Data type:
**VTMF_CardSecret** This

`struct`

represents the secrets used in the card masking operation by the encoding scheme of Barnett and Smart [BS03].- Member of VTMF_CardSecret:
*mpz_t***r** This member is the exponent (randomizer) used in the masking operation. It should be chosen uniformly and randomly from

*{\bf Z}_q*where*q*is the order of the finite abelian group*G*for which the DDH assumption holds.According to the results of Koshiba and Kurosawa (see

*Short Exponent Diffie-Hellman Problems*, PKC 2004, LNCS 2947) the length of this exponent can be shorten to a more efficient size (e.g. 160 bit), if the corresponding generator of*G*is adjusted as well. Under the additional DLSE (Discrete Logarithm with Short Exponents) assumption the DDH problem in*G*seems to be still hard. By such an optimization trick we gain a great performance advantage for almost all modular exponentiations that are computed during the masking operation, if the VTMF primitive was instantiated by the later explained class`BarnettSmartVTMF_dlog_GroupQR`

. Furthermore, the size of the card secret is substantially reduced which results in an improved communication complexity.

- Constructor on VTMF_CardSecret:
**VTMF_CardSecret***()* This default constructor initializes the secret with an empty member

`r`

.

- Constructor on VTMF_CardSecret:
**VTMF_CardSecret***(*`const VTMF_CardSecret&`

that) This is a simple copy-constructor and

`that`is the secret to be copied.

- Operator on VTMF_CardSecret:
*VTMF_CardSecret&***=***(*`const VTMF_CardSecret&`

that) This is a simple assignment-operator and

`that`is the secret to be assigned.

- Method on VTMF_CardSecret:
*bool***import***(*`std::string`

s) This method imports the content of the member

`r`

from the correctly formatted input string`s`. It returns`true`

, if the import was successful.

- Destructor on VTMF_CardSecret:
**~VTMF_CardSecret***()* This destructor releases all occupied resources.

- Member of VTMF_CardSecret:

- Operator on VTMF_CardSecret:
*std::ostream&***<<***(*`std::ostream&`

out,`const VTMF_CardSecret&`

cardsecret) This operator exports the content of the member

`r`

(of the given`VTMF_CardSecret`

`cardsecret`) to the output stream`out`.

- Operator on VTMF_CardSecret:
*std::istream&***>>***(*`std::istream&`

in,`VTMF_CardSecret&`

cardsecret) This operator imports the content of the member

`r`

(of the given`VTMF_CardSecret`

`cardsecret`) from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

All of the following data types are generic containers that can be
instantiated as C++ templates with the former explained `Card`

and `CardSecret`

data types, respectively. Note the maximum
number of stackable data is upper-bounded by `TMCG_MAX_CARDS`

.
There is no error reported, if this limit is exceeded.

- Data type:
**TMCG_Stack<**`CardType`> This

`struct`

is a simple container for cards of the specified

. Currently, the elements can be either of type`CardType``TMCG_Card`

or`VTMF_Card`

depending on which kind of encoding scheme is used. The`TMCG_Stack`

structure is mainly used to represent a stack of masked cards, i.e., playing cards that are stacked in a face-down manner. It can be either a public stack where all participants have access to or even a private stack, e.g. the players’ hand. If the corresponding card types are known it can also serve as an “open stack”, although`TMCG_OpenStack`

is more suitable in that case.- Member of TMCG_Stack:
*std::vector<*`CardType`>**stack** This is the container that is used internally for storing the cards.

- Constructor on TMCG_Stack:
**TMCG_Stack***()* This default constructor initializes an empty stack.

- Operator on TMCG_Stack:
*TMCG_Stack&***=***(*`const TMCG_Stack<`

that)`CardType`>& This is a simple assignment-operator and

`that`is the stack to be assigned.

- Operator on TMCG_Stack:
*bool***==***(*`const TMCG_Stack<`

that)`CardType`>& This operator tests two stacks for equality. It checks whether the sizes of the stacks and the contained cards are equal with respect to the implied order.

- Operator on TMCG_Stack:
*bool***!=***(*`const TMCG_Stack<`

that)`CardType`>& This operator tests two stacks for inequality. It returns

`true`

, if either the sizes do not match or at least two corresponding cards are not equal.

- Operator on TMCG_Stack:
*const*`CardType`&**[]***(*`size_t`

n) This operator provides read-only random access to the contained cards. It returns a const-reference to the

`n`th card from the top of the stack.

- Operator on TMCG_Stack:
`CardType`&**[]***(*`size_t`

n) This operator provides random access to the contained cards. It returns a reference to the

`n`th card from the top of the stack.

- Method on TMCG_Stack:
*size_t***size***()* This method returns the size of the stack.

- Method on TMCG_Stack:
*void***push***(*`const`

c)`CardType`& This method pushes the card

`c`to the back of the stack.

- Method on TMCG_Stack:
*void***push***(*`const TMCG_Stack<`

s)`CardType`>& This method pushes the stack

`s`to the back of the stack.

- Method on TMCG_Stack:
*void***push***(*`const TMCG_OpenStack<`

s)`CardType`>& This method pushes the cards of the open stack

`s`to the back of the stack.

- Method on TMCG_Stack:
*bool***empty***()* This method returns

`true`

, if the stack is empty.

- Method on TMCG_Stack:
*bool***pop***(*

c)`CardType`& This method removes a card from the back and stores the data in

`c`. It returns`true`

, if the stack was not empty and thus`c`contains useful data.

- Method on TMCG_Stack:
*void***clear***()* This method clears the stack, i.e., it removes all cards.

- Method on TMCG_Stack:
*bool***find***(*`const`

c)`CardType`& This method returns

`true`

, if the card`c`was found in the stack.

- Method on TMCG_Stack:
*bool***remove***(*`const`

c)`CardType`& This method removes the top-most card from the stack which is equal to

`c`. It returns`true`

, if the card was found and successfully removed.

- Method on TMCG_Stack:
*size_t***removeAll***(*`const`

c)`CardType`& This method removes every card from the stack which is equal to

`c`. It returns the number of removed cards.

- Method on TMCG_Stack:
*bool***import***(*`std::string`

s) This method imports the stack from the correctly formatted input string

`s`. It returns`true`

, if the import was successful.

- Destructor on TMCG_Stack:
**~TMCG_Stack***()* This destructor releases all occupied resources.

- Member of TMCG_Stack:

- Operator on TMCG_Stack:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_Stack<`

stack)`CardType`>& This operator exports the given

`stack`to the output stream`out`.

- Operator on TMCG_Stack:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_Stack<`

stack)`CardType`>& This operator imports the given

`stack`from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

- Data type:
**TMCG_OpenStack<**`CardType`> This

`struct`

is a simple container for cards of the specified

whose types are known. The elements are pairs where the first component is the type and the second component is the corresponding card. The card type is represented by a`CardType``size_t`

integer. Currently, the cards can be either of type`TMCG_Card`

or`VTMF_Card`

depending on which kind of encoding scheme is used.- Member of TMCG_OpenStack:
*std::vector<std::pair<size_t,*`CardType`> >**stack** This is the container that is used internally for storing the pairs.

- Constructor on TMCG_OpenStack:
**TMCG_OpenStack***()* This default constructor initializes an empty stack.

- Operator on TMCG_OpenStack:
*TMCG_OpenStack&***=***(*`const TMCG_OpenStack<`

that)`CardType`>& This is a simple assignment-operator and

`that`is the stack to be assigned.

- Operator on TMCG_OpenStack:
*bool***==***(*`const TMCG_OpenStack<`

that)`CardType`>& This operator tests two stacks for equality. It checks whether the types, the sizes, and the contained cards are equal with respect to the stack order.

- Operator on TMCG_OpenStack:
*bool***!=***(*`const TMCG_OpenStack<`

that)`CardType`>& This operator tests two stacks for inequality. It returns

`true`

, if either the sizes resp. types do not match or at least two corresponding cards are not equal.

- Operator on TMCG_OpenStack:
*const std::pair<size_t,*`CardType`>&**[]***(*`size_t`

n) This operator provides read-only random access to the contained pairs. It returns a const-reference to the

`n`th pair from the top of the stack.

- Operator on TMCG_OpenStack:
*std::pair<size_t,*`CardType`>&**[]***(*`size_t`

n) This operator provides random access to the contained pairs. It returns a reference to the

`n`th pair from the top of the stack.

- Method on TMCG_OpenStack:
*size_t***size***()* This method returns the size of the stack.

- Method on TMCG_OpenStack:
*void***push***(*`const std::pair<size_t,`

p)`CardType`>& This method pushes the pair

`p`to the back of the stack. The first component is the type and the second component is the corresponding card representation.

- Method on TMCG_OpenStack:
*void***push***(*`size_t`

type,`const`

c)`CardType`& This method pushes a pair to the back of the stack. The parameter

`type`is the card type and`c`is the corresponding card representation.

- Method on TMCG_OpenStack:
*void***push***(*`const TMCG_OpenStack<`

s)`CardType`>& This method pushes the pairs of the stack

`s`to the back of this stack.

- Method on TMCG_OpenStack:
*bool***empty***()* This method returns

`true`

, if the stack is empty.

- Method on TMCG_OpenStack:
*bool***pop***(*`size_t&`

type,

c)`CardType`& This method removes a pair from the back of the stack. It stores the card type in

`type`and the representation in`c`. It returns`true`

, if the stack was not empty and thus`type`and`c`contain useful data.

- Method on TMCG_OpenStack:
*void***clear***()* This method clears the stack, i.e., it removes all pairs.

- Method on TMCG_OpenStack:
*bool***find***(*`size_t`

type) This method returns

`true`

, if a pair with the first component`type`was found in the stack.

- Method on TMCG_OpenStack:
*bool***remove***(*`size_t`

type) This method removes the top-most pair with the first component

`type`from the stack. It returns`true`

, if such a pair was found and successfully removed.

- Method on TMCG_OpenStack:
*size_t***removeAll***(*`size_t`

type) This method removes every pair from the stack whose first component is equal to

`type`. Further it returns the number of removed pairs.

- Method on TMCG_OpenStack:
*bool***move***(*`size_t`

type,`TMCG_Stack<`

s)`CardType`>& This method moves the top-most card representation of the given

`type`to another stack`s`. It returns`true`

, if such a pair was found and successfully moved.

- Destructor on TMCG_OpenStack:
**~TMCG_OpenStack***()* This destructor releases all occupied resources.

- Member of TMCG_OpenStack:

- Data type:
**TMCG_StackSecret<**`CardSecretType`> This

`struct`

is a simple container for the secrets involved in the masking operation of cards. Additionally, the permutation of a corresponding shuffle of the stack is stored. The elements are pairs where the first component is a permutation index of type`size_t`

and the second component is a card secret of the specified

. Currently, such secrets can be either of type`CardSecretType``TMCG_CardSecret`

or`VTMF_CardSecret`

depending on which kind of encoding scheme is used.- Member of TMCG_StackSecret:
*std::vector<std::pair<size_t,*`CardSecretType`> >**stack** This is the container that is used internally for storing the pairs.

- Constructor on TMCG_StackSecret:
**TMCG_StackSecret***()* This default constructor initializes an empty stack secret.

- Operator on TMCG_StackSecret:
*TMCG_StackSecret&***=***(*`const TMCG_StackSecret<`

that)`CardSecretType`>& This is a simple assignment-operator and

`that`is the stack secret to be assigned.

- Operator on TMCG_StackSecret:
*const std::pair<size_t,*`CardSecretType`>&**[]***(*`size_t`

n) This operator provides read-only random access to the contained pairs. It returns a const-reference to the

`n`th pair from the top of the stack secret.

- Operator on TMCG_StackSecret:
*std::pair<size_t,*`CardSecretType`>&**[]***(*`size_t`

n) This operator provides random access to the contained pairs. It returns a reference to the

`n`th pair from the top of the stack secret.

- Method on TMCG_StackSecret:
*size_t***size***()* This method returns the size of the stack secret.

- Method on TMCG_StackSecret:
*void***push***(*`size_t`

index,`const`

cs)`CardSecretType`& This method pushes a pair to the back of the stack secret. The parameter

`index`is the permutation index and`cs`is the corresponding card secret.

- Method on TMCG_StackSecret:
*void***clear***()* This method clears the stack secret, i.e., it removes all pairs.

- Method on TMCG_StackSecret:
*size_t***find_position***(*`size_t`

index) This method searches for a given permutation index in the stack secret. It returns the corresponding position

^{7}in the stack secret, if the`index`was found. Otherwise, the size of the stack secret is returned. Please note that in this case the returned value is not a valid position for an access to the stack secret.

- Method on TMCG_StackSecret:
*bool***find***(*`size_t`

index) This method searches for a given permutation index in the stack secret. It returns

`true`

, if such an`index`was found.

- Method on TMCG_StackSecret:
*bool***import***(*`std::string`

s) This method imports the stack secret from a correctly formatted input string

`s`. It returns`true`

, if the import was successful.

- Destructor on TMCG_StackSecret:
**~TMCG_StackSecret***()* This destructor releases all occupied resources.

- Member of TMCG_StackSecret:

- Operator on TMCG_StackSecret:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_StackSecret<`

stacksecret)`CardSecretType`>& This operator exports the given

`stacksecret`to the output stream`out`.

- Operator on TMCG_StackSecret:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_StackSecret<`

stacksecret)`CardSecretType`>& This operator imports the given

`stacksecret`from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

of the stream is set, if any parse error occurred.

LibTMCG provides corresponding data types for keys used by the encoding scheme of Schindelhauer [Sc98], because in this scheme it is not efficient to perform the process of key generation for every new game session. These keys are called TMCG keys. However, they also can be utilized to encrypt and sign messages for the more general reasons of confidentiality and integrity, even if the card encoding scheme of Schindelhauer is not used. Therefore these structures may be of independent interest, for example to establish authenticated communication channels between players. However, like for all public key cryptosystems a trusted PKI (Public Key Infrastructure) is needed. This might not be a serious problem in distributed game environments, because the players can include key fingerprints in their individual profile or a service provider can issue public key certificates.

- Data type:
**TMCG_SecretKey** This

`struct`

represents the secret part of the key. The underlying public key cryptosystem is due to Rabin (see*Digitalized Signatures and Public-Key Functions as Intractable as Factorization*, MIT Technical Report 212, 1979) and Williams (see*A modification of the RSA public-key encryption procedure*, IEEE Transactions on Information Theory, 26(6):726–729, 1980) with minor modifications for encryption padding (SAEP scheme of Boneh [Bo01]) and digital signatures (PRab scheme of Bellare and Rogaway [BR96]).- Member of TMCG_SecretKey:
*std::string***name** This string contains the name or a pseudonym of the key owner.

- Member of TMCG_SecretKey:
*std::string***email** This string contains the email address of the key owner.

- Member of TMCG_SecretKey:
*std::string***type** This string contains information about the key type. The common prefix is

`TMCG/RABIN`

. It is followed by the decimal encoded bit size of the modulus*m*. The suffix`NIZK`

signals that the correctness of the key is shown by an appended non-interactive zero-knowledge proof. The single parts of the description are separated by underscore characters`_`

, e.g.,`TMCG/RABIN_2048_NIZK`

has the correct form. The suffix can be left empty, if the key is only used for encryption and signing (so-called non-NIZK key) without card encoding.

- Member of TMCG_SecretKey:
*std::string***nizk** This string contains two stages of the non-interactive zero-knowledge proof of Gennaro, Micciancio, and Rabin [GMR98]. The proof shows that

*m*was correctly generated as product of at most two primes and both are congruent to 3 (modulo 4). Further there is another non-interactive zero-knowledge proof appended which shows that the condition*y\in{\bf NQR}^\circ_m*holds.

- Member of TMCG_SecretKey:
*std::string***sig** This string contains a self signature of the public key.

- Member of TMCG_SecretKey:
*mpz_t***m** This is the public modulus

*m = p \cdot q*which is the product of two secret primes*p*and*q*. The size of*m*is determined by the security parameter`TMCG_QRA_SIZE`

.

- Member of TMCG_SecretKey:
*mpz_t***y** This is the public quadratic non-residue

*y\in {\bf NQR}^\circ_m*which is used in several zero-knowledge proofs of Schindelhauer’s encoding scheme [Sc98].

- Member of TMCG_SecretKey:
*mpz_t***p** This is the secret prime number

*p*which is a factor of the modulus*m*.

- Member of TMCG_SecretKey:
*mpz_t***q** This is the secret prime number

*q*which is a factor of the modulus*m*.

- Constructor on TMCG_SecretKey:
**TMCG_SecretKey***()* This default constructor initializes an empty secret key.

- Constructor on TMCG_SecretKey:
**TMCG_SecretKey***(*`const std::string&`

n,`const std::string&`

e,`const unsigned long int`

keysize`=TMCG_QRA_SIZE`

,`const bool`

nizk_key`=true`

) This constructor generates a new secret key, where

`n`is the name or a pseudonym of the owner,`e`is a corresponding email address,`keysize`is the desired bit length of the modulus*m*, and`nizk_key`indicates whether or not a NIZK proof will be appended. The default value of the third argument is set to`TMCG_QRA_SIZE`

, if`keysize`is omitted in the call. The default value of the fourth argument is set to`true`

, whenever it is omitted in the call. Depending on`keysize`and`nizk_key`the generation is a very time-consuming task that should be taken into account by the application designer.

- Constructor on TMCG_SecretKey:
**TMCG_SecretKey***(*`const std::string&`

s) This constructor initializes the key from a correctly formatted input string

`s`.

- Constructor on TMCG_SecretKey:
**TMCG_SecretKey***(*`const TMCG_SecretKey&`

that) This is a simple copy-constructor and

`that`is the key to be copied.

- Operator on TMCG_SecretKey:
*TMCG_SecretKey&***=***(*`const TMCG_SecretKey&`

that) This is a simple assignment-operator and

`that`is the key to be assigned.

- Method on TMCG_SecretKey:
*bool***check***()* This method tests whether the self signature is valid and whether the non-interactive zero-knowledge proofs are sound. It returns

`true`

, if all checks have been successfully passed. Due to the computational complexity of the verification procedure these checks are a very time-consuming task.

- Method on TMCG_SecretKey:
*std::string***fingerprint***()* This method returns the fingerprint of the key. The fingerprint is the hexadecimal notation of the hash value (using algorithm

`TMCG_GCRY_MD_ALGO`

) on the concatenated members`name`

,`email`

,`type`

,`m`

,`y`

,`nizk`

, and`sig`

.

- Method on TMCG_SecretKey:
*std::string***selfid***()* This method returns the real value of the self signature. The string

`ERROR`

is returned, if any parse error occurred. The string`SELFSIG-SELFSIG-SELFSIG-SELFSIG-SELFSIG-SELFSIG`

is returned, if the self signature`sig`

was empty.

- Method on TMCG_SecretKey:
*std::string***keyid***(*`const size_t`

size`=TMCG_KEYID_SIZE`

) This method returns the unique key identifier of length

`size`. The default value of the first argument is set to`TMCG_KEYID_SIZE`

, if`size`is omitted in the call.

- Method on TMCG_SecretKey:
*size_t***keyid_size***(*`const std::string&`

s) This method returns the length of the unique key identifier

`s`. Zero is returned, if any parse error occurred.

- Method on TMCG_SecretKey:
*std::string***sigid***(*`std::string`

s) This method returns the unique key identifier which is included in the signature

`s`. The string`ERROR`

is returned, if any parse error occurred.

- Method on TMCG_SecretKey:
*bool***import***(*`std::string`

s) This method imports the key from a correctly formatted input string

`s`. It returns`true`

, if the import was successful.

- Method on TMCG_SecretKey:
*bool***decrypt***(*`unsigned char*`

value,`std::string`

s) This method decrypts the given encryption packet

`s`and stores the content in`value`which is a pointer to a character array of size`TMCG_SAEP_S0`

. The method returns`true`

, if the decryption was successful.

- Method on TMCG_SecretKey:
*std::string***sign***(*`const std::string&`

data) This method returns a digital signature on

`data`.

- Method on TMCG_SecretKey:
*std::string***encrypt***(*`const unsigned char*`

value) This method encrypts the content of

`value`which is a pointer to a character array of size`TMCG_SAEP_S0`

. The method returns a corresponding encryption packet that can be decrypted by the owner of the secret key.

- Method on TMCG_SecretKey:
*bool***verify***(*`const std::string&`

data,`std::string`

s) This method verifies whether the signature

`s`on`data`is valid or not. It returns`true`

, if everything was sound.

- Destructor on TMCG_SecretKey:
**~TMCG_SecretKey***()* This destructor releases all occupied resources.

- Member of TMCG_SecretKey:

- Operator on TMCG_SecretKey:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_SecretKey&`

key) This operator exports the given

`key`to the output stream`out`.

- Operator on TMCG_SecretKey:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_SecretKey&`

key) This operator imports the given

`key`from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

is set, if any parse error occurred.

- Data type:
**TMCG_PublicKey** This

`struct`

represents the public part of the TMCG key.- Member of TMCG_PublicKey:
*std::string***name** This string contains the name or a pseudonym of the key owner.

- Member of TMCG_PublicKey:
*std::string***email** This string contains the email address of the key owner.

- Member of TMCG_PublicKey:
*std::string***type** This string contains information about the key type. The common prefix is

`TMCG/RABIN`

. It is followed by the decimal encoded bit size of the modulus*m*. The suffix`NIZK`

signals that the correctness of the key is shown by an appended non-interactive zero-knowledge proof. The single parts of the string are separated by underscore characters`_`

, e.g.,`TMCG/RABIN_2048_NIZK`

has the correct form. However, the suffix can be left empty, if the key is only used for encryption and signing.

- Member of TMCG_PublicKey:
*std::string***nizk** This string contains two stages of non-interactive zero-knowledge proof of Gennaro, Micciancio and Rabin [GMR98]. This gives strong evidence that

*m*was generated correctly. Further there is another non-interactive zero-knowledge proof appended which shows that the condition*y\in{\bf NQR}^\circ_m*holds.

- Member of TMCG_PublicKey:
*std::string***sig** This string contains the self signature of the public key.

- Member of TMCG_PublicKey:
*mpz_t***m** This is the public modulus

*m = p \cdot q*which is the product of two secret primes*p*and*q*. The size of*m*is determined by the security parameter`TMCG_QRA_SIZE`

.

- Member of TMCG_PublicKey:
*mpz_t***y** This is the public quadratic non-residue

*y\in {\bf NQR}^\circ_m*which is used by several zero-knowledge proofs of the toolbox.

- Constructor on TMCG_PublicKey:
**TMCG_PublicKey***()* This default constructor initializes an empty public key.

- Constructor on TMCG_PublicKey:
**TMCG_PublicKey***(*`const TMCG_SecretKey&`

skey) This constructor initializes the key using public values of the secret key

`skey`.

- Constructor on TMCG_PublicKey:
**TMCG_PublicKey***(*`const TMCG_PublicKey&`

pkey) This is a simple copy-constructor and

`pkey`is the key to be copied.

- Operator on TMCG_PublicKey:
*TMCG_PublicKey&***=***(*`const TMCG_PublicKey&`

that) This is a simple assignment-operator and

`that`is the key to be assigned.

- Method on TMCG_PublicKey:
*bool***check***()* This method tests whether the self signature is valid and whether the non-interactive zero-knowledge proofs are sound. It returns

`true`

, if all checks have been successfully passed. Due to the computational complexity of the verification procedure these checks are an extremely time-consuming task.

- Method on TMCG_PublicKey:
*std::string***fingerprint***()* This method returns the fingerprint of the key. The fingerprint is the hexadecimal notation of the hash value (using algorithm

`TMCG_GCRY_MD_ALGO`

) on the concatenated members`name`

,`email`

,`type`

,`m`

,`y`

,`nizk`

, and`sig`

.

- Method on TMCG_PublicKey:
*std::string***selfid***()* This method returns the real value of the self signature. The string

`ERROR`

is returned, if any parse error occurred. The string`SELFSIG-SELFSIG-SELFSIG-SELFSIG-SELFSIG-SELFSIG`

is returned, if the self signature`sig`

was empty.

- Method on TMCG_PublicKey:
*std::string***keyid***(*`const size_t`

size`=TMCG_KEYID_SIZE`

) This method returns the unique key identifier of length

`size`. The default value of the first argument is set to`TMCG_KEYID_SIZE`

, if`size`is omitted in the call.

- Method on TMCG_PublicKey:
*size_t***keyid_size***(*`const std::string&`

s) This method returns the length of the unique key identifier

`s`. Zero is returned, if any parse error occurred.

- Method on TMCG_PublicKey:
*std::string***sigid***(*`std::string`

s) This method returns the unique key identifier which is included in the signature

`s`. The string`ERROR`

is returned, if any parse error occurred.

- Method on TMCG_PublicKey:
*bool***import***(*`std::string`

s) This method imports the key from a correctly formatted input string

`s`. It returns`true`

, if the import was successful.

- Method on TMCG_PublicKey:
*std::string***encrypt***(*`const unsigned char*`

value) This method encrypts the content of

`value`which is a pointer to a character array of size`TMCG_SAEP_S0`

. The method returns a corresponding encryption packet that can be decrypted by the owner of the secret key.

- Method on TMCG_PublicKey:
*bool***verify***(*`const std::string&`

data,`std::string`

s) This method verifies whether the signature

`s`on`data`is valid or not. It returns`true`

, if everything was sound.

- Destructor on TMCG_PublicKey:
**~TMCG_PublicKey***()* This destructor releases all occupied resources.

- Member of TMCG_PublicKey:

- Operator on TMCG_PublicKey:
*std::ostream&***<<***(*`std::ostream&`

out,`const TMCG_PublicKey&`

key) This operator exports the given

`key`to the output stream`out`.

- Operator on TMCG_PublicKey:
*std::istream&***>>***(*`std::istream&`

in,`TMCG_PublicKey&`

key) This operator imports the given

`key`from the input stream`in`. The data has to be delimited by a newline character. The`failbit`

is set, if any parse error occurred.

- Data type:
**TMCG_PublicKeyRing** This

`struct`

is just a simple container for TMCG public keys. There are no particular methods provided by`TMCG_PublicKeyRing`

. You have to use the regular interface of the STL container`std::vector`

to access the single keys of the ring.- Member of TMCG_PublicKeyRing:
*std::vector<TMCG_PublicKey>***keys** This is the real container that is used to store the keys.

- Constructor on TMCG_PublicKeyRing:
**TMCG_PublicKeyRing***()* This default constructor initializes an empty public key ring.

- Constructor on TMCG_PublicKeyRing:
**TMCG_PublicKeyRing***(*`size_t`

n) This constructor initializes the container for storing exactly

`n`keys.

- Destructor on TMCG_PublicKeyRing:
**~TMCG_PublicKeyRing***()* This destructor releases all occupied resources.

- Member of TMCG_PublicKeyRing:

According to the behavior
of the `[]`

-operator, the zero denotes always the top-most position.

Next: Communication Interfaces, Up: Basic Structures [Contents][Index]