— Macro: TMCG_MR_ITERATIONS

Defines the number of iterations for the Miller-Rabin primality test. The default value is 64 which implies a soundness error probability \le 4^-64.

— Macro: TMCG_GROTH_L_E

Defines the security parameter \ell_e of Groth's interactive shuffle argument [Gr05]. The default value is 80 which implies a soundness error probability \le 2^-80. For the intended purposes of LibTMCG this bound seems to be reasonable.

— Macro: TMCG_DDH_SIZE

Defines the security parameter (field size in bit) of the group G which is used by the card encoding scheme of Barnett and Smart [BS03]. The underlying assumptions are DDH, CDH, and DLOG. The default value is 1024.

— Macro: TMCG_DLSE_SIZE

Defines the security parameter (subgroup size in bit) of the group G which is used by the card encoding scheme of Barnett and Smart [BS03]. The underlying assumptions are DLSE (related to DDH) and DLOG. The default value is 160.

— Macro: TMCG_GCRY_MD_ALGO

Defines the message digest algorithm for digital signatures and the Fiat-Shamir heuristic (see TODO). The security of the most non-interactive zero-knowledge proofs (NIZK) is related to the so-called random oracle model, i.e., we suppose that the instantiated hash function behaves like an ideal random function (which cannot hold in a real world scenario). However, this assumption seems to be reasonable, if the hash function is collision-resistant and carefully implemented. The default value GCRY_MD_RMD160 ¹ chooses the hash algorithm RIPEMD-160 (see TODO) which has an output length of 160 bit. Thus we gain a security level of approximately 2^80, assuming that a birthday-attack is the best known attack against this hash function.

— Macro: TMCG_KEYID_SIZE

Defines the length (in characters w.r.t. TMCG_MPZ_IO_BASE) for the distinctive suffix of the unique TMCG key identifier. The default value is 8 which spans a reasonable name space for at least 2^20 different TMCG keys (see TMCG_PublicKey).

Each key identifier starts with the string "ID" followed by the decimal encoded value of TMCG_KEYID_SIZE and the appended carret symbol "^". The final suffix contains TMCG_KEYID_SIZE alphanumerical characters from the self signature of TMCG key. The signature has enough entropy included to be used as unique key identifier.

— Macro: TMCG_KEY_NIZK_STAGE1

Defines the security parameter (number of iterations) of the NIZK proof (stage 1) which convince all verifiers that the TMCG key was correctly generated. The default value is 16 which implies a soundness error probability \le d^-16, where d = \rm gcd(m, \phi(m)). This parameter is only relevant for the card encoding scheme of Schindelhauer.

— Macro: TMCG_KEY_NIZK_STAGE2

Defines the security parameter (number of iterations) of the NIZK proof (stage 2) which convince all verifiers that the TMCG key was correctly generated. The default value is 128 which implies a soundness error probability \le 2^-128. This parameter is only relevant for the card encoding scheme of Schindelhauer.

— Macro: TMCG_KEY_NIZK_STAGE3

Defines the security parameter (number of iterations) of the NIZK proof (stage 3) which convince all verifiers that the TMCG key was correctly generated. The default value is 128 which implies a soundness error probability \le 2^-128. This parameter is only relevant for the card encoding scheme of Schindelhauer.

— Macro: TMCG_LIBGCRYPT_VERSION

Defines the required minimum version number of the GNU Crypto Library. The default value is "1.2.0". During the initialization of LibTMCG (see init_libTMCG) it is checked, whether the version number of the linked shared object fulfil this condition.

— Macro: TMCG_LIBGMP_VERSION

Defines the required minimum version number of the GNU Multiple Precision Arithmetic Library. The default value is "4.1.0". During the initialization of LibTMCG (see init_libTMCG) it is checked, whether the version number provided by the header file gmp.h and used at compile time of LibTMCG fulfil this condition.

— Macro: TMCG_MAX_CARDS

Defines the maximum number of stackable cards. The default value is 128.

— Macro: TMCG_MAX_PLAYERS

Defines the maximum number of players. The default value is 32. This parameter is only relevant for the card encoding scheme of Schindelhauer.

— Macro: TMCG_MAX_TYPEBITS

Defines the maximum number of bits to represent the card type in the scheme of Schindelhauer. On the other hand, this value determines the maximum size of the message space in the scheme of Barnett and Smart. The default value is 8 which implies that 256 different card types are possible.

— Macro: TMCG_MPZ_IO_BASE

Defines the input and output base of the std::iostream operators << and >> which are used to encode large integers (mpz_t). The default value is 36 which is currently the largest base supported by the GNU Multiple Precision Arithmetic Library.

— Macro: TMCG_PRAB_K0

Defines the security parameter k_0 (in characters) of the PRab scheme (see Bellare, Rogaway: The Exact Security of Digital Signatures – How to Sign with RSA and Rabin, 1996). The default value is 20 which implies a security level around 2^80.

— Macro: TMCG_QRA_SIZE

Defines the security parameter (size of the modulus m = p \cdot q in bit) of the TMCG key. The underlying assumptions are QRA and FACTOR. The default value is 1024. This parameter is only relevant for TMCG keys and Schindelhauer's encoding scheme.

— Macro: TMCG_SAEP_S0

Defines the security parameter s_0 (in characters) of the Rabin-SAEP scheme (see Boneh: Simplified OAEP for the RSA and Rabin Functions, 2002). The default value is 20 which implies a security around 2^80 against CCA (Chosen Ciphertext Attacks).

— Macro: TMCG_HASH_COMMITMENT

Defines whether shortened commitments are used in the shuffle verification procedure of Schindelhauer. The default value is true, because it will decrease the communication complexity significantly. However, as an immediate consequence the soundness property is violated, if the used hash function TMCG_GCRY_MD_ALGO is broken.

— Macro: TMCG_MAX_FPOWM_T

Defines the maximum size of admissible exponents (in bit) used by fast exponentiation procedures. The default value is 2048. Note that this parameter has a strong influence on the amount of memory allocated by LibTMCG since it determines the size of the precomputed tables. However, it should be at least greater than TMCG_DDH_SIZE and TMCG_QRA_SIZE.