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92 This document is part of the LibTomCrypt package and is hereby released into the public domain.
121 public key cryptography (via PKCS \#1 RSA, DH or ECCDH), and a plethora of support routines.
188 The project is hereby released as public domain.
254 related issue is if you use the same symmetric cipher, hash or public key state data in multiple threads. Normally
351 In the above example if the size of the RSA public key was more than 1024 bytes this function would return an error code
393 for a chaining mode or public key packet it is assumed that regardless of the actual size of \textit{unsigned char} only the
1164 It is initialized with a random \textit{nonce} that can be shared publicly, a \textit{header} which can be fixed and public, and a random secret symmetric key.
1189 random public string of length \textit{noncelen} octets. The \textit{header} parameter is the random (or fixed or \textbf{NULL}) header for the
1346 and the random \textit{nonce}. Note that \textit{nonce} must be a random (public) string the same length as the block ciphers
2664 used to expand a shorter bit string into a longer bit string. PRNGs are used wherever random data is required such as Public Key (PK)
3054 \chapter{RSA Public Key Cryptography}
3057 RSA wrote the PKCS \#1 specifications which detail RSA Public Key Cryptography. In the specifications are
3225 RSA is a public key algorithm that is based on the inability to find the \textit{e-th} root modulo a composite of unknown
3231 $\mbox{lcm}(p - 1, q - 1)$. The public key consists of the composite $N$ and some integer $e$ such that
3235 A person who wants to encrypt with your public key simply forms an integer (the plaintext) $M$ such that
3278 PK\_PRIVATE type.} in the form of a RSAPrivateKey (PKCS \#1 compliant). The second type, is a public RSA key which only includes the modulus and public exponent.
3595 As of v1.06 this function can also import OpenSSL DER formatted public RSA keys. They are essentially encapsulated RSAPublicKeys. LibTomCrypt will
3663 LibTomCrypt uses a unique format for ECC public and private keys. While ANSI X9.63 partially specifies key formats, it does it in a less than ideally simple manner. \
3670 flags BIT STRING(0), -- public/private flag (always zero),
3673 pubkey.x INTEGER, -- The X co-ordinate of the public key point
3674 pubkey.y INTEGER, -- The Y co-ordinate of the public key point
3678 flags BIT STRING(1), -- public/private flag (always one),
3681 pubkey.x INTEGER, -- The X co-ordinate of the public key point
3682 pubkey.y INTEGER, -- The Y co-ordinate of the public key point
3688 The first flags bit denotes whether the key is public (zero) or private (one).
3801 The following function exports an ECC public key in the ANSI X9.63 format:
3809 The ECC key pointed to by \textit{key} is exported in public fashion to the array pointed to by \textit{out}. The ANSI X9.63 format used is from
3813 The following function imports an ANSI X9.63 section 4.3.6 format public ECC key:
3825 The following function allows the importing of an ANSI x9.63 section 4.3.6 format public ECC key using user specified domain parameters:
3838 To construct a Diffie-Hellman shared secret with a private and public ECC key, use the following function:
3846 The \textit{private\_key} is typically the local private key, and \textit{public\_key} is the key the remote party has shared.
3868 plaintext in the array pointed to by \textit{in} of length \textit{inlen} octets. It uses the public ECC key pointed to by \textit{key}, and
3872 The data is encrypted to the public ECC \textit{key} such that only the holder of the private key can decrypt the payload. To have multiple
3873 recipients multiple call to this function for each public ECC key is required.
3885 This function will decrypt an encrypted payload. The \textit{key} provided must be the private key corresponding to the public key
3938 The ECC \textit{key} must be the public (or private) ECC key corresponding to the key that performed the signature.
3958 Since no useful public standard for DSA key storage was presented to me during the course of this development I made my own ASN.1 SEQUENCE which I document
3970 y INTEGER , -- public key, specifically,
3984 y INTEGER , -- public key, specifically,
3992 The leading BIT STRING has a single bit in it which is zero for public keys and one for private keys. This makes the structure uniquely decodable,
4038 \item $y = g^x \mbox{ (mod }p\mbox{)}$ the public key.
4057 ensures that the generator actually generates a prime order group. Tests seven and eight ensure that the public key
4111 This function will encrypt a small payload with a recipients public DSA key.
4127 a public key.
4155 depending on whether you want to export a private or public copy of the DSA key.
4958 The following chart gives the work factor for solving a DH/RSA public key using the NFS. The work factor for a key of order
5167 public key functions.
5276 \subsection{Symmetric Ciphers, One-way Hashes, PRNGS and Public Key Functions}
5277 There are a plethora of macros for the ciphers, hashes, PRNGs and public key functions which are fairly
5327 The library comes with three math descriptors that allow you to interface the public key cryptography API to freely available math
6364 @param e The "e" value (public key).
6381 @param which PK_PUBLIC for public RSA and PK_PRIVATE for private RSA
6448 The RSA Modular Exponentiation (ME) function is used by the RSA API to perform exponentiations for private and public key operations. In particular for
6456 /** The public exponent */