Key Blinding for Signature Schemes
draft-irtf-cfrg-signature-key-blinding-00

WG Working Group                                                F. Denis
Internet-Draft                                               Fastly Inc.
Intended status: Informational                                  E. Eaton
Expires: 23 December 2022                         University of Waterloo
                                                              C. A. Wood
                                                        Cloudflare, Inc.
                                                            21 June 2022

                   Key Blinding for Signature Schemes
               draft-irtf-cfrg-signature-key-blinding-00

Abstract

   This document describes extensions to existing digital signature
   schemes for key blinding.  The core property of signing with key
   blinding is that a blinded public key and all signatures produced
   using the blinded key pair are independent of the unblinded key pair.
   Moreover, signatures produced using blinded key pairs are
   indistinguishable from signatures produced using unblinded key pairs.
   This functionality has a variety of applications, including Tor onion
   services and privacy-preserving airdrop for bootstrapping
   cryptocurrency systems.

About This Document

   This note is to be removed before publishing as an RFC.

   The latest revision of this draft can be found at
   https://cfrg.github.io/draft-irtf-cfrg-signature-key-blinding/draft-
   irtf-cfrg-signature-key-blinding.html.  Status information for this
   document may be found at https://datatracker.ietf.org/doc/draft-irtf-
   cfrg-signature-key-blinding/.

   Discussion of this document takes place on the CFRG Working Group
   mailing list (mailto:cfrg@irtf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/cfrg/.

   Source for this draft and an issue tracker can be found at
   https://github.com/cfrg/draft-irtf-cfrg-signature-key-blinding.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  DISCLAIMER  . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   4
   3.  Key Blinding  . . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Ed25519ph, Ed25519ctx, and Ed25519  . . . . . . . . . . . . .   6
     4.1.  BlindPublicKey and UnblindPublicKey . . . . . . . . . . .   6
     4.2.  BlindKeySign  . . . . . . . . . . . . . . . . . . . . . .   6
   5.  Ed448ph and Ed448 . . . . . . . . . . . . . . . . . . . . . .   7
     5.1.  BlindPublicKey and UnblindPublicKey . . . . . . . . . . .   7
     5.2.  BlindKeySign  . . . . . . . . . . . . . . . . . . . . . .   7
   6.  ECDSA . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
     6.1.  BlindPublicKey and UnblindPublicKey . . . . . . . . . . .   8
     6.2.  BlindKeySign  . . . . . . . . . . . . . . . . . . . . . .   9
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   9.  Test Vectors  . . . . . . . . . . . . . . . . . . . . . . . .  10
     9.1.  Ed25519 Test Vectors  . . . . . . . . . . . . . . . . . .  10
     9.2.  ECDSA(P-384, SHA-384) Test Vectors  . . . . . . . . . . .  10
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  11

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     10.2.  Informative References . . . . . . . . . . . . . . . . .  11
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  12
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   Digital signature schemes allow a signer to sign a message using a
   private signing key and produce a digital signature such that anyone
   can verify the digital signature over the message with the public
   verification key corresponding to the signing key.  Digital signature
   schemes typically consist of three functions:

   *  KeyGen: A function for generating a private signing key skS and
      the corresponding public verification key pkS.

   *  Sign(skS, msg): A function for signing an input message msg using
      a private signing key skS, producing a digital signature sig.

   *  Verify(pkS, msg, sig): A function for verifying the digital
      signature sig over input message msg against a public verification
      key pkS, yielding true if the signature is valid and false
      otherwise.

   In some applications, it's useful for a signer to produce digital
   signatures using the same long-term private signing key such that a
   verifier cannot link any two signatures to the same signer.  In other
   words, the signature produced is independent of the long-term
   private-signing key, and the public verification key for verifying
   the signature is independent of the long-term public verification
   key.  This type of functionality has a number of practical
   applications, including, for example, in the Tor onion services
   protocol [TORDIRECTORY] and privacy-preserving airdrop for
   bootstrapping cryptocurrency systems [AIRDROP].  It is also necessary
   for a variant of the Privacy Pass issuance protocol [RATELIMITED].

   One way to accomplish this is by signing with a private key which is
   a function of the long-term private signing key and a freshly chosen
   blinding key, and similarly by producing a public verification key
   which is a function of the long-term public verification key and same
   blinding key.  A signature scheme with this functionality is referred
   to as signing with key blinding.  A signature scheme with key
   blinding extends a basic digital scheme with four new functions:

   *  BlindKeyGen: A function for generating a private blind key.

   *  BlindPublicKey(pkS, bk): Blind the public verification key pkS
      using the private blinding key bk, yielding a blinded public key
      pkR.

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   *  UnblindPublicKey(pkR, bk): Unblind the public verification key pkR
      using the private blinding key bk.

   *  BlindKeySign(skS, bk, msg): Sign a message msg using the private
      signing key skS with the private blind key bk.

   A signature scheme with key blinding aims to achieve unforgeability
   and unlinkability.  Informally, unforgeability means that one cannot
   produce a valid (message, signature) pair for any blinding key
   without access to the private signing key.  Similarly, unlinkability
   means that one cannot distinguish between two signatures produced
   from two separate key signing keys, and two signatures produced from
   the same signing key but with different blinding keys.

   This document describes extensions to EdDSA [RFC8032] and ECDSA
   [ECDSA] to enable signing with key blinding.  Security analysis of
   these extensions is currently underway; see Section 7 for more
   details.

   This functionality is also possible with other signature schemes,
   including some post-quantum signature schemes [ESS21], though such
   extensions are not specified here.

1.1.  DISCLAIMER

   This document is a work in progress and is still undergoing security
   analysis.  As such, it MUST NOT be used for real world applications.
   See Section 7 for additional information.

2.  Conventions and Definitions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The following terms are used throughout this document to describe the
   blinding modification.

   *  G: The standard base point.

   *  sk: A signature scheme private key.  For EdDSA, this is a a
      randomly generated private seed of length 32 bytes or 57 bytes
      according to [RFC8032], Section 5.1.5 or [RFC8032], Section 5.2.5,
      respectively.  For [ECDSA], sk is a random scalar in the prime-
      order elliptic curve group.

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   *  pk(sk): The public key corresponding to the private key sk.

   *  concat(x0, ..., xN): Concatenation of byte strings. concat(0x01,
      0x0203, 0x040506) = 0x010203040506.

   *  ScalarMult(pk, k): Multiply the public key pk by scalar k,
      producing a new public key as a result.

   *  ModInverse(x, L): Compute the multiplicative inverse of x modulo
      L.

   In pseudocode descriptions below, integer multiplication of two
   scalar values is denoted by the * operator.  For example, the product
   of two scalars x and y is denoted as x * y.

3.  Key Blinding

   At a high level, a signature scheme with key blinding allows signers
   to blind their private signing key such that any signature produced
   with a private signing key and blinding key is independent of the
   private signing key.  Similar to the signing key, the blinding key is
   also a private key that remains secret.  For example, the blind is a
   32-byte or 57-byte random seed for Ed25519 or Ed448 variants,
   respectively, whereas the blind for ECDSA over P-256 is a random
   scalar in the P-256 group.  Key blinding introduces four new
   functionalities for the signature scheme:

   *  BlindKeyGen: A function for generating a private blind key.

   *  BlindPublicKey(pkS, bk): Blind the public verification key pkS
      using the private blinding key bk, yielding a blinded public key
      pkR.

   *  UnblindPublicKey(pkR, bk): Unblind the public verification key pkR
      using the private blinding key bk.

   *  BlindKeySign(skS, bk, msg): Sign a message msg using the private
      signing key skS with the private blind key bk.

   For a given bk produced from BlindKeyGen, correctness requires the
   following equivalence to hold:

   UnblindPublicKey(BlindPublicKey(pkS, bk), bk) = pkS

   Security requires that signatures produced using BlindKeySign are
   unlinkable from signatures produced using the standard signature
   generation function with the same private key.

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4.  Ed25519ph, Ed25519ctx, and Ed25519

   This section describes implementations of BlindPublicKey,
   UnblindPublicKey, and BlindKeySign as modifications of routines in
   [RFC8032], Section 5.1.  BlindKeyGen invokes the key generation
   routine specified in [RFC8032], Section 5.1.5 and outputs only the
   private key.

4.1.  BlindPublicKey and UnblindPublicKey

   BlindPublicKey transforms a private blind bk into a scalar for the
   edwards25519 group and then multiplies the target key by this scalar.
   UnblindPublicKey performs essentially the same steps except that it
   multiplies the target public key by the multiplicative inverse of the
   scalar, where the inverse is computed using the order of the group L,
   described in [RFC8032], Section 5.1.

   More specifically, BlindPublicKey(pk, bk) works as follows.

   1.  Hash the 32-byte private key bk using SHA-512, storing the digest
       in a 64-octet large buffer, denoted b.  Interpret the lower 32
       bytes buffer as a little-endian integer, forming a secret scalar
       s.  Note that this explicitly skips the buffer pruning step in
       [RFC8032], Section 5.1.

   2.  Perform a scalar multiplication ScalarMult(pk, s), and output the
       encoding of the resulting point as the public key.

   UnblindPublicKey(pkR, bk) works as follows.

   1.  Compute the secret scalar s from bk as in BlindPublicKey.

   2.  Compute the sInv = ModInverse(s, L), where L is as defined in
       [RFC8032], Section 5.1.

   3.  Perform a scalar multiplication ScalarMult(pk, sInv), and output
       the encoding of the resulting point as the public key.

4.2.  BlindKeySign

   BlindKeySign transforms a private key bk into a scalar for the
   edwards25519 group and a message prefix to blind both the signing
   scalar and the prefix of the message used in the signature generation
   routine.

   More specifically, BlindKeySign(skS, bk, msg) works as follows:

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   1.  Hash the private key skS, 32 octets, using SHA-512.  Let h denote
       the resulting digest.  Construct the secret scalar s1 from the
       first half of the digest, and the corresponding public key A1, as
       described in [RFC8032], Section 5.1.5.  Let prefix1 denote the
       second half of the hash digest, h[32],...,h[63].

   2.  Hash the 32-byte private key bk using SHA-512, storing the digest
       in a 64-octet large buffer, denoted b.  Interpret the lower 32
       bytes buffer as a little-endian integer, forming a secret scalar
       s2.  Let prefix2 denote the second half of the hash digest,
       b[32],...,b[63].

   3.  Compute the signing scalar s = s1 * s2 (mod L) and the signing
       public key A = ScalarMult(G, s).

   4.  Compute the signing prefix as concat(prefix1, prefix2).

   5.  Run the rest of the Sign procedure in [RFC8032], Section 5.1.6
       from step (2) onwards using the modified scalar s, public key A,
       and string prefix.

5.  Ed448ph and Ed448

   This section describes implementations of BlindPublicKey,
   UnblindPublicKey, and BlindKeySign as modifications of routines in
   [RFC8032], Section 5.2.  BlindKeyGen invokes the key generation
   routine specified in [RFC8032], Section 5.1.5 and outputs only the
   private key.

5.1.  BlindPublicKey and UnblindPublicKey

   BlindPublicKey and UnblindPublicKey for Ed448ph and Ed448 are
   implemented just as these routines are for Ed25519ph, Ed25519ctx, and
   Ed25519, except that SHAKE256 is used instead of SHA-512 for hashing
   the secret blind to a 114-byte buffer (and using the lower 57-bytes
   for the secret), and the order of the edwards448 group L is as
   defined in [RFC8032], Section 5.2.1.

5.2.  BlindKeySign

   BlindKeySign for Ed448ph and Ed448 is implemented just as this
   routine for Ed25519ph, Ed25519ctx, and Ed25519, except in how the
   scalars (s1, s2), public keys (A1, A2), and message strings (prefix1,
   prefix2) are computed.  More specifically, BlindKeySign(skS, bk, msg)
   works as follows:

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   1.  Hash the private key skS, 57 octets, using SHAKE256(skS, 117).
       Let h denote the resulting digest.  Construct the secret scalar
       s1 from the first half of the digest, and the corresponding
       public key A1, as described in [RFC8032], Section 5.2.5.  Let
       prefix1 denote the second half of the hash digest,
       h[57],...,h[113].

   2.  Perform the same routine to transform the secret blind bk into a
       secret scalar s2, public key A2, and prefix2.

   3.  Compute the signing scalar s = s1 * s2 (mod L) and the signing
       public key A = ScalarMult(A1, s2).

   4.  Compute the signing prefix as concat(prefix1, prefix2).

   5.  Run the rest of the Sign procedure in [RFC8032], Section 5.2.6
       from step (2) onwards using the modified scalar s, public key A,
       and string prefix.

6.  ECDSA

   [[DISCLAIMER: Multiplicative blinding for ECDSA is known to be NOT be
   SUF-CMA-secure in the presence of an adversary that controls the
   blinding value.  [MSMHI15] describes this in the context of related-
   key attacks.  This variant may likely be removed in followup versions
   of this document based on further analysis.]]

   This section describes implementations of BlindPublicKey,
   UnblindPublicKey, and BlindKeySign as functions implemented on top of
   an existing [ECDSA] implementation.  BlindKeyGen invokes the key
   generation routine specified in [ECDSA] and outputs only the private
   key.  In the descriptions below, let p be the order of the
   corresponding elliptic curve group used for ECDSA.  For example, for
   P-256, p = 1157920892103562487626974469494075735299969552241357603424
   22259061068512044369.

6.1.  BlindPublicKey and UnblindPublicKey

   BlindPublicKey multiplies the public key pkS by an augmented private
   key bk yielding a new public key pkR.  UnblindPublicKey inverts this
   process by multiplying the input public key by the multiplicative
   inverse of the augmented bk.  Augmentation here maps the private key
   bk to another scalar using hash_to_field as defined in Section 5 of
   [H2C], with DST set to "ECDSA Key Blind", L set to the value
   corresponding to the target curve, e.g., 48 for P-256 and 72 for
   P-384, expand_message_xmd with a hash function matching that used for
   the corresponding digital signature algorithm, and prime modulus
   equal to the order p of the corresponding curve.  Letting

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   HashToScalar denote this augmentation process, BlindPublicKey and
   UnblindPublicKey are then implemented as follows:

BlindPublicKey(pk, bk)   = ScalarMult(pk, HashToScalar(bk))
UnblindPublicKey(pkR, bk) = ScalarMult(pkR, ModInverse(HashToScalar(bk), p))

6.2.  BlindKeySign

   BlindKeySign transforms the signing key skS by the private key bk
   into a new signing key, skR, and then invokes the existing ECDSA
   signing procedure.  More specifically, skR = skS * HashToScalar(bk)
   (mod p).

7.  Security Considerations

   The signature scheme extensions in this document aim to achieve
   unforgeability and unlinkability.  Informally, unforgeability means
   that one cannot produce a valid (message, signature) pair for any
   blinding key without access to the private signing key.  Similarly,
   unlinkability means that one cannot distinguish between two
   signatures produced from two separate key signing keys, and two
   signatures produced from the same signing key but with different
   blinds.  Security analysis of the extensions in this document with
   respect to these two properties is currently underway.

   Preliminary analysis has been done for a variant of these extensions
   used for identity key blinding routine used in Tor's Hidden Service
   feature [TORBLINDING].  For EdDSA, further analysis is needed to
   ensure this is compliant with the signature algorithm described in
   [RFC8032].

   The constructions in this document assume that both the signing and
   blinding keys are private, and, as such, not controlled by an
   attacker.  [MSMHI15] demonstrate that ECDSA with attacker-controlled
   multiplicative blinding for producing related keys can be abused to
   produce forgeries.  In particular, if an attacker can control the
   private blinding key used in BlindKeySign, they can construct a
   forgery over a different message that validates under a different
   public key.  One mitigation to this problem is to change BlindKeySign
   such that the signature is computed over the input message as well as
   the blind public key.  However, this would require verifiers to treat
   both the blind public key and message as input to their verification
   interface.  The construction in Section 6 does not require this
   change.  However, further analysis is needed to determine whether or
   not this construction is safe.

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8.  IANA Considerations

   This document has no IANA actions.

9.  Test Vectors

   This section contains test vectors for a subset of the signature
   schemes covered in this document.

9.1.  Ed25519 Test Vectors

   This section contains test vectors for Ed25519 as described in
   [RFC8032].  Each test vector lists the private key and blind seeds,
   denoted skS and bk and encoded as hexadecimal strings, along with the
   public key pkS corresponding to skS encoded has hexadecimal strings
   according to [RFC8032], Section 5.1.2.  Each test vector also
   includes the blinded public key pkR computed from skS and bk, denoted
   pkR and encoded has a hexadecimal string.  Finally, each vector
   includes the message and signature values, each encoded as
   hexadecimal strings.

// Randomly generated private key and blind seed
skS: 875532ab039b0a154161c284e19c74afa28d5bf5454e99284bbcffaa71eebf45
pkS: 3b5983605b277cd44918410eb246bb52d83adfc806ccaa91a60b5b2011bc5973
bk: c461e8595f0ac41d374f878613206704978115a226f60470ffd566e9e6ae73bf
pkR: e52bbb204e72a816854ac82c7e244e13a8fcc3217cfdeb90c8a5a927e741a20f
message: 68656c6c6f20776f726c64
signature: f35d2027f14250c07b3b353359362ec31e13076a547c749a981d0135fce06
7a361ad6522849e6ed9f61d93b0f76428129b9eb3f9c3cd0bfa1bc2a086a5eebd09

// Randomly generated private key seed and zero blind seed
skS: f3348942e77a83943a6330d372e7531bb52203c2163a728038388ea110d1c871
pkS: ada4f42be4b8fa93ddc7b41ca434239a940b4b18d314fe04d5be0b317a861ddf
bk: 0000000000000000000000000000000000000000000000000000000000000000
pkR: 7b8dcabbdfce4f8ad57f38f014abc4a51ac051a4b77b345da45ee2725d9327d0
message: 68656c6c6f20776f726c64
signature: b38b9d67cb4182e91a86b2eb0591e04c10471c1866202dd1b3b076fb86a61
c7c4ab5d626e5c5d547a584ca85d44839c13f6c976ece0dcba53d82601e6737a400

9.2.  ECDSA(P-384, SHA-384) Test Vectors

   This section contains test vectors for ECDSA with P-384 and SHA-384,
   as described in [ECDSA].  Each test vector lists the signing and
   blinding keys, denoted skS and bk, each serialized as a big-endian
   integers and encoded as hexadecimal strings.  Each test vector also
   blinded public key pkR, encoded as compressed elliptic curve points
   according to [ECDSA].  Finally, each vector lists message and
   signature values, where the message is encoded as a hexadecimal

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   string, and the signature value is serialized as the concatenation of
   scalars (r, s) and encoded as a hexadecimal string.

// Randomly generated signing and blind private keys
skS: 0e1e4fcc2726e36c5a24be3d30dc6f52d61e6614f5c57a1ec7b829d8adb7c85f456
c30c652d9cd1653cef4ce4da9008d
pkS: 03c66e61f5e12c35568928d9a0ffbc145ee9679e17afea3fba899ed3f878f9e82a8
859ce784d9ff43fea2bc8e726468dd3
bk: 865b6b7fc146d0f488854932c93128c3ab3572b7137c4682cb28a2d55f7598df467
e890984a687b22c8bc60a986f6a28
pkR: 038defb9b698b91ee7f3985e54b57b519be237ced2f6f79408558ff7485bf2d60a2
4dc986b9145e422ea765b56de7c5956
message: 68656c6c6f20776f726c64
signature: 5e5643a8c22b274ec5f776e63ed23ff182c8c87642e35bd5a5f7455ae1a19
a9956795df33e2f8b30150904ef6ba5e7ee4f18cef026f594b4d21fc157552ce3cf6d7ef
c3226b8d8194fc93df1c7f5facafc96daab7c5a0d840fbd3b9342f2ddad

10.  References

10.1.  Normative References

   [ECDSA]    American National Standards Institute, "Public Key
              Cryptography for the Financial Services Industry - The
              Elliptic Curve Digital Signature Algorithm (ECDSA)",
              ANSI ANS X9.62-2005, November 2005.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/rfc/rfc2119>.

   [RFC8032]  Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
              Signature Algorithm (EdDSA)", RFC 8032,
              DOI 10.17487/RFC8032, January 2017,
              <https://www.rfc-editor.org/rfc/rfc8032>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.

10.2.  Informative References

   [AIRDROP]  Wahby, R. S., Boneh, D., Jeffrey, C., and J. Poon, "An
              airdrop that preserves recipient privacy", n.d.,
              <https://eprint.iacr.org/2020/676.pdf>.

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   [ESS21]    Eaton, E., Stebila, D., and R. Stracovsky, "Post-Quantum
              Key-Blinding for Authentication in Anonymity Networks",
              2021, <https://eprint.iacr.org/2021/963>.

   [H2C]      Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S.,
              and C. A. Wood, "Hashing to Elliptic Curves", Work in
              Progress, Internet-Draft, draft-irtf-cfrg-hash-to-curve-
              16, 15 June 2022, <https://datatracker.ietf.org/doc/html/
              draft-irtf-cfrg-hash-to-curve-16>.

   [MSMHI15]  Morita, H., Schuldt, J., Matsuda, T., Hanaoka, G., and T.
              Iwata, "On the Security of the Schnorr Signature Scheme
              and DSA Against Related-Key Attacks", Information Security
              and Cryptology - ICISC 2015 pp. 20-35,
              DOI 10.1007/978-3-319-30840-1_2, 2016,
              <https://doi.org/10.1007/978-3-319-30840-1_2>.

   [RATELIMITED]
              Hendrickson, S., Iyengar, J., Pauly, T., Valdez, S., and
              C. A. Wood, "Rate-Limited Token Issuance Protocol", Work
              in Progress, Internet-Draft, draft-privacypass-rate-limit-
              tokens-02, 2 May 2022,
              <https://datatracker.ietf.org/doc/html/draft-privacypass-
              rate-limit-tokens-02>.

   [TORBLINDING]
              Hopper, N., "Proving Security of Tor’s Hidden Service
              Identity Blinding Protocol", 2013,
              <https://www-users.cse.umn.edu/~hoppernj/basic-proof.pdf>.

   [TORDIRECTORY]
              "Tor directory protocol, version 3", n.d.,
              <https://gitweb.torproject.org/torspec.git/tree/dir-
              spec.txt>.

Acknowledgments

   The authors would like to thank Dennis Jackson for helpful
   discussions that informed the development of this draft.

Authors' Addresses

   Frank Denis
   Fastly Inc.
   475 Brannan St
   San Francisco,
   United States of America
   Email: fde@00f.net

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Internet-Draft     Key Blinding for Signature Schemes          June 2022

   Edward Eaton
   University of Waterloo
   200 University Av West
   Waterloo
   Canada
   Email: ted@eeaton.ca

   Christopher A. Wood
   Cloudflare, Inc.
   101 Townsend St
   San Francisco,
   United States of America
   Email: caw@heapingbits.net

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