]> Fastly Inc.

fd@00f.net

Apple Inc.

frederic.jacobs@apple.com

Cloudflare

caw@heapingbits.net

Internet-Draft This document specifies an RSA-based blind signature protocol. RSA blind signatures were first introduced by Chaum for untraceable payments . It extends RSA-PSS encoding specified in to enable blind signature support. Discussion Venues Source for this draft and an issue tracker can be found at .

Introduction Originally introduced in the context of digital cash systems by Chaum for untraceable payments , RSA blind signatures turned out to have a wide range of applications ranging from electric voting schemes to authentication mechanisms. Recently, interest in blind signatures has grown to address operational shortcomings from applications that use Verifiable Oblivious Pseudorandom Functions (VOPRFs) , such as Privacy Pass . Specifically, VOPRFs are not necessarily publicly verifiable, meaning that a verifier needs access to the VOPRF private key to verify that the output of a VOPRF protocol is valid for a given input. This limitation complicates deployments where it is not desirable to distribute private keys to entities performing verification. Additionally, if the private key is kept in a Hardware Security Module, the number of operations on the key is doubled compared to a scheme where only the public key is required for verification. In contrast, digital signatures provide a primitive that is publicly verifiable and does not require access to the private key for verification. Moreover, shows that one can realize a VOPRF in the Random Oracle Model by hashing a signature-message pair, where the signature is computed using from a deterministic blind signature protocol. This document specifies a protocol for computing the RSA blind signatures using RSA-PSS encoding, and a family of variants for this protocol, denoted RSABSSA. In order to facilitate deployment, it is defined in such a way that the resulting (unblinded) signature can be verified with a standard RSA-PSS library.

Requirements Notation 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 when, and only when, they appear in all capitals, as shown here.

Notation The following terms are used throughout this document to describe the protocol operations in this document:

• bytes_to_int and int_to_bytes: Convert a byte string to and from a non-negative integer. bytes_to_int and int_to_bytes are implemented as OS2IP and I2OSP as described in , respectively. Note that these functions operate on byte strings in big-endian byte order.
• random_integer_uniform(M, N): Generate a random, uniformly distributed integer R such that M <= R < N.
• inverse_mod(x, n): Compute the multiplicative inverse of x mod n. This function fails if x and n are not co-prime.
• len(s): The length of a byte string, in bytes.
• random(n): Generate n random bytes using a cryptographically-secure pseudorandom number generator.

Blind Signature Protocol The core RSA Blind Signature Protocol is a two-party protocol between a client and server where they interact to compute sig = Sign(skS, msg), where msg is the private message to be signed, and skS is the server's private key. In this protocol, the server learns nothing of msg, whereas the client learns sig and nothing of skS. The protocol consists of three functions, Blind, BlindSign, and Finalize, described below.

• Blind(pkS, msg): encodes an input message msg and blinds it with a randomly generated blinding factor using the server's public key pkS, producing a blinded messsage for the server and the inverse of the blind.
• BlindSign(skS, blinded_msg): performs the raw RSA private key operation using private key skS on the client's blinded message blinded_msg, and returns the output.
• Finalize(pkS, msg, blinded_sig, inv): unblinds the server's response blinded_sig using the inverse inv to produce a signature, verifies it for correctness using message msg and public key pkS, and outputs the signature upon success.

Using these three functions, the core protocol runs as follows: blind_sig = BlindSign(skS, blinded_msg) blind_sig <---------- sig = Finalize(pkS, msg, blind_sig, inv) ]]> Upon completion, correctness requires that clients can verify signature sig over private input message msg using the server public key pkS by invoking the RSASSA-PSS-VERIFY routine defined in Section 8.1.2 of . The Finalize function performs that check before returning the signature. In the remainder of this section, we specify Blind, BlindSign, and Finalize.

Blind The Blind function encodes an input message and blinds it with the server's public key. It outputs the blinded message to be sent to the server, encoded as a byte string, and the corresponding inverse, an integer. RSAVP1 and EMSA-PSS-ENCODE are as defined in Section 5.2.2 and Section 9.1.1 of , respectively. If this function fails with an "invalid blind" error, implementations SHOULD retry the function again. The probability of multiple such errors in sequence is negligible. The blinding factor r MUST be randomly chosen from a uniform distribution. This is typically done via rejection sampling.

BlindSign BlindSign performs the RSA private key operation on the client's blinded message input and returns the output encoded as a byte string. RSASP1 is as defined in Section 5.2.1 of . = n, raise "invalid message" and stop 4. s = RSASP1(skS, m) 5. blind_sig = int_to_bytes(s, kLen) 6. output blind_sig ]]>

Finalize Finalize validates the server's response, unblinds the message to produce a signature, verifies it for correctness, and outputs the signature upon success. Note that this function will internally hash the input message as is done in Blind.

Message Randomization Message randomization is the process by which the message to be signed and verified is augmented with fresh randomness. As such, message randommization is a procedure invoked before the protocol in , as it changes the contents of the message being signed. We denote this process by the function Randomize(msg), which takes as input a message msg and produces a randomized message randomMsg. Its implementation is shown below.

RSABSSA Variants In this section we define different named variants of RSABSSA. Each variant specifies a hash function, RSASSA-PSS parameters as defined in , and whether or not message randomization (as described in ) is performed on the input message. Future specifications can introduce other variants as desired. The named variants are as follows:

1. RSABSSA-SHA384-PSS-Randomized: This named variant uses SHA-384 as the hash function, MGF1 with SHA-384 as the PSS mask generation function, a 48-byte salt length, and uses message randomization.
2. RSABSSA-SHA384-PSSZERO-Randomized: This named variant uses SHA-384 as the hash function, MGF1 with SHA-384 as the PSS mask generation function, an empty PSS salt, and uses message randomization.
3. RSABSSA-SHA384-PSS-Deterministic: This named variant uses SHA-384 as the hash function, MGF1 with SHA-384 as the PSS mask generation function, 48-byte salt length, and does not use message randomization.
4. RSABSSA-SHA384-PSSZERO-Deterministic: This named variant uses SHA-384 as the hash function, MGF1 with SHA-384 as the PSS mask generation function, an empty PSS salt, and does not use message randomization. This is the only variant that produces deterministic signatures over the input message.

The RECOMMENDED variants are RSABSSA-SHA384-PSS-Randomized or RSABSSA-SHA384-PSSZERO-Randomized. Not all named variants can be used interchangeably. In particular, applications that provide high-entropy input messages can safely use named variants without message randomization, as the additional message randomization does not offer security advantages. See and for more information. Applications that require deterministic signatures can use the RSABSSA-SHA384-PSSZERO-Deterministic variant, but only if their input messages have high entropy. Applications that use RSABSSA-SHA384-PSSZERO-Deterministic SHOULD carefully analyze the security implications, taking into account the possibility of adversarially generated signer keys as described in . When it is not clear whether an application requires deterministic or randomized signatures, applications SHOULD use one of the recommended variants with message randomization.

Implementation and Usage Considerations This section documents considerations for interfaces to implementations of the protocol in this document. This includes error handling and API considerations.

Errors The high-level functions specified in are all fallible. The explicit errors generated throughout this specification, along with the conditions that lead to each error, are listed in the definitions for Blind, BlindSign, and Finalize. These errors are meant as a guide for implementors. They are not an exhaustive list of all the errors an implementation might emit. For example, implementations might run out of memory.

Signing Key Usage and Certification A server signing key MUST NOT be reused for any other protocol beyond RSABSSA. Moreover, a server signing key MUST NOT be reused for different RSABSSA encoding options. That is, if a server supports two different encoding options, then it MUST have a distinct key pair for each option. If the server public key is carried in an X.509 certificate, it MUST use the RSASSA-PSS OID . It MUST NOT use the rsaEncryption OID .

Security Considerations Bellare et al. proved the following properties of Chaum's original blind signature protocol based on RSA-FDH:

• One-more-forgery polynomial security. This means the adversary, interacting with the server (signer) as a client, cannot output n+1 valid message and signature tuples after only interacting with the server n times, for some n which is polynomial in the protocol's security parameter.
• Concurrent polynomial security. This means that servers can engage in polynomially many invocations of the protocol without compromising security.

Both results rely upon the RSA Known Target Inversion Problem being hard. However, this analysis is incomplete as it does not account for adversarially-generated keys. This threat model has important implications for appliations using the blind signature protocol described in this document; see for more details. Lastly, the design in this document differs from the analysis in only in message encoding, i.e., using PSS instead of FDH. Note, importantly, that an empty salt effectively reduces PSS to FDH, so the same results apply.

Timing Side Channels and Fault Attacks BlindSign is functionally a remote procedure call for applying the RSA private key operation. As such, side channel resistance is paramount to protect the private key from exposure . Implementations SHOULD implement some form of side channel attack mitigation, such as RSA blinding as described in Section 10 of . Failure to apply such mitigations can lead to side channel attacks that leak the private signing key. Beyond timing side channels, describes the importance of implementation safeguards that protect against fault attacks that can also leak the private signing key. These safeguards require that implementations check that the result of the private key operation when signing is correct, i.e., given s = RSASP1(skS, m), verify that m = RSAVP1(pkS, s). Implementations SHOULD apply this (or equivalent) safeguard to mitigate fault attacks, even if they are not implementations based on the Chinese remainder theorem.

Message Robustness An essential property of blind signature protocols is that the signer learns nothing of the message being signed. In some circumstances, this may raise concerns of arbitrary signing oracles. Applications using blind signature protocols should take precautions to ensure that such oracles do not cause cross-protocol attacks. This can be done, for example, by keeping blind signature keys distinct from signature keys used for other protocols, such as TLS. An alternative solution to this problem of message blindness is to give signers proof that the message being signed is well-structured. Depending on the application, zero knowledge proofs could be useful for this purpose. Defining such a proof is out of scope for this document. Verifiers should check that, in addition to signature validity, the signed message is well-structured for the relevant application. For example, if an application of this protocol requires messages to be structures of a particular form, then verifiers should check that messages adhere to this form.

Message Entropy As discussed in , a malicious signer can construct an invalid public key and use it to learn information about low-entropy with input messages. Note that some invalid public keys may not yield valid signatures when run with the protocol, e.g., because the signature fails to verify. However, if an attacker can coerce the client to use these invalid public keys with low-entropy inputs, they can learn information about the client inputs before the protocol completes. Based on this fact, using the core protocol functions in is possibly unsafe, unless one of the following conditions are met:

1. The client has proof that the signer's public key is honestly generated. presents some (non-interactive) honest-verifier zero-knoweldge proofs of various statements about the public key.
2. The client input message has high entropy.

The named variants that use message randomization -- RSABSSA-SHA384-PSS-Randomized and RSABSSA-SHA384-PSSZERO-Randomized -- explicitly inject fresh entropy alongside each message to satisfy condition (2). As such, these variants are safe for all application use cases. Note that these variants effectively mean that the resulting signature is always randomized. As such, this interface is not suitable for applications that require deterministic signatures.

PSS Salt Choice For variants that have a non-zero PSS salt, the salt MUST be generated from a cryptographically secure pseudorandom number generator. If the PSS salt is not generated randomly, or is otherwise constructed maliciously, it might be possible for the salt to encode information that is not present in the signed message. For example, the salt might be maliciously constructed to encode the local IP address of the client. As a result, implementations SHOULD NOT allow clients to provide the salt directly.

Key Substitution Attacks RSA is well known to permit key substitution attacks, wherein an attacker generates a key pair (skA, pkA) that verify some known (message, signature) pair produced under a different (skS, pkS) key pair . This means it may be possible for an attacker to use a (message, signature) pair from one context in another. Entities that verify signatures must take care to ensure a (message, signature) pair verifies with a valid public key from the expected issuer.

Alternative RSA Encoding Functions This document document uses PSS encoding as specified in for a number of reasons. First, it is recommended in recent standards, including TLS 1.3 , X.509v3 , and even PKCS#1 itself. According to , "Although no attacks are known against RSASSA-PKCS#1 v1.5, in the interest of increased robustness, RSA-PSS is recommended for eventual adoption in new applications." While RSA-PSS is more complex than RSASSA-PKCS#1 v1.5 encoding, ubiquity of RSA-PSS support influenced the design decision in this draft, despite PKCS#1 v1.5 having equivalent security properties for digital signatures Full Domain Hash (FDH) encoding is also possible, and this variant has equivalent security to PSS . However, FDH is less standard and not used widely in related technologies. Moreover, FDH is deterministic, whereas PSS supports deterministic and probabilistic encodings.

Alternative Blind Signature Protocols RSA has some advantages as a signature protocol, particularly around verification efficiency. However, the protocol in this document is not without shortcomings, including:

• RSA key and signature sizes are larger than those of alternative blind signature protocols;
• No evaluation batching support, which means that the cost of the protocol scales linearly with the number of invocations; and
• Extensions for features such as threshold signing are more complex to instantiate compared to other protocols based on, for example, Schnorr signatures.

There are a number of blind signature protocols beyond blind RSA. This section summarizes these at a high level, and discusses why an RSA-based variant was chosen for the basis of this specification, despite the shortcomings above.

• Blind Schnorr : This is a three-message protocol based on the classical Schnorr signature protocol over elliptic curve groups. Although simple, the hardness problem upon which this is based -- Random inhomogeneities in a Overdetermined Solvable system of linear equations, or ROS -- can be broken in polynomial time when a small number of concurrent signing sessions are invoked , leading to signature forgeries. Even with small concurrency limits, Wagner's generalized attack leads to subexponential forgery speedup. For example, a limit of 15 parallel sessions yields an attack runtime of approximately 2^55, which is substantially lower than acceptable security levels. In contrast, the variant in this specification has no such concurrency limit.
• Clause Blind Schnorr : This is a three-message protocol based on a variant of the blind Schnorr signature protocol. This variant of the protocol is not known to be vulnerable to the attack in , though the protocol is still new and under consideration. The three-message flow necessarily requires two round trips between the client and server, which may be prohibitive for large-scale signature generation. Further analysis and experimentation with this protocol is needed.
• BSA : This is a three-message protocol based on elliptic curve groups similar to blind Schnorr. It is also not known to be vulnerable to the ROS attack in . Kastner et al. proved concurrent security with a polynomial number of sessions. For similar reasons to the clause blind Schnorr protocol above, the additional number of round trips requires further analysis and experimentation.
• WFROS-based Schemes : This work contains four proposed schemes, each of which are three-message protocols based on a variant of the blind Schnorr signature protocol. Security of these schemes depend on the Weighted Fractional ROS problem, for which the authors prove an exponential and unconditional lower bound, and therefore have tighter security bounds than the Clause Blind Schnorr schemes. The performance of the scheme is similar to Clause Blind Schnorr, yet signing is more efficient. Similarly to Clause Blind Schnorr schemes, the two round trips required by three-message flows need further analysis and experimentation.
• Blind BLS : The Boneh-Lynn-Shacham protocol can incorporate message blinding when properly instantiated with Type III pairing group. This is a two-message protocol similar to the RSA variant, though it requires pairing support, which is not common in widely deployed cryptographic libraries backing protocols such as TLS. In contrast, the specification in this document relies upon widely deployed cryptographic primitives.

Beyond blind signature protocols, anonymous credential schemes with public verifiability such as U-Prove may be used instead of blind signature protocols. Anonymous credentials may even be constructed with blind signature protocols. However, anonymous credentials are higher-level constructions that present a richer feature set.

Post-Quantum Readiness The blind signature protocol specified in this document is not post-quantum ready since it is based on RSA. (Shor's polynomial-time factorization algorithm readily applies.)

IANA Considerations This document makes no IANA requests.

References Normative References This document provides recommendations for the implementation of public-key cryptography based on the RSA algorithm, covering cryptographic primitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax for representing keys and for identifying the schemes. This document represents a republication of PKCS #1 v2.2 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series. By publishing this RFC, change control is transferred to the IETF. This document also obsoletes RFC 3447. In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. This document updates RFC 4055. It updates the conventions for using the RSA Encryption Scheme - Optimal Asymmetric Encryption Padding (RSAES-OAEP) key transport algorithm in the Internet X.509 Public Key Infrastructure (PKI). Specifically, it updates the conventions for algorithm parameters in an X.509 certificate's subjectPublicKeyInfo field. [STANDARDS-TRACK] Informative References n.d. Brave Software Brave Software Cloudflare Google LLC Cloudflare This document specifies two variants of the the two-message issuance protocol for Privacy Pass tokens: one that produces tokens that are privately verifiable, and another that produces tokens that are publicly verifiable. The privately verifiable issuance protocol optionally supports public metadata during the issuance flow. This memo profiles the X.509 v3 certificate and X.509 v2 certificate revocation list (CRL) for use in the Internet. An overview of this approach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regarding the format and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples are provided in the appendices. [STANDARDS-TRACK] This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations. This document supplements RFC 3279. It describes the conventions for using the RSA Probabilistic Signature Scheme (RSASSA-PSS) signature algorithm, the RSA Encryption Scheme - Optimal Asymmetric Encryption Padding (RSAES-OAEP) key transport algorithm and additional one-way hash functions with the Public-Key Cryptography Standards (PKCS) #1 version 1.5 signature algorithm in the Internet X.509 Public Key Infrastructure (PKI). Encoding formats, algorithm identifiers, and parameter formats are specified. [STANDARDS-TRACK] Paderborn Uninversity, Paderborn, Germany Paderborn University, Paderborn, Germany Ruhr-University Bochum, Bochum, Germany Stanford University University of Waterloo Carnegie Mellon University NTT Research and ENS, Paris Cloudflare, Inc. Algorand BLS is a digital signature scheme with aggregation properties. Given set of signatures (signature_1, ..., signature_n) anyone can produce an aggregated signature. Aggregation can also be done on secret keys and public keys. Furthermore, the BLS signature scheme is deterministic, non-malleable, and efficient. Its simplicity and cryptographic properties allows it to be useful in a variety of use- cases, specifically when minimal storage space or bandwidth are required.

Test Vectors This section includes test vectors for the blind signature protocol defined in . The following parameters are specified for each test vector:

• p, q, n, e, d: RSA private and public key parameters, each encoded as a hexadecimal string.
• msg: Input messsage being signed, encoded as a hexadecimal string. The hash is computed using SHA-384.
• msg_prefix: Message randomizer prefix, encoded as a hexadecimal string. This is only present for variants that use message randomization.
• random_msg: The message actually signed. If the variant does not use message randomization, this is equal to msg.
• salt: Randomly-generated salt used when computing the signature. The length is either 48 or 0 bytes.
• encoded_msg: EMSA-PSS encoded message. The mask generation function is MGF1 with SHA-384.
• inv: The message blinding inverse, encoded as a hexadecimal string.
• blinded_msg, blind_sig: The protocol values exchanged during the computation, encoded as hexadecimal strings.
• sig: The output message signature.

RSABSSA-SHA384-PSS-Randomized Test Vector

RSABSSA-SHA384-PSSZERO-Randomized Test Vector

RSABSSA-SHA384-PSS-Deterministic Test Vector

RSABSSA-SHA384-PSSZERO-Deterministic Test Vector